Mechanism in two-phase reaction systems: coupled mass transfer and chemical reaction

Research in Chemical Kinetics, Volume 2 R.G. Compton and G. Hancock (editors) © 1994 Elsevier Science B.V. All rights reserved.

193

Mechanism in two-phase reaction systems: coupled mass transfer and chemical reaction John H. Atherton Z E N E C A Fine Chemicals Manufacturing Organisation, Blackley, Manchester, M 9 3 D A , United K i n g d o m . Abstract T w o - p h a s e reaction systems are of considerable practical importance. This review is intended both as an introduction to the subject, a guide to primary sources covering a wide range of application areas, and a review of the present state of the art. Proposals are m a d e towards a m o r e consistent approach to the determination of reaction m e c h a n i s m s in these systems. 1. I N T R O D U C T I O N M a n y chemical processes, both industrial and naturally occurring, involve reactions in multiphase systems. This article is about reactions in which at least one p h a s e is a liquid. S o m e important systems in which coupled m a s s transfer and chemical reaction occur include: * respiration processes in living creatures, in which gaseous oxygen has to react with haemoglobin in solution [1]. * electrochemical processes e.g. electrical storage cells, where m a s s transport limits performance [2]. * solvent extraction in metalwinning i.e. the extraction of metal ions from aqueous solution using complexing agents soluble in organic solvents [3]. * dyeing of textiles with reactive dyes [4]. Within the chemical industry the examples are legion. T h e text by D o r a i s w a m y and S h a r m a [5] lists m a n y hundreds of examples. The m o r e important generic types comprise: * catalytic reduction processes, for example in the manufacture of margarine [6]

194

* gas absorption or ' s c r u b b i n g ' processes [7], in which gaseous products are recovered (e.g. in the manufacture of ammonia) or in which polluting waste gases are absorbed for destruction. * carbonylation of alcohols, for example in the manufacture of acetic acid from methanol and carbon m o n o x i d e [8]. * phase transfer catalysis in the manufacture of fine chemicals [9]. * extractive reaction in liquid/liquid systems, for e x a m p l e in the nitration of acid insoluble aromatic c o m p o u n d s with nitric acid [10]. * Grignard chemistry [11]. * metathesis reactions in solid-liquid systems, for example in the fluorination of chloroaromatic c o m p o u n d s using potassium fluoride [12]. Chemists are familiar with the kinetics of h o m o g e n e o u s chemical processes. Multiphase processes provide an additional complication, because now m a s s t r a n s f e r is coupled to chemical reaction. T h e way in which this affects the overall reaction rate and selectivity of a chemical reaction is the subject of this review. T w o groups of specialist - electrochemists and chemical engineers - have been almost entirely responsible for the development of the subject to its present state. Building on early studies of diffusion in h o m o g e n e o u s systems by G r a h a m [13] and Fick [14], electrochemists were the first to recognise the influence of diffusion processes on chemical reactions. Around the years 1904 - 1905 Nernst [15] initiated the development of quantitative theories of mass transfer coupled to electrode reactions. Electrochemists have continued to be in the forefront of research into reactions in liquid-solid systems, and have extended their techniques to the study of liquid-liquid systems [16]. Chemical engineers have led research in the area of gasliquid reactions, driven initially by the need for a quantitative understanding of gas absorption processes used in the scrubbing of water soluble c o m p o n e n t s from inert gas streams, and more recently by the requirement to optimise multiphase chemical processes. Seminal papers on gas absorption by Higbee [17] and Danckwerts [18] initiated an avalanche of studies in the area, which were later extended to liquid-liquid, liquid-solid and gas-liquid-solid systems [5]. Early theoretical treatments of 'diffusional kinetics' by Frank-Kamenetskii (1955)[19] and Levich (1962)[20] put the subject on a sound theoretical footing. Textbooks by Astarita (1967)[21], Danckwerts (1970)[22], Sherwood, Pigford and Wilke (1975)[23], and S h a r m a and D o r a i s w a m y (1985)[5] are representative of the best textbooks to e m e r g e from the chemical engineering community. T h e work they summarise represents a considerable intellectual triumph in bringing together concepts of diffusion, physicochemical hydrodynamics and chemical kinetics to provide a unified theory covering coupled diffusion and chemical reaction.

195

2. R E A C T I O N M E C H A N I S M IN T W O - P H A S E R E A C T I O N S Y S T E M S There are at least four distinct m e c h a n i s m s by which reaction m a y occur. In the context of this chapter ' m e c h a n i s m ' refers to the m e a n s by which two reactants, which are nominally mutually insoluble, c o m e together in order to react. It does not refer to the details of the bond reorganisation processes normally considered as the ' m e c h a n i s m ' of a reaction. 2.1 Extractive reaction Extractive reaction is the term used to describe a system where reaction follows or is concomitant with partition of a component from one phase where it is stable to a phase where it reacts. Reaction m a y take place in the bulk phase, or, if it is very fast, in the diffusion film in the fluid where reaction occurs. Examples include: * ester hydrolysis [24] * nitration [25] or sulphonation [26] of aromatic c o m p o u n d s in sulphuric acid as solvent * absorption of carbon dioxide in aqueous amine solutions [27]

ORGANIC ^ 0

PHASE

f AQUEOUS PHASE

>

PRODUCT

Figure 1. Extractive reaction In practice it usually involves extraction of an organic reactant into water (Figure 1), but this does not have to be the case. T h e kinetics of extractive reaction have been studied for a large n u m b e r of systems covering a wide range of reaction rates [5]. 2.2. P h a s e transfer catalysis Phase transfer catalysis involves the transport of an inorganic ion into an organic phase by m e a n s of a large organic quaternary a m m o n i u m or p h o s p h o n i u m salt [28]. T h e quaternary salt m a y be partitioned between the two phases (Figure 2A) or it m a y be only soluble in the organic phase (Figure 2 B ] . In the latter case the transport m e c h a n i s m must involve interfacial ion exchange [29].

196

organic phase

aqueous phase

2 A

2 B

Figures 2A and 2 B . Phase transfer catalysis with (2A) and without (2B) partitioning of the quaternary salt

Despite its wide use in synthesis there has been no systematic study of the m e c h a n i s m of phase transfer catalysis covering a wide range of reaction rates. 2.3. Catalytic two-phase reactions Catalytic two-phase reactions, so called by their inventor M . M a k o s z a [30], are sometimes lumped along with phase transfer catalysis but are mechanistically distinct. T h e y appear to involve interfacial deprotonation of an acidic species using 5 0 % aqueous sodium or potassium hydroxide in the presence of a quaternary a m m o n i u m salt, followed by subsequent alkylation of the derived carbanion/quaternary salt ion pair in the organic phase [31](Figure 3). T h e m e c h a n i s m has received little quantitative study.

organic phase

aqueous phase

Figure 3. Catalytic two-phase reactions.

2.4 Interfacial reactions True interfacial reactions are rare. They typically occur with highly reactive components with little or no mutual solubility. Well known examples are the interfacial polymerisation of water

197

insoluble diacid chlorides and water soluble diamines to give polyamides [32], and the extraction of metal ions from water using water-insoluble c o m p l e x i n g agents [33].

organic phase

aqueous phase

Figure 4. Interfacial reaction in the extraction of cupric ion from water 3. T H E O R Y O F M A S S T R A N S F E R IN N O N - R E A C T I N G S Y S T E M S 3.1 Diffusion in a s t a g n a n t s y s t e m [21,22] Consider t w o fluid p h a s e s A and Β in contact in a quiescent system. T h e A p h a s e is organic and the Β phase is aqueous. T h e ' A ' c o m p o n e n t is slightly soluble in the Β phase. Quantitative treatment of the time dependence of the transfer of Ά ' into the Β p h a s e assumes that at the interface the two phases are at equilibrium, and that transport of the solute ' A ' in the Β phase is purely by molecular diffusion. T o solve this problem requires the application of F i c k ' s First L a w of diffusion, which states that the diffusion rate j of a substance is proportional to the negative of the concentration gradient, the proportionality constant being k n o w n as the diffusion coefficient D. Stated mathematically, (1)

-ft *dx

j J

Consider a thin slab of unit cross sectional area and thickness dx. Figure 5 shows the model for the mathematical treatment, w h e r e c is the concentration of Ά ' in the Β p h a s e and χ is the distance from the interface. T h e concentration gradient at χ is At χ + dx (the exit from the slab) the change in concentration gradient due to diffusion is the product of the rate of c h a n g e of concentration gradient, 3 c / 3 x , and the slab thickness, dx. T h e rate of change of concentration in the slab is the difference between the rate at which material diffuses into the slab, which is -D(3c/3x), and the rate at which it diffuses out, which is -D[3c/3x + d x . 3 c / 3 x ] . T h e accumulation rate is the rate of change of concentration in the slab multiplied by the slab v o l u m e , which for a slab of unit cross sectional area is dx.

dc/dx.

2

2

2

2

i.e. accumulation = [diffusion in] - [diffusion out]

dc/dx,

198

sat neat organic phase

c=0 X

>

interface

Figure 5. Diffusion into a stagnant m e d i u m from a saturated interface

Thus

dc fM dx.dt .D l& JJ

/

-D

>

dc +, dx. &c — dx dx )

(2)

2

which reduces to

dc

= D

(cP±

(3)

Integration provides the expression (4)

c

=

c

er

(4)

c

sat- f

which relates the concentration of ' A ' in the Β phase to distance and time. Details of the integration and values of the error function erfc are given in Crank [34]. Concentration profiles for different exposure times are shown in Figure 6 for a solute having a diffusion coefficient of 10" c m s"\ typical of that for a small molecule in aqueous solution at room temperature (Table 1). 5

2

199

Figure 6. Concentration profiles for increasing contact times, diffusion of a solute into a stagnant liquid. It is evident that in unstirred systems the approach to saturation in a macroscopic system will be extremely slow. If the system is stirred it is intuitively obvious that the rate of transfer of Ά ' into the Β phase will increase. This occurs for two reasons. In the first place, forced convection reduces the transport time from near the surface to the bulk solution. Secondly, if the system is stirred vigorously enough then one phase will be dispersed in the other as droplets and the interfacial area available for mass transfer will increase. B u t even with good stirring there is still a finite time required to achieve saturation which is greater than that just required to allow h o m o g e n e o u s mixing of phase B. This is because of diffusional resistance to mass transfer on the Β (aqueous) side of the interface. Three models have been used to describe this. 3.2 N e r n s t film t h e o r y N e r n s t ' s film theory [15] was developed to account for the diffusional resistance to dissolution processes which occurs even in stirred solutions. H e assumed that at the boundary between a solid and a stirred liquid there is a thin, essentially stagnant layer of liquid. Transport from the surface of the solid to the bulk of the solution is assumed to occur solely by molecular diffusion, and consequently there exists a concentration profile across the film. Nernst considered the s t e a d y s t a t e case and so this profile can be approximated by a straight line (Fig. 7). In his paper of 1904 he discussed the effect of diffusion close to the solid surface on the dissolution of magnesia in acid, and on electrochemical processes. Nernst used F i c k ' s first law, which applies to steady state diffusion, to derive the flux expression (5).

200

_

Ζ) C

J ~ g { sat

. C

buW

2

1

where j is the flux in mol c m ' s" , D is the diffusion coefficient in c m s~\ and δ is the thickness of the diffusion film. 2

Figure 7. Nernst diffusion layer In real situations δ is not usually k n o w n independently, and the lumped term D/δ, which has units of velocity (cm s" ) is widely used for correlation purposes. It is k n o w n as the mass transfer coefficient, k . However, δ would not be expected to change with solute, so under similar hydrodynamic conditions k should vary as D. For a wide range of solutes the range of values of D is quite small (Table 1) and so k is expected to be relatively insensitive to solute structure. 1

L

L

L

Table 1 Diffusion coefficients in water at 20°C/10" c m s" . 5

Helium Carbon m o n o x i d e Acetic acid Benzene Diethy lamine Benzyl alcohol Nicotine Lactose

2

1

6.8 2.03 1.19 1.02 0.97 0.82 0.53 0.46

Taken from: T.K.Sherwood, R.G.Pigford and C.R.Wilke, M a s s Transfer, K o g a k u s h a Ltd., 1975; C.R.Wilke, Chem. Eng. Progr., 45 (1949) 2 1 8 .

McGraw-Hill

201

3.3 P e n e t r a t i o n t h e o r y Higbee developed his 'penetration theory' [17] to explain gas absorption rates in absorption c o l u m n s , where, because the absorbing fluid is flowing over a packing, n e w surface is constantly being generated. Because the surface lifetimes are short, typically fractions of a second, the absorption occurs in a thin film which is rapidly replaced. Under these conditions the Nernst equation, which applies to steady state systems, is not applicable. H i g b e e assumed that the surface lifetime w a s a characteristic of the particular absorption equipment being used, and used equation (6), which is an integrated form of (4), to calculate the absorption rates for different surface lifetimes. In equation (6) the units of q are m o l c m ' for an exposure time of t seconds. 2

e

Dt

(6)

Ac

Comparison with the flux expression (5) shows that the m a s s transfer coefficient k surface exposure time t is given by (7)

L

for a

e

D_

(7)

This function is plotted in Figure 8 for a component with a diffusion coefficient of 10" c m s" , where t is in seconds. 5

j

2

1

cm

Figure 8. M a s s transfer coefficient vs log surface exposure time.

