Temperature dependences of limiting activity coefficients and Henry's law constants for N-methylpyrrolidone, pyridine, and piperidine in water

Fluid Phase Equilibria 282 (2009) 100–107

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Temperature dependences of limiting activity coefficients and Henry’s law constants for N-methylpyrrolidone, pyridine, and piperidine in water Milan Bernauer, Vladimír Dohnal ∗ Department of Physical Chemistry, Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republic

a r t i c l e

i n f o

Article history: Received 27 February 2009 Received in revised form 30 April 2009 Accepted 6 May 2009 Available online 14 May 2009 Keywords: Limiting activity coefficient Henry’s law constant Temperature dependence N-methylpyrrolidone Pyridine Piperidine

a b s t r a c t Limiting activity coefficients (1∞ ) of N-methylpyrrolidone (NMP), pyridine, and piperidine in water were measured at several temperatures in the range from 333 K to 373 K. Three experimental techniques, namely Rayleigh distillation, differential distillation, and the method of circulation still, were employed for the purpose. A comprehensive review is further presented of experimental data on the limiting activ¯ E,∞ ), and heat capacities (C¯ E,∞ ) of ity coefficients 1∞ , infinite dilution partial molar excess enthalpies (H 1 p,1 these aqueous solutes. Additionally, to verify fragmentary literature information, solution heat capacity for NMP was also determined in this work using Picker flow microcalorimeter. For each solute, the compiled data were critically evaluated and together with the data measured in this work correlated with a suitable model equation providing adequate simultaneous description of the equilibrium measurements and the calorimetric information. As a result, a recommended thermodynamically consistent temperature dependence of 1∞ was established in the range from the melting point to the normal boiling point of water. Analogous recommendations were derived also for the temperature dependence of the Henry’s law constants (kH ). © 2009 Elsevier B.V. All rights reserved.

1. Introduction This work is a part of our systematic study on gas–liquid partitioning and limiting activity coefficients of aqueous organic compounds containing nitrogen. Recently, we have presented results for the temperature dependence of limiting activity coefficients (1∞ ) and Henry’s law constants (kH ) of aniline, nitrobenzene, and cyclohexylamine [1] and of N-methylated (C1 and C2) fatty acid amides [2]. As a continuation, we focus here further on three nitrogen heterocyclic compounds N-methylpyrrolidone (NMP), pyridine, and piperidine. These substances belong to large-scale production chemicals with many industrial applications, serving in particular as extraction solvents, reaction media, and precursors to agrochemicals, pharmaceuticals, rubber chemicals and dyes. In their production and use, these substances often interact with water, which makes the thermodynamic characterization of their aqueous dissolution and/or hydration of essential importance. Accurate data on respective infinite dilution properties are needed also for the improvement of predictive schemes and for development and testing of solution theories. For the three solutes examined, we carried out specialized gas–liquid partitioning measurements by suitable techniques in

∗ Corresponding author. Tel.: +420 2 2044 4297; fax: +420 2 2044 4333. E-mail address: [email protected] (V. Dohnal). 0378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2009.05.005

the range of temperatures from 333 K to 373 K. Combining the present data and other relevant 1∞ measurements from the literature with existing calorimetric data on respective derivative thermal properties and correlating them simultaneously by a suitable model equation we establish recommended thermodynamically consistent temperature dependences of 1∞ and kH which can be considered to be truly reliable in a broader temperature range from 273 K to 373 K. 2. Experimental 2.1. Materials N-methylpyrrolidone (puriss, 99%), pyridine (99.9%), and piperidine (99.9%), used as solutes were all obtained from Sigma–Aldrich. Their declared purity was verified by gas chromatography using a DB-5 capillary column. Before the measurements, they were dried with 4 Å molecular sieves and stored in the dark. Water used as the solvent was distilled and subsequently treated by a Milli-Q Water Purification System (Millipore, USA). 2.2. Apparatus and procedure To determine the limiting activity coefficients, three experimental techniques were employed in this work: Rayleigh distillation (RDIST), differential distillation (DDIST), and the method of the cir-

M. Bernauer, V. Dohnal / Fluid Phase Equilibria 282 (2009) 100–107

culation still (CIRC). While the RDIST and CIRC are well-established and extensively used techniques in our laboratory [3–6], the DDIST method has been implemented by us only recently [2]. The three methods were used alternatively to cope well with different volatility conditions of systems studied. In general, the CIRC method was used at temperatures from 343 K to 373 K where the sufficiently high water vapor pressure ensures uncompromised performance of the Cottrell pump. The RDIST and DDIST methods were then applied in the temperature range from 333 K to 353 K, the temperature interval being delimited at the lower end by the acceptability of the duration of the experiments and at the upper end by feasibility of the water thermostatization. Each method has been described previously; given below is thus only their brief outline supplemented by some details specific to the present application. In the treatment of all VLE data the vapor phase was considered as an ideal gas, since our estimations showed vapor phase nonideality corrections to be negligible compared to experimental uncertainties. 2.3. Rayleigh distillation (RDIST) method The RDIST technique is based on measuring the changes of the solution mass and the solute concentration resulting from a partial one-stage equilibrium distillation of a highly dilute solution (x1 < 10−3 ) which is accomplished by passing a slow stream of an inert gas (nitrogen) through the thermostated solution under study. From the RDIST measurement, 1∞ is calculated by the following equation: 1∞ =

ps2 ps1



1+

ln(A1 /A01 )



ln