Note that in this model the mass transfer coefficient is proportional to the square root of the diffusion coefficient.

202

3.4 S u r f a c e r e n e w a l m o d e l Danckwerts [18] considered H i g b e e ' s assumption of equal lifetimes for all surface elements to be unsatisfactory and proposed that the lifetimes were better represented by an age distribution function, wherein the fractional rate of replacement of surface elements, ' S ' , is proportional to the number of elements of that age. T h e average absorption rate is given by the expression

SAc/

A

(8)

,exp(-St)dt

1

where S is a proportionality constant which is the rate of surface renewal, so that S" is the average lifetime of surface elements. Integration leads to the pleasingly simple expression ; =

(9)

sfDSAc

Again, comparison with the flux expression (5) can be carried out showing that k

L

= JDS

(10)

T h e problem with these expressions is that they contain a term for surface lifetime which is difficult to access experimentally. Astarita [21] appeared to find the distinction between H i g b e e ' s 'diffusion t i m e ' and D a n c k w e r t s ' 'surface lifetime' somewhat pedantic (the numerical difference is between a multiplier of 2/(π) = 1.13 (Higbee) and 1 (Danckwerts)), and proposed defining an 'equivalent diffusion t i m e ' , t by the expression ι/2

D

(kf

= ^

(11)

Here diffusion time m e a n s the length of time for which diffusion can be considered as occurring into a stagnant fluid, either because there has been little 'surface r e n e w a l ' (Danckwerts), or the penetration of the diffusing solute has not reached a depth at which convective motion is occurring in the fluid (Higbee). It is noteworthy that the same expression, albeit with a different m e a n i n g for ' t \ can be obtained from film theory. F r o m the definition *, = L

(12) δ

here k has dimensions of velocity, so the transport time t across the diffusion film is given by L

d

203

t d

f

(13)

Substituting this into (11) gives (kf

= h

(14)

which is the same form as that proposed by Astarita to define the diffusion time for absorption under transient diffusion conditions, but with a different meaning for the diffusion time. 3.5 M a s s t r a n s f e r w h e n t h e s o u r c e p h a s e is a s o l u t i o n This case w a s first treated by W h i t m a n [35] for the case of absorption of a soluble gas from a mixture with an inert insoluble gas. For extraction of a solute from an organic solvent into water the concentration profiles are as shown in Figure 9.

bulk aqueous phase r

organic I aqueous diffusion diffusion film film

Figure 9. Two-film theory: concentration profiles across the interfacial region. Again, it is assumed that the concentrations across the interface are at equilibrium, so that the relative concentrations can be described by a distribution coefficient Ρ = c / c . T h e flux expressions are: o i

C

/ = Ko^ o

C

~ o,i) = Ka^aa.i

'

a q i

(

1

5

)

where k and k refer to the m a s s transfer coefficients in the organic and aqueous phases respectively. After eliminating the interfacial concentrations this leads to the expression L o

L a q

204

J =

1

(16)

Ρ

|

For transfer from the aqueous phase to the organic the terms in the numerator are reversed:

aq

J =

ι

ο (17)

Ρ

t

k

k

3.6. M a s s t r a n s f e r t o s m a l l s p h e r e s [23] T h e foregoing theory applies to diffusion with respect to surfaces which are essentially planar with respect to the thickness of the diffusion film. If this is not the case, as for small particles, then the boundary conditions are changed leading to a different solution to the diffusion equation. For steady state diffusion the situation is shown in Figure 10.

Figure 10. Boundary conditions for diffusion from a small sphere. 2

T h e total flux at the surface is 47t(R ) j 0

1

mol s" .

F r o m F i c k ' s First Law, the flux through a shell radius R is (18)

2

-4nR D*dR These two fluxes are equal. Equating and integrating after rearrangement gives

f-Λ JO 2 R

whence

.

D_

2

jR

r-

Jc,

d c

(19)

205

1

00

R

D Q

(20)

" JRI

This reduces to

D (c, -

(21)

cj

T h e term j / ( c , - c j has units of velocity and is equivalent to the m a s s transfer coefficient. Hence O L _

D

j

(22)

~

or m o r e familiarly L

ρ

D

=2

(23)

where dp is the diameter of the sphere. T h e term on the left hand side is k n o w n as the S h e r w o o d number. It is dimensionless, and in this context defines the m a s s transfer coefficient to a ' s m a l l ' sphere which is stagnant with respect to the fluid in which it is i m m e r s e d . It is important because small spheres (typically dp < 50 pm) have a very low settling velocity in the fluid in which they are suspended and so the mass transfer coefficient can be estimated by assuming that the Sherwood number is equal to 2 [5].

3.7. Diffusion times in two-phase systems It is helpful to put some real values on the diffusion timescale involved in interphase mass transfer. T h e s e timescales will vary with both the physical properties of the diffusing solute and the hydrodynamic conditions, but some useful generalisations can be m a d e . Given values of k and D the diffusion time t can be calculated from equation (11). Values of D , typical values of the aqueous side k and diffusion times t thus calculated are shown in T a b l e 2. T h e temperature is 25°C unless otherwise noted. L

D

L

D

206

Table 2. Diffusion coefficients, measured values of k and diffusion times t calculated from equation (11). L

compound

5

10 D/ c m s.

conditions

2

D

3

10 k / L

to/s.

ref.

3.0

36

cm s

reactive dissolution of 7-acetyl-theophylline

0.49

tablet at the base of a stirred vessel

4-t-butylcyclohexanone

0.59

stirred dispersion of the solid ketone in water

1.37

3.1

37

n-hexyl formate

0.68

stirred dispersion of the liquid ester in aqueous sodium hydroxide

1.1 to 1.6

2.7 -5.6

38

phenyl benzoate

0.58

stirred dispersion of the solid ester in aqueous sodium hydroxide

1.0

iodine in aqueous iodide.

1.77

flat interface cell

1.81

carbon dioxide

2.0

absorption in various aqueous solutions in a packed column

carbon dioxide

2.0

constant interfacial area cell, 24 - 60 rpm

oxygen (33°C)

2.71

constant interfacial area cell, 150 r p m

oxygen (22°C)

2.31

dispersed gas bubbles in stirred reactor

general (gases)

1.0

gas b u b b l e d through

liquid

1.4 - 2.71

5

100

15-40

39

5.4

40

0.7

41

10 - 2.74

42

1.1

43

0.0023

44

0.005 to 0.04

21

207

For liquid-liquid and solid-liquid systems at 25°C, t is typically 3 - 6 seconds. In the case of gas-liquid systems it is more difficult to generalise. In gently stirred systems with a flat interface k is the same as for liquid-liquid systems, leading to a t of around 1 - 10 s. In a packed column Danckwerts [41] found the surface renewal rate to be 1.45 s" corresponding to a t of 0.7 s. For dispersions of a gas in a liquid in a stirred vessel values of k are much less and t is typically in the range 0.005 to 0.04 s. T h e reason why the diffusion times for gas bubbles dispersed in water are so m u c h less than for liquid-liquid systems is that freely rising bubbles have a much greater velocity relative to the continuous phase than for the liquid-liquid case, and surface lifetimes are thus much less. D

L

D

1

D

L

D

5

1

A typical value of the film thickness 5, calculated from k = 10" c m s" and D = 0.5 χ 10" c m s" is thus 5 χ 10" c m or 50 pm. L

5

2

1

3

4. T H E O R Y O F M A S S T R A N S F E R W I T H C H E M I C A L R E A C T I O N T h e theory will be discussed with reference to e x t r a c t i v e r e a c t i o n , which is the area in which the majority of work has been carried out. In the previous section the principles governing interphase m a s s transfer were described, and the concepts of diffusion film and interphase diffusion time were introduced. T o develop the subject quantitatively it is helpful to categorise the reaction in terms of its rate relative to the coupled m a s s transfer processes. There are three distinct cases, sometimes referred to as ' r e g i m e s ' : 1. Reaction is too slow to occur in the diffusion film. 2. Reaction is fast enough to occur entirely within the diffusion film. 3. Reaction is instantaneous within the film. T h e r e are obviously transition regions between these three cases for which the mathematics can b e c o m e quite complex. These are discussed in detail elsewhere [5,21,22]. Interfacial reactions are discussed later. It is helpful to generalise about the range of reaction rates which correspond cases. For l i q u i d - l i q u i d systems at r o o m temperature a diffusion time in the seconds has been indicated earlier. Reactions significantly slower than t will bulk phase; those significantly faster will occur within the diffusion film. Very (say 9 0 % reaction) are therefore D

to the range occur rough

above 3 - 6 in the limits

t r > 1 minute; i.e. kj < ~ 2 χ 10" s" : little reaction in the film 2

1

1

t, < 0.3 sec; i.e. kj > ~ 5 s" : reaction occurs mainly in the film. Here t,. is Ifl^ There is an intermediate range where the cases overlap but a large n u m b e r of reactions fall cleanly into one region or the other.

208

T h e ratio of chemical reaction rate vs the transport time across the film is critical in determining the characteristics of the system. It is usually possible to obtain the chemical reaction rate from the literature or by measurement using conventional techniques of h o m o g e n e o u s reaction kinetics. 4 . 1 . R e a c t i o n slow r e l a t i v e to m a s s t r a n s f e r Consider a neat organic liquid Ά ' in contact with an aqueous solution containing a reactive anion ' B ' which is insoluble in the organic phase. Reaction occurs via partition of the organic species into the aqueous solution, where it reacts (Figure 1). ' A ' could for e x a m p l e be an ester and ' B ' hydroxide ion. T h e overall reaction rate is a function of two processes which are occurring in series. First the reactant has to diffuse into the aqueous phase, and then chemical reaction occurs. There will thus be a concentration profile across the diffusion film on the aqueous side of the interface between the two solutions. (Figure 11). In this case, because the organic reactant is a neat liquid, there is no diffusional resistance on the organic side of the interface.

Figure 1 1 . Concentration profiles across the film for reaction slow relative to diffusion time T h e driving force for transfer of ' A ' to the aqueous solution (B phase) is the difference between the saturation and bulk concentration of ' A ' in the Β phase. So:

rate (q) =

- c j

mol s

1

(24) 1

where k is the mass transfer coefficient, c m s" , A is the interfacial area, c m , c is the solubility of A in the Β phase, mol c m ' , c , is the actual bulk concentration of A in the Β phase, mol c m ' . L

2

3

sat

3

bu

k

209

T h e chemical reaction rate q is simply given by: = k ^ V

q

(25)

assuming first-order or pseudo first-order reaction of ' A ' in the receiving (B) p h a s e and where V is the v o l u m e of the p h a s e in which reaction occurs. These two rates must be equal so (26) k

C

lA( sat

C

"

bull)

"

K

C

V

b u l k

Putting a = A/V and rearranging this gives:

mol k

cm

3

(27)

a

L

+

Κ

which after substituting back and rearranging gives:

rate (r) =

1 Κ

mol c m

1

t

k

3

s'

1

(28)

a L

where a is the interfacial area per unit volume of the receiving phase. This shows that the overall rate can be limited by physical or chemical processes, depending on which is the faster. W h e n chemical reaction is more rapid than mass transfer equation 28 reduces to (29) T

=

C

k

a

bulk L

and when m a s s transfer is faster than reaction then equation 28 reduces to

r

=

(30)

c ^ K

A c o m m e n t is needed on units. It is necessary to have the length dimension in the area term the same as that in the concentration term. So if k is in c m s" then the concentrations must be expressed in mol cm" . T h e interfacial area term here is c m ' i.e the interfacial area per unit v o l u m e of the Β phase. 1

L

3

1

W h e n the source phase is a solution of the ' A ' c o m p o n e n t the treatment has to include the possibility of diffusional resistance on each side of the interface (Figure 12).

210

aqueous phase reaction r a t e

organic phase

aqueous phase

Figure 12. Concentration profiles near the interface when the source phase is a solution: slow reaction N o w the m a s s balances b e c o m e (31) Again putting a = A/V and eliminating the interfacial concentrations gives mol cm

r 1

1

•3 so - l

3

(32)

1

4.2. F a s t r e a c t i o n c o u p l e d to diffusion This case is important and the relevant expressions can be derived simply from first principles [21,22]. Figure 13 shows the situation, which is similar to that described earlier for diffusion in the absence of reaction (Section 3.1). T h e accumulation is reduced by destruction of the reactant. This rate is the product of the reaction rate, l^c (mol c m ' s" and the slab volume, which for a slab of unit cross sectional area is dx cm" . 3

3

1}

211

sat reaction rate =

k c.dx r

neat organic phase

c=0 interface

Figure 13. Diffusion with reaction into an infinite m e d i u m . A mass balance over the slab gives: accumulation = [diffusion in] - [diffusion out] - [reaction] Thus

j dc dx.— = dt

/

[" ( - 1 -

-D \

dc +, dx. c^c 1 — dx dx 2

(33)

kcdx r

which reduces to (34)

kc

dt

[dxV At steady state dc/dt = 0 so that this expression further n à c , D. = kc

simplifies to

2

2

dx

'

Integration of this expression is accomplished using the substitution

(35)

212

2

de , dc θ = — so that dx dx a

1

dQ dx

d6dc dc dx =

d6 dc

Q

(36)

Equation (37) becomes

dQ DQ.dc

(37)

k.c

Integration once gives (38)

dc

whence

α

= —

=

dx

Κ

-c.

Ν ζ)

(39)

t

(the m i n u s sign appears because dc/dx has to be a negative quantity) A further integration gives

r de J~c

Κ "

(40)

\ D*

which finally leads to the expression

c — = exp c

(41)

t

where c is the concentration in the fluid at the point of contact with the source phase (x = 0). This expression gives the concentration profile of the reacting species. If the reaction time is much less than the diffusion time then reaction will occur within the film, and so even reaction in a stirred system will conform to this regime. Figure 14 shows the calculated concentration profile for such a case, in which the reaction rate has been chosen such that reaction is just complete within a typical film thickness of 50 pm (Section 3.7). x

213

1

0.8 D = 10 Ç

5

cm

2

s

1

0.6 0.4 0.2 0

—ι

0

5

1

1

1

1

1

1

1

10

15

20

25

30

35

40

45

50

x/^m Figure 14. Typical concentration profile for first order reaction coupled with diffusion from a plane surface. F r o m equation 41 the flux at the surface can be obtained:

—)

(42)

-

F i c k ' s first law gives

-D*

(43)

=c D i

)

dx Note that the bulk v o l u m e of the phase in which reaction occurs does not appear in the rate expression. Because reaction occurs close to the surface the rate is dependent on the interphase area and not on the bulk phase volume. W h e n the source phase is a solution the concentration profiles across the films are as shown in Figure 15:

^ a q j

-Oq,i

C=0

organic phase

Figure

aqueous phase

15. Concentration profiles for a fast reaction where the source phase is a solution.

214

T h e mass balances are: (44)

Elimination of the interfacial concentrations gives:

J =

Ρ

t

(45)

1

Provided that (46)

the kinetics can still be studied.

4.3. INSTANTANEOUS REACTIONS

This case has been treated by Astarita [21] and will not be reproduced here. T h e concept of instantaneous reactions occurring in the diffusion film is obviously only meaningful for second- or higher-order reactions - an instantaneous first-order reaction would occur at the interface. 4 . 4 . INTERFACIAL REACTIONS

Heterogeneous catalysis is the c o m m o n e s t example of reaction at the solid-liquid interface. This subject has been the subject of recent reviews [45], including one covering catalysis by colloidal solids [46]. B i r c u m s h a w and Riddiford summarised the general treatment for reaction at a surface with a solute [47]. For the case of a pseudo first order reaction occurring at a solid surface they use the model shown in Figure 16

c = c , bulk solid

Figure 16. Model for a pseudo first order surface reaction

215

T h e rate of the chemical process is given by Ac

r= K i

(47)

V

where k is the rate constant for the surface process, and the rate of the transport process is given by s

(48)

Γ =

V Eliminating the surface concentration gives (49)

Here the rate constant is a composite of the mass transfer coefficient and the surface rate. In the case of reactions where the chemical and transport rates are similar then it is necessary to use techniques which control k in order to dissect the two rates. L

Adsorption of reactant or product at the surface can lead to complex expressions in the case of ' m i x e d ' regimes where chemical reaction and transport processes are of similar magnitude, but in m a n y cases one process or the other dominates the rate. An actual e x a m p l e where reaction is slow relative to mass transport is exemplified later in this review. T h e only rigorous treatment of interfacial kinetics at a l i q u i d - l i q u i d interface is by Albery and Choudhery [33]. T h e model follows that used for the treatment of reactions between gases adsorbed on solid surfaces [48]. Langmuirian adsorption of the reactants at the interface is assumed. M a s s transport contributions are ignored in the overall model; their contributions to individual steps are separately dissected using controlled hydrodynamic techniques. T h e treatment is exemplified below for a second-order surface reaction between two adsorbed components Q and W to give product U, which is rapidly desorbed. Figure 17 illustrates the model Q (solution) II

Q (surface)

U (solution) * k.2s

U (surface)

W (surface)

W (solution) Figure 17. Reaction between two adsorbed c o m p o n e n t s at an interface.

216

For each c o m p o n e n t the fractional coverage of the surface is denoted x, with x vacant sites. T h u s

x

w

+x

Q

+x

vs

= 1

vs

denoting

(50)

T h e rate of the surface reaction is given by k

X

X

(51)

J = 2s Q W

where k is the rate constant for the surface process, and Q and W are the concentrations in solution adjacent to the interface. Elimination of the surface concentrations gives: 2s

j

KQ Q

KW W

K K QW Q

W

Use of this type of equation is discussed later in the context of the extraction of cupric ion from water using water insoluble ligands (Section 7.3).

5. C R I T E R I A F O R D E T E R M I N A T I O N O F R E A C T I O N M E C H A N I S M I N T W O PHASE REACTION SYSTEMS A n y experimental technique for the study of reactions in liquid-solid systems should be tested against a n u m b e r of criteria to ensure that it will provide an u n a m b i g u o u s result. * Transport of the reactant to or from the interface should be well-defined, calculable and preferably controllable. If transport is not well characterised it will not be possible to separate out the contributions to the overall kinetics from m a s s transport and chemical reaction. * T h e interface between the two phases should be well defined in terms of area and topography. In the case of gas-liquid and liquid-liquid systems this can be a major difficulty. * There should be good control of the solution phase conditions, ideally with constant conditions being maintained whilst the relevant measurements are made. This m a y not be possible with a ' b a t c h ' reactor; use of continuous flow techniques m a k e s it easier to achieve ' c h e m o s t a t i c ' conditions. * Transport to the detector system should be either rapid with respect to the chemical changes occurring, or else well defined and calculable. In the next three sections the principal methods available for the study of two-phase reactions will be described, together with a critical review of their application to specific problems.

217

6. L I Q U I D - S O L I D S Y S T E M S B i r c u m s h a w and Riddiford reviewed the literature on 'Transport Control in Heterogeneous Reactions' in 1953 [47], Early work aimed at testing N e r n s t ' s film theory mainly involved studies of the dissolution of metals in acidic media. T h e subject has advanced considerably since then. A n u m b e r of different techniques have been used to study liquid-solid systems. Early work used a dispersion of the solid in mechanically agitated fluid, referred to here as a dispersed p o w d e r reactor. Using this equipment it is not always possible to disentangle m a s s transport and chemical kinetics. T h e next development was the use of solid substrates which were rotated in the liquid. B y varying the rotation speed the thickness of the hydrodynamic boundary layer could be varied, and hence the individual contributions of chemical kinetics and mass transfer to the overall rate could be dissected. T h e most popular of these techniques is the rotated disk. Other recent developments include the wall-jet electrode, whose use to date has primarily been in the area of analysis, but which has also been used to study colloidal deposition, and the channel flow cell, which has recently been shown to be a powerful technique for the elucidation of reaction mechanism. For both of these latter techniques the primary measurement technique is electrochemical, but observation of the substrates by microscopy plays an important part in interpretation. It has been shown earlier that, for a chemical reaction in a heterogeneous system, either chemical reaction or mass transfer can be rate limiting. Locating the site of reaction, whether in solution or on the solid surface, is fundamental to understanding the overall process. It is obvious that heterogeneous catalysis or the dissolution of metals occurs on the solid surface, since the solid itself is completely insoluble in the medium. With reactive solids which are slightly soluble diagnosis is m o r e difficult, and there are some snags for the unwary. Not infrequently it is said that a demonstration that the rate is proportional to m a s s of solid i.e. interfacial area, is diagnostic for a surface reaction. T h e preceding theory shows that this criterion is inadequate: a reaction which occurs in solution but is fast enough to be complete within the diffusion film will also fit this condition. 6.1. Dispersed powder reactor T h e dispersed p o w d e r reactor is no more than a vessel in which the solid is uniformly dispersed by mechanical agitation in the liquid phase. T h e design is not critical provided that the criterion of 'fully dispersed' is met. A c o m m o n design which is used by the author is shown in Figure 18. Under fully dispersed conditions, which can usually be verified by observation, the Sherwood number equals 2 and transport to the solid is fixed and calculable provided that the particle size of the solid is k n o w n , and the solid does not change in size or shape for the duration of the experiment. Given proper characterisation of the solid then useful kinetic information can be obtained. Table 3 summarises the situation.

218

Figure 18. Dispersed p o w d e r reactor. Agitator: four bladed 60° pitched turbine, p u m p i n g d o w n w a r d s . Four vertical wall baffles, one tenth of the vessel diameter, set at right angles on the diameter.

Table 3. Liquid solid reactions: effect of mass of solid on overall reaction rate

Reaction ' r e g i m e '

Rate vs mass of p o w d e r

very slow

no effect

slow

asymptotes to a m a x i m u m

fast

directly proportional

surface

directly proportional

In the reaction of benzyl bromide with sodium acetate in toluene solvent at 101°C [49]

+

OAC

+

BR

the rate w a s shown to be independent of the m a s s of sodium acetate and the reaction was therefore slow relative to m a s s transfer. In the a u t h o r ' s laboratory the H A L E X reaction between potassium fluoride and 1,3-

219

dichloro-4-nitrobenzene ( D C N B ) in dimethylformamide has been studied, initially using the dispersed p o w d e r reactor [50].

CI

N 0

2

It w a s found that: * the solubility of potassium fluoride in dimethylformamide at 120°C w a s ca 6 χ 10" M ; in saturated potassium chloride the solubility is 3 χ 10" M . * the surface area of the potassium fluoride based on light scattering m e t h o d s w a s 960 c m g . * the dissolution rate of potassium fluoride, measured by conductivity, w a s 8.4 χ 10" c m sec" . * the h o m o g e n e o u s reaction rate between fluoride ion (as caesium fluoride) and l,3-dichloro-4-nitrobenzene (measured by its disappearance) w a s 2 9 0 ± 50 c m m o l ' s \ 4

2

4

l

4

1

3

1

Eleven reactions were carried out under heterogeneous reaction conditions over concentration ranges of 0.006 to 1.2 M ( D C N B ) and 0.19 to 4.9 mois of potassium fluoride per kg. of solvent. Initial rates were measured. T h e pseudo first order rate constant for the h o m o g e n e o u s reaction under these conditions calculated from the product of the measured second-order rate constant and the concentration of D C N B w a s in the range 1.74 χ 10" to 0.35 s" so the reaction w a s too slow to be in the diffusion film. A model w a s therefore developed to test the hypothesis that the reaction occurred in the bulk solvent phase following dissolution of potassium fluoride. Following equations (24) and (25) and equating the h o m o g e n e o u s reaction rate with the dissolution rate gives: 3

1

q = k V[DCNB}[F-] = ^ ( [ F " t 2

- [F])

mol s~*

(53)

where k is the second-order rate constant for the h o m o g e n e o u s reaction. [ F ] is the actual fluoride concentration in solution (not directly measurable). [ F ] is the saturation fluoride concentration under reaction conditions, 3 χ 10" m o l cm" . [ D C N B ] is the concentration of dichloronitrobenzene, mol cm" . 2

s a t

7

3

3

220

Rearranging a n d eliminating the unknown actual fluoride concentration gives:

mol s'

q =

(54)

ι k [DCNB]

k

2

L

A

Figure 19 shows the correlation, which is plotted on a log scale in order to e n c o m p a s s the wide concentration range covered.

1

log [(calculated r a t e ) / 1 0 ° m o l s ]

—

8

—1

log[(measured r a t e ) / 1 0

mol s ]

Figure 19. Calculated vs observed reaction rates for the heterogeneous reaction between l,3-dichloro-4-nitrobenzene a n d potassium fluoride. At the left hand side of the plot the overall rate is limited by the chemical reaction rate; at the right hand side by the solid dissolution rate. T h u s the reaction rate in the heterogeneous system can be correlated very well with that calculated from the independently measured h o m o g e n e o u s rate and the solubility and dissolution rate of the potassium fluoride. Benzylation of pyrrolidin-2-one (PyH) using toluene as solvent with potassium carbonate as the base and quaternary a m m o n i u m salts as catalyst [51]:

α

tr

-ο

+

c h ch ci 6

5

2

+

k co 2

3

L Xo + H

K

H

C

0

3

+

K

C

I

I

Η

t H

C

H

2 6 5

is believed to occur via an interfacial deprotonation mechanism similar to the C T P m e c h a n i s m of M a k o s z a [30,31].

221

Py-H(solution) + K C 0 ( s ) 2

3

+

+

P y K ( i n t e r p h a s e ) + Q Cl"(solution) +

Q P y ( s o l u t i o n ) + PhCH Cl(solution) 2

+

>

Py'K (interphase) + K H C 0 ( s )

>

Q P y ( s o l u t i o n ) + KCl(s)

>

PhCH -Py + Q Cl(solution)

3

+

+

2

Evidence for this m e c h a n i s m is strong and includes * the stated insolublity of carbonate in the system potassium carbonate/toluene/quaternary a m m o n i u m chloride * a reaction rate which is directly proportional to the weight of potassium carbonate taken and therefore proportional to surface area. If the assertion of complete insolubility is correct then the reaction must occur at the interface. However, the previous example shows that this condition m u s t be rigorously fulfilled. A reagent which is only slightly soluble but which reacts rapidly in solution will, under appropriate conditions, show a rate which is proportional to interfacial area. T h u s if for equation (28), \^ > k a , the dissolving reagent will be c o n s u m e d as fast as it dissolves and the rate will be proportional to the mass of solid reactant. L

Although the conclusions of this study are probably correct, there remain s o m e features of the reaction which are not satisfactorily explained and which need to be addressed before it can be said that this reaction is properly understood. In particular, the complete lack of reactivity of sodium carbonate, and the unusual dependence of the reaction rate upon agitation intensity require further investigation. T h e conclusions would have been m o r e secure if the authors had measured: * the solubility of carbonate in the organic phase under the reaction conditions, in the absence of benzyl chloride * the rate of formation and the equilibrium solubility of the pyrrolidinone anion in the presence of the quaternary a m m o n i u m salt * the h o m o g e n e o u s rate for benzylation of the pyrrolidinone anion * the effect of benzyl chloride concentration on the reaction rate

For a surface reaction which is first order with respect to the solute it is not possible to dissect the chemical reaction and m a s s transfer components using the dispersed p o w d e r reactor. Nonetheless, it is possible to study the surface kinetics when the chemical rate is demonstrably slower than mass transport. Thus in the heterogeneous oxidation of hydrazine by solid barium chromate in aqueous sodium acetate buffer [52]:

3N H (t) 2

4

+

4Cr{VI)(s)

- 4Cr(///)(s) +

3N (g)+ 2

+

1 2 t f (/)

(55)

the initial rate w a s found to be proportional to the m a s s of barium chromate, which is essentially insoluble in the reaction m e d i u m . Evidence that the reaction occurs in an adsorbed

222

surface film c a m e from the dependence of rate on hydrazine concentration, which showed a rate profile corresponding to Langmuirian adsorption of hydrazine on the solid surface i.e.

1 =

•1

1

(56)

A plot of 1/r vs 1/[N H ], shown in Figure 20, gave a straight line from which k, and K were obtained. 2

0

1

4

3

5

7 2

[ N H ] j / 10 M 2

a d s

9

1

4

Figure 20. Plot of 1/rate vs 1/[N H ] for the oxidation of hydrazine with barium chromate. 2

4

Although the authors did not chose to do so, it is easy to demonstrate that the value of k, is a pure kinetic term, with no contribution from mass transfer. Using the approximation that the Sherwood n u m b e r is 2 (equation 21) and taking dp = 6 χ 10" c m and the diffusion coefficient of hydrazinium ion in water as 3 χ 10" c m s" gives k = 1 0 c m s" . A typical experiment uses 8 g of barium chromate with a surface area of 3.3 m g" , i.e. a surface area of 2.64 χ 10 c m . The chemical reaction rate with [ N H ] = ΙΟ" M is 2.7 χ 10" M s" which for a reaction v o l u m e of 0.085 1 corresponds to 2.295 χ 10" mol s" or a mass transfer rate of 8.69 χ 10" mol cm" s" or a mass transfer coefficient of 8.69 χ 10" c m s" . T h e actual reaction rate is thus m a n y orders of magnitude less than the transport limited rate, and thus the true chemical kinetics are being studied. 3

5

2

1

2

1

L

2

5

2

2

2

2

1

5

1

1

4

6

12

1

1

7

1

6.2. R o t a t e d disk t e c h n i q u e s A disk rotating in a fluid acts as a p u m p . Fluid is drawn towards the disk, spun around and thrown outwards (Figure 21). Under laminar flow conditions the rotated disk has two useful characteristics. First, the boundary layer thickness is independent of the position on the disk (excluding edge effects). Second, the flow induced by the disk and thence the diffusion boundary layer thickness δ can be rigorously calculated from fluid mechanics theory [20,53]. T h e rotated disk is thus a useful tool which since the 1940's has been used by electrochemists

223

( A d a m s [2] and Japanese workers [54] have reviewed the early literature), and more recently has found use by chemists studying the rates of reactions at liquid-solid interfaces.

Figure 2 1 . Fluid flow at a rotating disk Gregory and Riddiford [53] carried out a careful and precise study of transport to a rotating disk by studying the dissolution of zinc in aqueous iodine solution. T h e y refined the earlier theory of Levich [20] and showed that the diffusion film thickness δ is given by the expression i - -Ô = 1 . 8 0 5 £ > ν ω [0.8934 + 0.316(D/v) 3

6

2

0 3 6

(57)

]

1

where ν is the kinematic viscosity and ω is the rotation speed in radians s" . T h e second term is only needed when species with a very high diffusion coefficient are involved, such as H in water.

+

For the case of a dissolving disk where surface dissolution is a first order process in undersaturation the concentration profile may be depicted as shown in Figure 22, and the flux j at the surface is given by (58) At steady state this flux equals the flux to the bulk, i.e. (59)

224

Rearranging this expression gives

1 j

1

(60)

c.sat - c,bulk\ 5 Λ

C=C,' s a t .

bulk

Figure 22. Concentration profile for first order dissolution at a solid surface. At infinite rotation speed the film thickness is zero, so the intercept on the 1/j axis for a plot of 1/j vs co^ (known as a Koutecky-Levich plot [55]) gives the rate constant for the dissolution and m a y be calculated if the solubility is known. T h e diffusion coefficient D can be calculated from the slope. T h e majority of dissolution processes are purely transport controlled, i.e. they b e h a v e as if the liquid is in equilibrium with the solid at the point of contact. In these cases l/k^ « δ/D and the Koutecky-Levich plot will pass through the origin. If a surface process is slow relative to diffusion then the plot will show a positive intercept. This provides a simple test for transport control (Figure 23). surface limited

2

j /mol c m s

transport limited

ca)-i/2

Figure 2 3 . Surface and transport limited processes studied by the rotated disk. A case studied in the author's laboratory proved an exception to the general rule. From the dissolution study of potassium fluoride in hot dimethylformamide discussed earlier k w a s found to be 8.4 χ 10" c m s" . This is much lower than the value of 1.93 χ 10* c m s" L

4

1

2

1

225

calculated from the k n o w n particle size distribution and extrapolated diffusion coefficient (6.92 χ 10~ c m s" ) assuming that the Sherwood number is 2. T h e rotated disk technique w a s used to study the dissolution of a pressed disk of potassium fluoride in dimethylformamide at 125°C. A large positive intercept was found for the Koutecky-Levich plot, confirming the existence of a rate limiting surface process. For potassium fluoride a rate constant for the surface process of 6.92 χ 10" c m s' was obtained from the intercept, and from the slope a solubility of 7.5 χ 10" mol cm" was obtained, which is satisfyingly close to the independently measured value of 6 χ 10" mol cm" . Although these results confirm the existence of a surface limiting process precise interpretation of the intercept values is problematical because of uncertainties as to the surface micro structure and the effective available surface area. 5

2

1

3

7

1

3

7

3

Complications can arise due to coating of the surface of the disk during reaction. Dissolution of bismuth metal by tri-iodide ion in acidified potassium iodide m e d i u m was studied by the rotated disk method [56]. Bi Bil

3

+

l~

-

Bil

+

J~

-

B i l l

3

3

3

(61)

At the lower concentrations of iodide a change in rate was observed with time (Figure 24)[56], which was shown by visual observation to be due to coating of the bismuth surface by the intermediate bismuth tri-iodide.

3

I o g | (l încrement)/cm £ 10

3

60

120

180

240

t / min

Figure 24. Rate inhibition by surface coating: plot of logarithm of I " increment vs time, ω = 31.42 rad s" , at 25°C. 3

1

Only one study of organic liquid-solid reactions using the rotating disk has been reported to date [57]. It concerned the kinetics of nitration of benzene, toluene, N-methylnitroamine

226

and N-methylpicramide with solid nitronium tetrafluoroborate using ethyl acetate as solvent. Hydrolysis with water to give nitric acid was also studied. T h e results are interesting but difficult to interpret because of the unusual units in which the reaction rates are expressed: concentration p e r unit time p e r unit area (mol Γ c m min" . B y manipulation of the data in the paper it is possible to c o m p a r e the relative surface rates provided that the same v o l u m e of solution w a s taken for each experiment quoted. Plots of reciprocal rate vs ω' are shown in Figure 2 5 . 1

2

0

1Λ

benzene

water 1

5

2

k~ /l0 cm s

• toluene • N-methylpîcramîde

••y<~ .:~---:

• N — methylnîtroamine

0

0.1

0.2

0.3

0.4

0.5

U-y(rad"^)

Figure 2 5 . Plots of reciprocal rate vs ω

M

for nitration with nitronium tetrafluoroborate.

A s the authors note, reaction with water is purely diffusion controlled, which is not surprising. Apparent surface reaction rates for toluene, N-methylnitroamine and N methylpicramide, which are given by the intercepts on Figure 2 5 are experimentallly indistinguishable. This is surprising, since nitration rates are very sensitive to substrate structure [58], although comparative h o m o g e n e o u s rate data for the last two c o m p o u n d s is not available for comparison. It suggests a c o m m o n rate determining step for these three processes, which could be related to dissolution of the nitronium salt. Alternatively, the overall rates may be dominated by adsorption or desorption processes. For a process showing simple first- or pseudo first-order kinetics at the surface the slope of the Levich plots are calculable from equation (57) and provide a check on the controlling mechanism. If surface adsorption processes are significant then the transport rates no longer show the same relationship to δ. In this case, because the volume of the solution is not k n o w n , the theoretical slopes cannot be compared with those found, and n o firm conclusions can b e drawn. T h e r e are thus a number of interesting questions which have been raised by this study, and

227

further work in the area is desirable. Because the area is n e w and the methodology is still developing there is not yet a consistent approach to experimental design. This matter will be addressed further in the Conclusions to this review. 6.3. W a l l - j e t t e c h n i q u e s . Wall-jet techniques involve directing a fine laminar jet of liquid at right angles to a planar surface. The hydrodynamics of the system are k n o w n [59], the flow pattern being shown in Figure 26 [60]. T h e contour shows the boundary between fluid m o v i n g towards the wall and fluid m o v i n g away. Impinging jet

Figure 26. Flow pattern at the wall jet. 5/4

T h e diffusion film thickness increases as R where R is the radial distance from the centre of the jet, so unlike the rotated disk electrode (RDE) the surface is not uniformly accessible to the reacting fluid. This makes the wall jet (WJE) a more discriminating tool than the rotated disk in distinguishing between alternative electrochemical m e c h a n i s m s . This aspect has been discussed in detail recently [60], and will be exemplified briefly here for the case of an E C E m e c h a n i s m , shown below.

A ± e~ = Β Β - C C ± e~ = Ρ

(62)

Here A undergoes an electron transfer at the electrode to give an intermediate Β which is transformed chemically to C which then reacts electrochemically to give product P . This process is studied by determining h o w the number of electrons n transferred for each A reacted varies with mass transport. If Β is lost from the region of the electrode faster than its transformation to C then n approaches unity; if the converse, then n tends to 2. With an electrode which is not uniformly accessible the variation of n with the flow parameter (the flow parameter is rotation speed ω for a rotated disk or flow rate ν for a wall jet) varies less sharply. This can be seen by comparing the working curves for a rotated disk and wall jet for the E C E m e c h a n i s m (Figure 27). For the R D E the flow parameter is a function of ω for the W J E it is a function of v" . eff

eff

eff

eff

3/2

228

0.5

-1.5

I.5

-0.5

flow parameter Figure 27. Plots of n

eff

vs flow parameters for the wall jet and rotated disk electrodes.

Alternative m e c h a n i s m s are tested against these ' w o r k i n g c u r v e s ' which c o m p a r e n with a transport parameter. That for the wall jet can be seen to have a wider range and lower slope than for the rotated disk and this gives a wider range of accessible kinetics and greater discrimination between alternative mechanisms. eff

Although the wall-jet has been developed by electrochemists it has potential for use in the study of non-electrochemical m e c h a n i s m s at solid surfaces. As an example, the kinetics of deposition of colloidal carbon on treated and untreated glass has been studied in the apparatus shown in Figure 28 [61].

Photo multiplier tube

Microscope

Microscope table

1 Colloid

Figure 28. Wall j e t apparatus for study of colloidal deposition [61].

229

It was shown that on glass pretreated with an aminoalkylsiloxane the deposition was essentially diffusion controlled, as demonstrated by the reasonable straight line fit found when the flux j is plotted against R . For untreated glass the deposition was m u c h slower and showed m i x e d kinetic control, for which, although the data treatment is m o r e c o m p l e x , a rate constant could still be extracted. Figure 29 [61] compares the radial variation of deposition for treated and untreated glass, and contrasts the very sharp peak obtained under pure transport control with the flatter ' v o l c a n o ' obtained for deposition in the ' m i x e d ' regime. 5/4

-2

-1

cm ms

10!

Figure 29. Comparison of flux rates for deposition of colloidal carbon onto glass under conditions of (A) transport control and (B) mixed transport/kinetic control. This technique has untapped potential for the study of reaction m e c h a n i s m s at liquid-solid interfaces. 6.4. C h a n n e l - f l o w t e c h n i q u e s T h e channel flow cell has been developed rapidly in the past few years by C o m p t o n ' s group at Oxford University [62 - 6 7 ] . Originally devised to study electrochemical processes, its use has n o w been generalised to permit study of the reactive dissolution of solids, both inorganic and organic, and of reaction and adsorption/desorption processes at solid-liquid interfaces. At the present time detection methods are electrochemical. T h e central element of the technique (Figure 30) is a tube of rectangular cross section through which the liquid phase flows. Into one wall is e m b e d d e d the reactive solid together with a d o w n s t r e a m detector electrode and, if required, an upstream generator electrode.

230

Solid s u b s t r a t e

Detector electrode

> Flow

Figure 30. Schematic of the channel flow cell. Like the wall jet, the surface of the reactive solid in the channel flow cell is not uniformly accessible to the flowing fluid. Within the channel the flow can be precisely defined mathematically. W h e n reaction occurs at or near the solid surface between a solute and the reactive solid the concentration of solute is depleted, and this concentration, or that of a reaction product, is measured at the detector electrode (Figure 31).

reagent flow

>

- ΊΓ_Γ

~~ - *

substrate

detector

Figure 3 1 . Transport with reaction in the channel flow cell. Kinetic m o d e l s of the reaction under study are tested by c o m p a r i n g w o r k i n g curves of calculated current vs flow rate with measured values. Data treatment is preferably by numerical m e t h o d s . Application of the ' b a c k w a r d implicit' (BI) method, first applied to channel systems by Anderson and Moldoveanu [68] has been further developed by C o m p t o n ' s group [63]. This method uses a fine two-dimensional grid to define the flow cell. Considering a small section of the grid (Figure 32)

C

y=j+1

, i.J-Hl

I

,

1

C

i-1.J

x=i-1

C

i.j

x=i

c

i+1.j

x=i+1

Figure 3 2 . Grid for modelling concentration profiles using the B I method.

231

the concentration gradient at (i,j) is approximated by the slope of the line joining c(i,j) to the previous point c(i-l j ) i.e.

ÔÇ dx

C =

0J) ~ « - U ) (x, - χ._ ) C

λ

Computation starts by calculating implicitly all the concentrations in the grid for the given boundary conditions. Inputs to the calculation are the kinetic parameters, including preequilibria, for the model to be tested, and k n o w n concentrations at the upstream boundary, that is, the solution upstream of the reactive solid. For each flow rate a two dimensional concentration profile is calculated within the cell, and the corresponding calculated fluxes at the detector electrode are compared with those measured. T h e adjustable parameters in the model are varied until a best fit is obtained between the observed and calculated fluxes. This technique was initially developed during a study of the dissolution of calcite (macrocrystalline calcium carbonate)[65,66], during which it was shown conclusively for the first time that the rate of dissolution under acid conditions is a heterogeneous process, first order in [H ] at the surface. It has also proved to be a useful technique for the investigation of a variety of other reactions in liquid-solid systems including the dyeing of cotton cloth with reactive dyes [69,70], bleaching of a dyed cloth using bromine [64], adsorption of copper ions on a calcite surface [67], and, very recently, in a study of the mechanism of reaction of cyanuric chloride with water soluble amines [71]. +

M e a s u r e m e n t of the kinetics of dyeing of cotton cloth with a reactive P R O C I O N dye

cellulose has been accomplished in one case by determining the concentration of d y e d o w n s t r e a m of the substrate by electrochemical reduction [69] and in another case by following the release of chloride ion [70]. In the first case the situation is as in Figure 3 1 : some dye is adsorbed and the difference in concentration between the upstream concentration and that at the electrode, which is a function of flow rate, can be used to deduce the kinetics. Rate constants for the dyeing process at p H 11.2 were in the range 2 - 5 χ 10" c m s" . 4

1

For the Cu(II) adsorption studies the double electrode system was used [67]. Cu(II) was generated at an upstream copper electrode by stepping the potential to that at which copper dissolved to form Cu(II), which then flowed over the calcite crystal to the detector electrode (Figure 33).

232

Figure 3 3 . S c h e m e for measurement of rate of copper adsorption on a calcite surface. Analysis of the current-time transient at the detector electrode permitted deduction of the adsorption kinetics. A rate constant of 0.8 ± 0.3 c m s" was obtained for the adsorption rate. This is m u c h faster than typical m a s s transfer coefficients under laminar flow conditions, and under experimental conditions with less rapid hydrodynamics e.g. the dispersed p o w d e r reactor, the measured rate would be that controlled by mass transfer. 1

Reaction of cyanuric chloride with aqueous solutions of amines is used in the production of P R O C I O N dyes.

In the first part of a study of the mechanism of this process [71] the dissolution of cyanuric chloride in water was examined using the channel flow cell. In this type of study it is c o m m o n to use pressed pellets of the substrate. Here it was found that the use of such pellets gave ambiguous results: hydrolysis within the porous solid gave kinetics apparently consistent with a m i x e d m e c h a n i s m involving a surface hydrolysis in parallel with hydrolysis in solution following dissolution. Studies using fused pellets with no surface porosity showed that there w a s no heterogenous component to the reaction; thus the process comprises dissolution of the solid followed by hydrolysis in solution. This observation has general relevance for the study of surface reactions using pressed pellets. For the second part of the study the homogeneous kinetics were measured for the model reaction, that of monoprotonated N,N-dimethyl-p-phenylenediamine with cyanuric chloride. Then the kinetics of the heterogeneous reaction were measured in the channel flow cell. It w a s found that the results could be fitted very well using the predetermined parameters i.e. no new term involving a reaction at the solid surface was required. Reaction therefore occurs via dissolution of cyanuric chloride followed by reaction with the amine in solution.

233

T h e channel flow cell is thus an extremely versatile technique for the study of liquid-solid reaction kinetics which can cover a range of surface kinetics up to a limit of around 10 c m s" . It does suffer from the disadvantage at the present time that data treatment can require a great deal of computer time. 1

6.5. Overview: liquid-solid reactions M e t h o d s for the rigorous study of liquid-solid reactions are well defined but are still not generally used. There are a large number of reactions which are nominally heterogeneous w h o s e secrets are waiting to be unravelled. In studying such reactions it is necessary in the first instance to determine whether the reaction is occurring in the bulk solution phase or not. M e a s u r e m e n t of the rate as a function of surface area of solid will enable this distinction to be m a d e . A reaction which occurs in the bulk solution phase can then be characterised by measuring: * * * * *

solubilities pre-reaction equilibria in solution h o m o g e n e o u s reaction rates m a s s transfer rates with and without reaction reaction rates as a function of interfacial area

T h e most difficult distinction to m a k e is between reactions which are fast and occur in the diffusion film, and those which actually occur on the solid surface. Probing this area of chemistry is one of this a u t h o r ' s current interests. Here the criteria described in section 5 need to b e addressed. A technique giving control of hydrodynamics will be required. 7. L I Q U I D - L I Q U I D S Y S T E M S M e t h o d s for studying interfacial reaction kinetics in liquid-liquid systems were comprehensively reviewed by Hanna and Noble in 1985 [72]. T h e present review attempts to provide a critical review of studies of mechanism in two-phase systems with an emphasis on organic chemistry. A fundamental requirement is that, in processes where m a s s transfer is coupled to reaction, the contribution of the two processes to the overall rate can be dissected. In a n u m b e r of papers this is not addressed and the experimental design and interpretation is unsatisfactory. If this review opens a w i n d o w on these areas then it will have served its purpose.

7.1. T h e constant interfacial area cell T h e s e cells in a n u m b e r of designs can provide useful data if properly used. Various modifications of the original Lewis cell [73] are in use [5,74,75]. Nitsch [74] favours a design with a gauze at the interface to minimise interfacial turbulence. S h a r m a ' s design [5] is shown schematically in Figure 34. T h e numerous correlations for the m a s s transfer coefficients in these cells have been reviewed [74,75]. Values of k are generally in the region of 10" c m s" at agitator speeds in the region of 1 s" . 3

L

1

1

234

Figure 34. Constant interfacial area stirred cell. This technique, albeit with cells differing in details of design, has been widely used to study organic reaction mechanisms. It is instructive to consider the limitations of this equipment in the slow reaction regime. A two-phase system with a phase depth where reaction occurs of 2 c m will be considered (Figure 35).

source phase

2 cm

reacting p h a s e

Figure 35. Reaction in a system with a flat interface. First of all the time to saturate the aqueous phase with a neat organic liquid present as an overlayer will be estimated. T h e rate of change of concentration in the aqueous phase is given by

where a is the interfacial area per unit volume of the aqueous phase. For a parallel sided vessel a is equal to the reciprocal of the solution depth. Integration gives

235

1 - exp(-k at)

(65)

L

3

1

1

For k = 10" c m s" , which is typical of this equipment, and a = 0.5 c m ' , the half life for simple physical saturation is 23 minutes. T h e rate expression for reaction in the bulk phase has been developed earlier (26): L

Csat

r=

ϊ

66

()

Γ

+

W h e n k, » k a the overall rate becomes insensitive to 1^ which then cannot be measured by this technique. A simple example illustrates the point. It is desired to study a reaction where a c o m p o u n d A X as an overlayer dissolves in a lower aqueous phase where it reacts with Β to liberate X, which remains in the aqueous phase. It is assumed that the chemical reaction is first-order in A X . T h e overall rate of formation of X is given by (66). If (66) is divided through by the chemically limited rate k c there is obtained L

r

_r_

sat

1

=

'a. " !

+

67

K_ ka

<>

L

where r is the rate of the reaction in the absence of a mass transfer limitation. Putting k a = 0.5 xlO" c m s" gives the following response of r / r to k,.. (Table 4): lim

3

1

L

lim

Table 4. Constant interfacial area stirred cell: response of r/r

-6

10 10" 10" 10° ΙΟ" 10

5

4

2

1

3

lim

1

to k, for k a = 0.5 χ 10" c m s" L

0.998 0.980 0.833 0.333 0.048 0.005

5

1

Only in the area where k, < 10" s" can the response of r to k, be measured. For rate constants much higher than this the kinetics will be coupled with, and eventually dominated by, mass transfer. O n c e the reaction rate becomes sufficiently high for reaction to be complete in the diffusion film this system again becomes useful, because now the rate is independent

236

of the phase volume in which reaction occurs. This regime: if, in the constant interfacial area cell, the independent of the phase v o l u m e in which reaction 'interfaciaf or else be complete inside the diffusion

provides a useful check of the reaction reaction rate in moles per unit time is occurs, then the reaction m u s t be either film.

W h e n the source phase is a solution the situation is further complicated, particularly if, as is c o m m o n , reaction occurs via partition of an organic component into the aqueous phase (equation (32)). N o w the effective m a s s transfer coefficient, k , is given by L e f f

1

Ρ

1

k

k

(68)

k 3

1

5

1

If Ρ is say 100 and k and k are each 10~ cm s" then k ~ 10" c m s" . Again taking a = 0.5, kefja = 5 χ 10" s" and now is only accessible when its magnitude is less than this, corresponding to say i > 38 h. L o

6

L a q

L e f f

1

Vl

T h e s e c o m m e n t s are relevant to a study of the hydrolysis of aromatic esters in a two-phase toluene-aqueous sodium hydroxide system which used both unstirred and stirred reactors [761. It w a s shown that the overall hydrolysis rate w a s equal to the rate of diffusion from toluene into the aqueous phase. Overall reaction times in the unstirred systems were in excess of 100 hours, whilst the relevant ester hydrolyses in the aqueous phase had half lives of minutes, so this should not have caused surprise. Equation (32) is relevant here. T h e point was well made, however, that under these conditions the relative rates of hydrolysis of different esters was determined by their partition behaviour and not by their intrinsic reactivity (Table 5). Table 5. Relative hydrolysis rates of dimethyl phthalates in h o m o g e n e o u s and two-phase systems at 25 °C. isomer ortho meta para

homogeneous ratet 1.77 0.85 0.99

3

V i O ' M" s n

6

1

heterogeneous r a t e t f 12.6 50 112

1

1

k / 1 0 " s" (The absolute values, but not the ratios, are specific to the system dimensions).

Sharma has successfully used the constant interfacial area cell in this fast reaction regime to study a variety of two-phase liquid-liquid systems [5]. An example is the use of the technique to obtain the kinetics of the hydrolysis of neat formate esters over aqueous sodium or potassium hydroxide solutions [24,38]. Reaction occurs in the aqueous phase. At hydroxide concentrations greater than 2 M the hydrolyses studied were sufficiently fast to be complete within the diffusion film. For the second-order reaction the rate is given by j = c (Dk [OH"])^ provided that the flux rate is not so high as to deplete the hydroxide concentration within the diffusion film. i.e. replacement of hydroxide ion in the diffusion film must be faster than the above reaction rate. T h e necessary conditions are discussed elsewhere [5]. A typical plot of sat

2

237

the absorption rate vs hydroxide concentration is shown in Figure 36. At [ K O H ] = 3.51M, k = 19.8 M s . T h e decreasing rate with increasing potassium hydroxide concentration, which at first sight is surprising, is due mainly to two factors. T h e second-order rate constant s h o w s a negative salt effect, and the solubility of the ester is reduced as the concentration of potassium hydroxide is increased. 1

2

7

2

1 0 j / m o l cm s

1

4h

2

4

6

[KOH]/M

2

7

Figure 36 Absorption rate j (mol cm" s'VlO" ) vs [KOH] for the reaction of η-butyl formate with aqueous potassium hydroxide at 30°C [24]. T h e constant interfacial area cell has recently been employed in a detailed study of the hydrolysis of η-butyl acetate using phase transfer catalysis ( P T C ) [77]. T h e reaction scheme is shown in Figure 37.

organic phase

Q CI

CH,COOC„H

3

+

ft

4 9

QOH

C H O H + Q CKjCOO 4

g

interface 0

+

Q OH

Q CH C00

Q + OH

3

+

Q +CH C00 3

aqueous phase CH COOC H 3

4

g

+

OH

>C H OH 4

g

+

C^COO

Figure 37. Reaction scheme for the phase transfer catalysed hydrolysis of butyl acetate.

238

Reaction is rapid enough to occur in the diffusion films. Modelling of the system is necessarily complex, involving simultaneous solution of the m a s s balances and m a s s transfer and reaction rates for all the species shown. Rates of m a s s transfer of the quaternary a m m o n i u m salt and the rate of the uncatalysed hydrolysis were measured separately [78,79]. A plot of rate of reaction in the organic film vs the concentration of quaternary a m m o n i u m hydroxide on the organic side of the interface gave a satisfying straight line over a range of conditions, in agreement with the proposed model. A second-order rate constant in the organic phase of 47 M" s" w a s obtained for the hydrolysis in the organic p h a s e at 25°C, in contrast with a value of 0.56 M" s" for reaction in the aqueous phase at the same temperature. Direct measurement of the hydrolysis rate in the organic phase would have provided a useful check on the validity of the model. This excellent paper is the first detailed study of the m e c h a n i s m of a phase-transfer catalysed reaction in the fast reaction regime, and points the way to a rigorous study of this area of chemistry. 1

1

1

1

A study [80] of the reaction between benzoyl chloride and aniline in a two-phase waterchloroform system was unsatisfactory in that it failed to identify unambiguously the reaction site or to explain the reaction profiles obtained. N o attempt was to m a d e to determine the h o m o g e n e o u s reaction rate of benzoyl chloride with aniline in the suggested reaction phase. This interesting system deserves a more rigorous study. It has been claimed that the hydrolyses of 1-bromoadamantane [81,82] and 1-phenethyl chloride [82] in a water-organic solvent system are S 1 reactions occurring at the water-solvent interface. Facts quoted in support of the case were N

* rate interfacial area and independent of either phase v o l u m e * activation energy found to be 96 kJ mol" , essentially the same as that for the h o m o g e n e o u s reaction in water. 1

An alternative explanation, not considered by the authors, is that it is a fast reaction occurring in the diffusion film on the aqueous side of the interface. Pertinent results for the 1-bromoadamantane case at 75°C, either provided or derived from data in the two papers are: 7

1

* a reaction rate constant of 1.66 χ 10" cm s" * a partition coefficient c / c of 1/0.0007 measured on the methoxy analogue. org

aq

1

From the subsequent literature [83] a value of 1.9 s" has been derived by the reviewer for the rate of the h o m o g e n e o u s hydrolysis of 1-bromoadamantane in 100% water at 75°C. Using the W i l k e - C h a n g correlation [84] a diffusion coefficient of 1.76 χ 10" c m s" has been calculated. 5

1

2

1

T h e rate constant of 1.9 s" for the h o m o g e n e o u s reaction implies that any aqueous phase reaction in this unagitated system will be substantially complete within the diffusion film, and hence the reaction rate for this case will be proportional to interfacial area and not to the aqueous phase volume. Another way of looking at this is to calculate the reaction layer thickness ζ which is given by [85]:

239

ζ =

D

N

(69) k 3

1

This gives a value of 3 χ 10" c m s" , which shows that an aqueous side reaction would occur within the diffusion film. Given the low m a s s transfer coefficient there will be no organic side resistance and so the m a s s transfer coefficient can be calculated from D , k and Ρ using the expression (cf. equations (45) and (46)) (70)

6

1

giving k = 4 χ 10" c m s" . L

This is a factor of 2 4 greater than the measured value, but the use of the m e t h o x y analogue to estimate Ρ is quite unsatisfactory and could be substantially in error. Calculation of the difference in octanol-water partition by the method of Hansch [86] suggests that Ρ for the b r o m o c o m p o u n d is 7 times that of the methoxy analogue. In the nearest measured analogy, Ρ for benzyl bromide is 37 times that of benzyl methyl ether [87]. T h u s the calculated reaction is of the same order as that required to be consistent with a reaction occurring in the aqueous diffusion film. M o r e plausible is the argument based on comparison of the activation energy with that for the h o m o g e n e o u s process. For a reaction in the film the apparent activation energy for the term (Dk) is the arithmetic mean of the separate activation energies for D and k. T h u s with the assumption that Ρ is independent of temperature an activation energy of 55 kJ mol" is expected. A measured value of 96 kJ mol" is therefore evidence against a film model, but the precision of this data was not good, and there is little practical experience of the m e a s u r e m e n t of activation energies in this type of system. In the opinion of this reviewer the case for an interfacial reaction is 'not p r o v e n ' . 1/z

1

1

Also discussed by the same authors is the hydrolysis of 1-phenethyl chloride in toluenewater and toluene-aqueous sodium hydroxide. T h e s e results are also claimed to be evidence for a rate limiting surface reaction, but are shown here to be explained satisfactorily by a m e c h a n i s m involving reaction in the aqueous diffusion layer. From the first result in Table 5 of reference 82 the mass transfer coefficient with reaction, k , is found to be 3.34 χ 10" c m s" . T h e h o m o g e n e o u s hydrolysis rate for phenethyl chloride in water at 70°C has been calculated by this reviewer from the published data [88] to be 4.0 s" . Again using the WilkeC h a n g m e t h o d the diffusion coefficient in water at 70°C is calculated to be 1.9 χ 10" c m s" . N o partition coefficient for toluene-water is available but the octanol-water partition coefficient for 2-bromoethylbenzene, which is probably a good model, is 891 [87]. For the film model w e then have r

5

L

1

1

5

1

240

5

ιr V^X \/l.93 χ Κ Γ χ 4 fc, = - — = = 9.9 χ 10 Ρ 891 n f t

_!

1 / ν 6

cm

s

(71) K

.

J

1

This result is only a factor of three smaller than the measured value, and appears to this reviewer to show that the data can be explained by a fast reaction in the diffusion film. A related study of the hydrolysis of triphenylmethyl chloride (trityl chloride) in a two phase aqueous-organic system has been reported by Silanek e t al [89]. Ph C-Cl 3

+ H0

- Ph C-OH

2

+ HCl

3

(72)

M o s t of the work refers to toluene as the organic solvent. They found: * * * *

rate interfacial area rate «= concentration of trityl chloride in the toluene phase E = 46.8 kJ m o l in the range 45° - 60°C E = 6.9 kJ mol" at temperatures > 65°C 1

act

1

act

* reaction rate at 50°C given by k

r L

4

1

= 1.25 xlO" c m s" .

T h e effect of added salts is interesting. Table 6 is reproduced directly from their paper. Table 6 Effect of salts on the rate of hydrolysis of trityl chloride in a water-toluene system [89]. Salt salt concn./M lOVcm s none

1.33

sodium chloride

0.1

1.07

sodium chloride

1.0

0.86

potassium bromide

0.1

2.04

0.1

0.58

Br

0.1

0.66

sodium lauryl sulphate

0.1

1.35

+

( C H ) N Cl" 4

9

4

(C H ) N 4

9

4

+

Based on these results they conclude 'that the reaction site is the laminar layer adjacent to the interface on the aqueous phase s i d e ' . This conclusion m a y be correct, but in this case it is possible that the reaction is interfacial ! S o m e simple calculations can be used to show this. It is necessary to estimate D, Ρ and k in order to calculate the rate expected on the basis of a reaction in the diffusion film. A recent study [90] gives the rate constant for the h o m o g e n e o u s hydrolysis of trityl chloride in 9 0 % acetone/water at 25°C as 3.9 s" . In order to estimate the rate in 1 0 0 % water it has been assumed that the rate changes with solvent composition in the same way as for the related benzhydryl chloride. For benzhydryl chloride r

1

241

6

1

1

the solvolysis rate at 25°C in 9 0 % acetone/water is 4.6 χ 10" s" [91]; in water it is 20 s" (personal communication, from T.W. Bentley, University of Swansea). Applying an equivalent factor to the trityl chloride case gives a rate constant at 25°C of 1.7 χ 1 0 s" , and correcting to 50°C using S i l a n e k ' s activation energy gives k^ = 7.3 χ 1 0 s" ! From the W i l k e - C h a n g relationship [84] the diffusion coefficient can be computed as 5.2 χ 10" c m s" . It is obviously impossible to measure the partition coefficient directly, but calculation of the octanol-water partition using the Hansch method [86] gives a value of 10 . Calculation of the rate assuming a film model and using equation (70) gives a value for the m a s s transfer coefficient with reaction of 2 χ 10" c m s" . This is 6 times lower than the m e a s u r e d value, which leaves open the possibility that this reaction is interfacial. T h e lack of any plateau in the rate vs concentration profile does not necessarily exclude an interfacial process, since the m e a s u r e m e n t s m a y all have been m a d e in a region where the adsorption isotherm is linear. 7

7

1

1

6

2

1

6

5

1

7

Calculation of the reaction layer thickness from ( D / k ^ gives a value of 2.5 χ 10" cm. T h u s the reaction must at least occur very close to the interface or, if there is significant interfacial stabilisation of the transition state [85], it could actually occur at the liquid-liquid interface. T h e rate retardation by sodium chloride is probably a c o m m o n ion effect, given that potassium bromide accelerates the rate. It is difficult to rationalise the rate increase in the presence of potassium bromide with a reaction in the aqueous phase, since it should increase Ρ and hence decrease the rate. It is possible that the rate decrease caused by the quaternary salts is caused by displacement of trityl chloride from the interface. M e a s u r e m e n t of adsorption isotherms would have greatly assisted in clarifying the site of reaction. T h e first reported study of a reaction at a liquid-liquid interface was by Bell, w h o studied the oxidation of N-benzoyl-o-toluidine in solution in benzene with aqueous p e r m a n g a n a t e [92]. Ο

Ο

H e demonstrated that: * the rate showed a plateau at a concentration of N-benzoyl-o-toluidine corresponding to the m a x i m u m in its adsorption isotherm at the benzene-water interface. * the rate was independent of agitation speed. * the rate w a s proportional to the concentration of permanganate in the aqueous phase. * in the plateau region the reaction rate increased by 13 times on increasing the temperature by 10°C.

242

T h e first item of evidence provides good support for B e l l ' s conclusion that the reaction occurs at the liquid-liquid interface. T h e second and third points are consistent with that hypothesis and are required by the proposed mechanism but do not of themselves prove it. It is a pity that this early study was not followed up. T h e very large temperature coefficient for the reaction is particularly interesting and deserves further investigation.

7.2. Kinetics in dispersed liquid-liquid systems Chemical reaction kinetics can under some circumstances be studied in dispersed liquidliquid systems. For a neat liquid stirred with a second phase with which it reacts by the extractive m e c h a n i s m it is necessary to consider * which phase is continuous and which is dispersed * the mass transfer coefficient k in each phase * the reaction regime - whether the chemical kinetics are fast or slow relative to mass transfer * the interfacial area L

7.2.1. Phase continuity and its relationship to the mass transfer rates. W h e n two immiscible liquids are dispersed one becomes the dispersed (droplet) phase; the other phase is then k n o w n as the continuous phase. T h e main factor determining which phase b e c o m e s dispersed is the phase volume ratio, but most systems show an ambivalent region where either phase can be dispersed depending on how the fluids are mixed [93]. At a phase v o l u m e ratio of 2:1 the phase with the smaller volume will almost certainly be the dispersed phase. Outside the drop i.e. in the continuous phase, k is only weakly dependent on drop size and hydrodynamic conditions within a stirred vessel e.g [38]. Experimental correlations are available [94] but are outside the scope of this review. Values in the region of 1 - 2 χ 10" c m s" were obtained by Sharma for the case of formate esters dispersed in aqueous sodium hydroxide. S h a r m a and Doraiswamy quote the range 3 - 10 χ 10" c m s" for liquid-liquid dispersions [5]. For droplets with a diameter < 0.15 c m the inside of the drop is essentially stagnant [94], and so transport to the inside surface of the droplet can only be by diffusion. For a drop of diameter 0.15 c m the time to extract 5 0 % of a solute (D = 10" c m s) from the drop, assuming a surface concentration of zero, is 1.5 minutes. So if the receiving phase, or a source phase which is a solution is dispersed, then the reaction rate could be limited by the rate of pure diffusive transport within the drop. L

3

1

3

1

5

2

7.2.2. Reaction regime It has already been shown that the response of reaction rate to interfacial area is dependent on the reaction regime. For a reaction which occurs in a bulk phase the rate is a function of interfacial area (equation 28). Figure 38 shows a plot of the overall rate as a fraction of the chemically limited rate (r/r ) vs a for the case where k,. is numerically equal to k . T h e rate asymptotes to the chemically limited rate. lim

L

243

r

0

1

2

3

4

5

α/cm

6

7

8

9

10

1

Figure 38 Response of overall reaction rate to interfacial area per unit v o l u m e of reacting phase, a cm" , in the ' s l o w ' reaction regime, for the case where k is numerically equal to k . 1

r

L

For a reaction which is fast enough to occur within the diffusion film the rate for a neat source phase is given by equation (43), and now the rate is independent of the p h a s e v o l u m e s : it is linearly dependent on the interfacial area. W h e n the source phase is a solution the possibility of the controlling resistance being m a s s transfer in that phase needs to be considered (equations 32 and 45). 7.2.3. I n t e r f a c i a l a r e a T h e interfacial area will depend on a number of factors including agitator speed, vessel configuration, viscosity of the continuous and disperse phases, and interfacial tension. Various m e a n s have been used to measure interfacial area, including chemical m e t h o d s [95], photography [96], and an ingenious method based on depletion of surfactant from a bulk phase to the interface [97]. For a reactor similar to that shown in Figure 18 S h a r m a [38] measured the dependence of interfacial area on agitator speed by measuring the rate of hydrolysis of a neat formate ester in contact with aqueous sodium hydroxide solution. T h e rate per unit area w a s measured in a constant interfacial area cell, and this rate w a s used to calculate the area in the dispersed system. Figure 39 shows the derived plot of interfacial area vs agitator speed. As the agitator speed is increased beyond 2000 r p m the interfacial area and hence droplet size shows no further change, presumably due to the coalescence rate b e c o m i n g equal to the droplet formation rate.

244

iooo Γ­

-1

800 h

α/cm

600 Π­

400 h

200 h

Ο

400

800

1200

1600

2000

2400

-1 stirring r a t e / m i n Figure 39. Interfacial area vs agitator speed for the system n-octyl formate - 2 M sodium hydroxide [38]. 7.2.4. Kinetic studies in dispersed liquid-liquid systems M e n g e r [98] studied the imidazole catalysed hydrolysis of p-nitrophenyl laurate in a rapidly stirred two-phase system. Heptane was used as the solvent. H

0 4-

His conclusion, that the hydrolysis is interfacial in nature, appears to be valid. T h e main evidence is: * the rate is proportional to agitator speed, and hence approximately to interfacial area, in the range 600 to 1700 rpm. This result is inconsistent with a reaction occurring in either bulk phase, but could of itself be explained by a reaction occurring in the diffusion film.

245

* p-nitrophenyl laurate and p-nitrophenyl palmitate hydrolyse at the same rate in the two-phase system, despite the difference in molecular weight which would be expected to correlate with aqueous phase solubility. This is inconsistent with a reaction occurring in the aqueous phase, either in the bulk or in the diffusion film, since the rate should follow the aqueous solubility. * the rate shows a saturation effect with an increase in concentration of p-nitrophenyl laurate in the aqueous phase. This is good evidence for a surface reaction since the observation is difficult to explain otherwise. T h e argument would have been even m o r e persuasive if it had been backed up by adsorption isotherm data measured independently of the reaction, as w a s done by Bell [92]. * addition of small amounts of lauric acid caused a dramatic decrease in rate; vs added lauric acid could be correlated by a Freundlich isotherm. Again, this to be powerful evidence for a surface process. T h e caveat here is that the interfacial transport processes could also be inhibited by a strongly adsorbed film [99].

the rate appears rate of surface

Taken together, the above four observations appear to this reviewer to be adequate evidence for a surface process. But the technique does have a serious limitation when in depth studies are required. Because the absolute interfacial area is not k n o w n it is not possible to determine true interfacial kinetics. As M e n g e r indicates, only observations of changes relative to a reference point can be m a d e . Even these observations may not be valid if the variable being investigated also has an effect on the interfacial area. T h u s , the observation of a zero activation energy for the hydrolysis may not reflect the true kinetics and could be d u e to a change in the adsorption isotherm. Alternatively, the effect could be due to a decrease in interfacial area with temperature caused by an increase in the coalescence rate. S o m e reviewers [100] have gone too far in suggesting that proportionality of rate to agitator speed is an adequate criterion for an interfacial reaction. This is not so. Although interfacial area can be directly proportional to agitator speed within the 'fully dispersed' region, a reaction which occurs completely within the diffusion film will also have a rate directly proportional to interfacial area. M a n y reactions carried out under conditions of p h a s e t r a n s f e r c a t a l y s i s ( P T C ) are kinetically slow relative to mass transfer under the operating conditions normally chosen in the laboratory. In their seminal paper on P T C , Starks and O w e n s [101] showed the response of their prototype reaction to agitation (Figure 40).

246

—I

0

100

1

1

1

200

300

400

1

500

stirring r a t e / m i n

2000

^

Figure 4 0 . Response of reaction rate to agitation: reaction between 1-chlorooctane and sodium cyanide using ( C H ) P B u Br" as phase transfer catalyst. +

1 6

3 3

3

A similar plateau in the plot of rate vs stirring speed was observed in the heterogeneous isomerisation of allylbenzene to 2-methylstyrene using concentrated aqueous sodium hydroxide and a phase transfer catalyst [102].

T h e s e are typical of reactions which occur relatively slowly in the bulk phase. Once the system is fully dispersed the concentration of reactive anion in the organic p h a s e remains at equilibrium with that in the aqueous phase; further increase in the agitation rate has no effect on the reaction rate. This is not always the case, as was shown in a study of the nucleophilic substitution reaction between 2,4-dinitrohalogenobenzenes and azide ion under P T C conditions [103]. For chlorodinitrobenzene the reaction rate increased linearly with the concentration of phase transfer catalyst, consistent with a reaction in the bulk organic phase which is proportional to the concentration of dissolved azide and which is slow relative to m a s s transfer. In contrast, the results for fluorodinitrobenzene appear to be consistent with a process which is rate limited by transport of azide, since the rate asymptotes to a m a x i m u m with increasing concentration of catalyst. Figure 41 c o m p a r e s the results obtained for the fluoro- and chlorocompounds.

247

12 10 8 6 4 2

"

0

1

2

3

4

5

6

4

10 [catalyst]/M

Figure 4 1 . Plots of rate constants for nucleophilic substitutions of halogen by N " in 2,4dinitrohalogenobenzenes in the presence of C H P B u N " under P T C conditions in chlorobenzene/water at 25° C. Data plotted from ref. 103. 3

+

1 6

3 3

3

3

But there is a difficulty with this simple explanation: although at low catalyst loadings the rate of reaction of the fluoro c o m p o u n d is higher than that of the chloro analogue, the reverse is the case at high catalyst loadings. If the rate constant for the h o m o g e n e o u s reaction of the fluoro c o m p o u n d is higher than that of the chloro c o m p o u n d , then its reaction rate in the twophase system should, other things being equal, always be the higher of the two. T h u s insufficient data is available to permit interpretation of these results, and further study of this interesting system is desirable. M a k o s z a invented the term c a t a l y t i c t w o - p h a s e r e a c t i o n to describe the process of forming and reacting a carbanion by interfacial deprotonation of a C-H acid using concentrated sodium or potassium hydroxide as the base [30,31](Figure 3). T h e kinetics of the prototype process, the alkylation of phenylacetonitrile with tetraoctylammonium bromide ( T O A B r ) as the catalyst, have been investigated in a dispersed liquid-liquid system [104].

/CN

Br V

50% NaOH

Jp=%

_

/CN

*

Variables investigated were the reactant and catalyst concentrations, temperature and agitator speed. Evidence cited to support an interfacial m e c h a n i s m for the process include the facts that: * the reactions did not show a linear relationship between rate and either catalyst concentration or sodium hydroxide concentration.

248

* the rate is much less sensitive to bromide concentration than would be expected for a phase transfer process in which hydroxide was transferred into the organic phase in competition with bromide ion. * the reaction rate is highly sensitive to stirring rate: no plateau was seen within the range investigated. On the basis of these results an interfacial m e c h a n i s m was proposed, essentially the same as that shown in Figure 3. T h e s e data show clearly that transport processes are important in determining the overall reaction rate. But the only piece of data which is strongly supportive of an interfacial m e c h a n i s m is the relative insensitivity of the rate to bromide concentration; the other evidence cited c o m e s into the category of 'not inconsistent with the proposed m e c h a n i s m . ' T h e conclusion is probably correct but it does rely on a single piece of evidence. M a k o s z a and Bialecka [105] studied the uncatalysed reaction between phenylacetonitrile and alkyl halides in contact with 5 0 % aqueous sodium hydroxide. Here the low concentration of sodium phenylcyanomethide in the organic phase (3.6 χ 10" M ) w a s cited in favour of an interfacial mechanism. Further evidence comes from product studies in a system using a mixture of alkyl iodides and bromides. In the uncatalysed system the bromides alone are unreactive, but in a mixed system products derived from the alkyl bromide are also obtained. In a control experiment without the phenylacetonitrile it was shown that there is no conversion of alkyl bromide to iodide by adding sodium iodide to the system. This exchange in the reactive system w a s attributed to reaction of iodide ion, generated by reaction on the organic side of the interface, with the alkyl bromide in the system (Figure 42). 5

PhCHCN 4

Να "

R—I

R ι > PhCHCN + Γ Na

/ R—Br / > R - l + PhCHCN +

+

Na X~"

R' ι > PhCHCN + I

4

No "

Na+

Figure 42. Uncatalysed two-phase alkylation of phenylacetonitrile. A related process, the dehydrobromination of (2-bromoethyl)benzene has been studied using tetraoctylammonium bromide (TOABr) as the catalyst [106].

This lipophilic quaternary a m m o n i u m salt is completely partitioned into the organic phase. T h e reaction was zero order with respect to the organic substrate and showed a pronounced saturation effect with respect to the catalyst concentration. An activation energy of 33.6 kJ mol* was found, which can be compared with a value of 87.8 kJ mol" found [107] for the same dehydrobromination carried out under h o m o g e n e o u s conditions using sodium ethoxide in ethanol. It is apparent in this case also that mass transport is important in determining the 1

1

249

overall rate, but the experimental methods, although adequate to demonstrate that point, are not capable of providing a quantitative description of the rate processes involved. T h e r e are considerable opportunities to apply the quantitative techniques described in this review to the study of the kinetics and m e c h a n i s m of phase transfer catalysis and catalytic two-phase reactions. Even the apparently simple process of diffusion of a typical phase transfer catalyst in an organic solvent showed unexpected complications [108]: the rate of transport of tetrabutylammonium nitrate across a liquid m e m b r a n e of n-heptyl cyanide varied with the salt concentration in dilute solution 10" M , but in m o r e concentrated solution ( > 1 0 M ) as the square of the concentration. 4

2

S o l v e n t e x t r a c t i o n of cupric ion from dilute aqueous solution using organic ligands is a major commercial application of two-phase liquid-liquid processes (Figure 4). Typical ligands are extremely water insoluble - a value of 0.3 pmol Γ has been obtained for 2-hydroxy-5nonylbenzophenone oxime [109]. 1

Processes using this and related ligands have been the subject of intensive study over m a n y years [3,33]. As with the organic reactions discussed earlier, a particular point of interest has been location of the reaction site in order to develop a rational kinetic model of these systems. Early work produced conflicting results. Perez de Ortiz, Flett and Cox [110] reviewed the early work and pointed out that the discrepancies were due to the neglect of m a s s transfer contributions in the data treatment and development of the chemical reaction m e c h a n i s m s . A c o m m o n assumption [111] was that diffusional resistances could be completely eliminated by using a high intensity mixer e.g. the Morton reactor [112]. F r o m the foregoing theory it should be evident that this need not be so: although for a reaction which occurs in one or other bulk phase the mass transfer c o m p o n e n t can be eliminated by intense mixing, this cannot be the case for a reaction which occurs in the film or at the interface, since the film resistance cannot be eliminated. Osseo-Asare has recently [113] provided a thoughtful critique of the criteria necessary to establish the site of the rate determining step in the extraction of metal ions by organic ligands. H e properly pointed out the necessity for obtaining, for the organic ligand, adsorption isotherms over the full concentration range up to surface saturation, as well as distribution coefficients, in order to avoid ambiguity in the interpretation of results.

250

7.3. T h e r o t a t i n g diffusion cell This apparatus, which was invented by Albery [16], has been widely used to study interphase m a s s transfer, but to date there are only three published studies of its application to reacting systems [33,114,115a]. Figure 4 3 shows the equipment.

A - Rotating cell Β — Porous membrane C - Cylindrical baffle D — Outer compartment I-

Inner compartment

0 — Outer compartment

Figure 4 3 . T h e rotating diffusion cell. T h e entire cell, including the cylindrical baffle, can be rotated in the outer fluid. Contact between the fluids in the inner and outer compartments is normally m a d e at the outer face of the porous m e m b r a n e at the base of the rotating cell. It has been shown [16] that proper hydrodynamics are obtained on both sides of the m e m b r a n e . T h e basic principle of the technique is simple and is similar to that of the rotated disk: reaction rates are measured at various rotation speeds, and the rates are extrapolated to zero diffusion layer thickness using the same Koutecky-Levich plot. In this case the intercept value is c o m p o s e d of any interfacial resistance together with the m e m b r a n e resistance, which is usually calculated [16] but can be measured [116]. Figure 4 4 illustrates this.

membrane

reaction

Figure 44. Schematic of the Koutecky-Levich plot for the rotating diffusion cell.

251

M u c h early w o r k using this cell w a s concerned with determining w h e t h e r or not there is any interfacial resistance to the physical transport of simple organic solutes from water to organic solvents and vice-versa. T h e r e h a s been s o m e controversy concerning this work. Leahy [116] h a s demonstrated that great care is needed to ensure that the accuracy and precision of m e a s u r e m e n t is sufficient to permit meaningful extrapolation A triumph of this technique has been its use to elucidate the m e c h a n i s m of the extraction of cupric ion from water using an oxime e x t r a d a n t (Figure 4 ) [ 3 3 ] . A m o d e l based on interfacial reactions w a s developed, tested against the experimental results, and c o m p a r e d with alternative m o d e l s involving reactions in a reaction layer. T h e m o d e l used is shown in Figure 4 5 . concentration

c

I

organic

2HL

interface

vs

HL

^

ν , ^

HL

k

aqueous

Cu

2 +

Cu

concentration

CuL

HL

v.

CuL

C

k

-1

2 +

H

-

U

L

2

^1T7

v

2

s

2

2H

+

+

2H

+

h

m

Figure 4 5 . Reaction m e c h a n i s m for cupric ion extraction process. Steady state treatment of this model led, after the elimination of s o m e terms shown to be experimentally insignificant, to the expression

1

1

ι

ml

km

kl

x

2

ι

1

(73)

k

3

w h e r e K = ^ / k T h e experimental results were extrapolated where appropriate to the true surface rate using a Koutecky-Levich plot, and the individual kinetic and adsorption parameters were obtained by assessing the effect of p H and Cu**, ligand and product concentrations on the overall rate. B y varying the conditions different terms could be m a d e rate controlling and thus the individual values for k „ k . j , k , k , and K were determined. U n d e r extraction conditions k and k_ were shown to be insignificant. t

P

2

2

3

0

3

Alternative m o d e l s involving reaction in the bulk aqueous phase or in a thin layer on the aqueous side of the interface did not fit the data and gave calculated fluxes, based on a measured h o m o g e n e o u s rate constant for the reaction of cupric ion with the ligand of 1 0 c m mol" s" and a m e a s u r e d distribution coefficient for the ligand of 10 , which were too low by several orders of magnitude. T h u s the conclusion that the reaction site is the interface is secure by a large margin. 7

3

1

1

4

252

A similar treatment w a s used to determine the kinetic parameters for the stripping of C u ^ from the ligand, a process which occurs at low p H . T h e authors pointed out the usefulness of the reciprocal form used in equation (73). Each term can be identified with a possible rate limiting step, so that the effect of concentration changes on each step can be more easily seen. This is a powerful technique for the elucidation of reaction m e c h a n i s m s in two-phase liquid-liquid systems, but in this context has been little used outside the Imperial College group where the technique originated. 7.4. Overview: liquid-liquid systems. In this area of chemistry the subject is still in its infancy. There are no c o m m o n l y agreed standards for experimental work, with many workers making tentative ventures into the field. This is not to decry any individual contributions. Kinetics in heterogeneous systems are more difficult to study than their h o m o g e n e o u s counterparts, because there are m o r e variables in the system. An aspect of chemistry in two-phase systems which fascinates chemists w h o enter the area is the possibility of identifying truly interfacial reactions. T h e first problem is to define what is m e a n t by an interfacial reaction. Several times throughout this review it has been noted that workers have effectively defined an interfacial reaction as one which has a linear dependence on interfacial area. This is an inadequate and imprecise definition, because it fails to distinguish between an interfacial reaction and a reaction which occurs in a thin reaction layer. Albery [115b] has provided a clear exposition of the difference between the two cases in the context of the copper extraction process described earlier. I cannot improve on his words so I will reproduce them here: "The distinction is real, and will lead to different rate laws for the variation of the observed rate with the concentration of aqueous reactant. For an interfacial reaction the transition state must be located within a few angstroms of the surface. T h e reactants are partly solvated by both solvents. For the reaction layer, the transition states are entirely in the aqueous phase and are located all over the reaction layer. T h e thickness of this layer can be as large as 10" cm. Its thickness, 6, is determined by the balance between the diffusion of the oxime and the rate of its reaction with C u : 2

2+

δ =

D

(74)

2+

T h e thickness of the reaction layer thus varies with [ C u ] , and this is why a different rate law will be observed. For very fast reactions the thickness δ can approach molecular dimensions of 2 angstroms or so; under these conditions the distinction between the reaction layer and the interface b e c o m e s blurred. However, such a thin reaction layer requires k [ C u ] to be as large as 1 0 s" . Such a large value can only be found if the reaction is diffusion controlled and the concentration of C u is larger 2+

11

1

2

2 +

253

than 1 M . T h e s e conditions are not found for our system. Hence in our system (and m o s t similar systems) the reaction layer would have to be at least several p m thick and the distinction between the interfacial reaction and the reaction layer is a real one. T h e diffuseness of the liquid-liquid interface can only extend over a matter of angstroms and therefore cannot really affect the distinction between the interfacial reaction (angstrom) and the reaction layer (>pm). W e d o not claim that an interfacial reaction takes place in a simple unimolecular layer. T h e reorganisation of the solvents m u s t extend through several layers, but the reaction zone is nevertheless much smaller than 1 pm." In m a n y cases statements as to the locus of a reaction are m a d e on the basis of inadequate data. A single supporting piece of evidence is not good enough. Consideration should be given to m e a s u r e m e n t of: * * * * *

partition coefficients h o m o g e n e o u s reaction rates reaction rates as a function of interfacial area m a s s transfer rates with and without reaction, over the same concentration range as: adsorption isotherms for reactants and products

It m a y also be useful, as w a s done by M e n g e r [98] and later suggested by Robinson [117] in another context, to change the distribution coefficient (P) by modifying the hydrophobicity of a reactant at a site away from the reactive centre. This should alter the rate of a reaction in a thin layer by an amount inversely proportional to the change in P, but have lesser effect on an interfacial reaction. T h e best single piece of evidence for an interfacial reaction is the demonstration that the reaction layer model cannot give a rate high enough to explain the measured heterogeneous rate. Albery succeeded in doing this for the copper extraction process, but there are no other firm examples for liquid-liquid reactions. Next c o m e s the demonstration that the reaction rate follows the independently measured adsorption isotherm for the reactant, as w a s done by Bell [92] and, albeit in a system of unknown interfacial area, by M e n g e r [98]. Albery and Choudhery [85] have shown h o w the locus of a reaction is dependent on the relative reaction rates at the surface and in h o m o g e n e o u s solution, the distribution coefficient, and the interfacial area per unit volume. T h e y pointed out that the site of reaction can change simply as a result of the change in interfacial area per unit v o l u m e , and cautioned against assuming that a m e c h a n i s m identified as dominant under one set of conditions is generally applicable. T h e recent studies of catalytic two-phase reactions by Lasek and M a k o s z a amplify this point [118]. A n u m b e r of techniques have been described recently which help to throw more light on the nature of processes close to interfaces. E S C A (electron scanning for chemical analysis) has been used to characterise the equilibrium distribution of quaternary a m m o n i u m salts at the air-water interface [119]. N M R has been used to study the concentration of a solute being

254

transferred across a liquid-liquid interface [120], but the time resolution used (tens of minutes) m e a n s that, if it w a s desired to apply this technique to reacting systems, only very slow chemical reactions could be studied. Measurements of dynamic surface tension and highfrequency surface elastic modulus have been used to show that the adsorption of two nonionic surfactants is controlled by the rate of diffusion to the surface [121]. F T I R - A T R has been used to probe the structure and reactivity of thin films [122]. 8. GAS-LIQUID R E A C T I O N S M u c h of the theory necessary for the understanding of coupled mass transfer and chemical reaction was developed within the chemical engineering c o m m u n i t y because of the need to understand quantitatively gas absorption processes. Experimental techniques were developed to a high standard during the 20 years from 1950, and have not significantly advanced since D a n c k w e r t s ' classic monograph of 1970 [22]. A great deal of the work in this area is connected with the practical aspects of gas absorption in different items of industrial equipment and will not be discussed here. However, s o m e elegant techniques were developed for quantitative study of the kinetics of gas-liquid reactions. T w o which appear to have stood the test of time are the constant interfacial area cell [123] and the laminar jet. T h e constant interfacial area cell has been described earlier in the context of liquid-liquid reactions, and the principles involved are the same for gas-liquid reactions. In the l a m i n a r j e t apparatus a short jet of liquid passes through a gas and is collected in an exit tube slightly larger than the jet. T h e jet flows in an atmosphere of the p u r e gas whose absorption characteristics are to be studied. Typically the jet diameter is 1 m m and the jet length is 5 to 7 0 m m . Jet velocities in the range 1 - 10 m s" are employed, and contact times are in the region 1 - 2 0 m s . Under these conditions the absorbing gas penetrates only a very small distance into the liquid and hence the kinetics simplify to those of diffusion into an infinite fluid. An exemplary paper by M a n o g u e and Pigford [124] reports the measurement of the absorption kinetics of phosgene into both water and aqueous sodium hydroxide. 1

For pure physical absorption equation (5) obtained by Higbee can be used (124) to obtain the expression q = ïc^yjDvh

l

75

mol s~

() 1

where q is the absorption rate (mol s" ) c is the saturation concentration of the gas in the liquid ν is the volumetric flow rate of the liquid jet h is the length of the jet. sat

S o m e small corrections for end effects are required. A typical plot of absorption rate q vs (h)^ is shown in Figure 46.

255

Ο

10

20

h /2/ 1

c m

30

V2

Figure 4 6 . Plot of absorption rate q vs square root of the jet length for the absorption of p h o s g e n e into water at 15°C [124]. At the lower temperatures investigated, chemical reaction was too slow to influence the absorption rate, so by using the calculated value of the diffusion coefficient of p h o s g e n e its solubility was calculated from the slope of the above plot. At higher temperatures chemical reaction b e c a m e significant and estimates of the rate constant for the solvolysis were obtained using an expression modified to include chemical reaction. Values for the solubility of p h o s g e n e in water and the first-order rate constant for its hydrolysis are shown in Table 7. This technique thus permits measurement of solubility for a species with a half life around 100 msec! This is a remarkable achievement derived from a combination of expertise in theoretical aspects of m a s s transfer with chemical reaction, together with practical skills in equipment design and operation. Table 7. Solubility of phosgene in water and the first-order rate constant for solvolysis, obtained from the laminar jet experiment. Temp./°C

solubility/M

15 25 35 45.5

0.109 0.069 0.046 0.027

1

k /s" . r

3* 6* 22 75

* extrapolated from the results obtained at the higher temperatures. Taken from reference 124.

256

Absorption of p h o s g e n e into aqueous sodium hydroxide was studied under first-order conditions using the same equipment. At the exposure times used in the shorter jets the sodium hydroxide concentration was not significantly depleted in the j e t and so the absorption rate is given by equation (43) derived earlier, where k = k [OH"]. A second order rate constant k = 1.6 χ 10 M" s" w a s obtained at 25°C. T h e precision of the derived rate constants is not high, but the reasons for this are not entirely clear. Nonetheless this technique provides data probably to better than ± 2 0 % which would be very difficult to acquire by other m e a n s . 2

4

1

1

2

9. C O N C L U S I O N S T h e study of organic reaction m e c h a n i s m s in two-phase systems is still in its infancy. In m a n y cases the site of reaction is u n k n o w n , and in difficult cases resolution of this question alone can require a major effort, particularly in liquid-liquid systems. T h e level of sophistication to which mechanistic questions can be addressed is limited by the lack of precision of measurement, which is probably an order of magnitude less than that achievable in h o m o g e n e o u s systems. W i d e r application of the more advanced techniques described in this review to the study of organic reaction mechanisms is desirable. A fascinating area of chemistry is awaiting exploration! References 1. F.J.W. Roughton in 'Progress in Biophysics and Biophysical Chemistry,' Pergamon, 1959, ed. J.A.V. Butler and B . Katz, p . 55-104, 2. R.N. A d a m s , Electrochemistry at Solid Electrodes, Marcel Dekker, N e w York, 1969. 3. T.C. L o , M.H.I. Baird and C. Hanson, Handbook of Solvent Extraction, John Wiley & Sons, 1983. 4. T h e theory of coloration of textiles, 2nd ed., edited by A. Johnson, p u b . Society of Dyers and Colourists (1989). 5. L.K. Doraiswamy and M . M . Sharma, Heterogeneous Reactions, vol.2, John Wiley, 1984. 6. J.W.E. Coenen, J. A m . Oil C h e m i s t s ' S o c , 53 (1976) 382. 7. W . P . M . van Swaaij and G.F. Versteeg, Chem. Eng. Sci., 47 (1992) 3181 8. Frank E. Paulik, Catalysis Reviews, 6 (1972) 49 9. During the period 1975 to M a y 1993 there are 75 patents cited in the ' D e r w e n t ' index which refer to phase transfer catalysis. 10. Industrial and Laboratory Nitrations, A C S S y m p o s i u m Series No. 22, American Chemical Society, Washington D C , 1976. 11. H . M . Walborsky, Acc. C h e m . Res., 23 (1990) 286. 12. L. Dolby-Glover, Chem. and Ind., 1986, 518. 13.T. G r a h a m , Philosophical Transactions of the Royal Society of London, 140 (1850) 1. 14. A. Fick, Philosophical Magazine, 10 (1855) 30. 15. W . Nernst, Z. Physik. Chem., 47 (1904) 52. 16. W.J. Albery, J.F. Burke, E.B. Leffler and J. Hadgraft, J . C h e m . S o c , Faraday Trans. I, 7 2 (1976) 1618. 17. R. Higbee, Trans. Amer. Inst. C h e m . Engrs., 31 (1935) 365. 18. P.V. Danckwerts, Ind. Eng. Chem., 4 3 (1951) 1460.

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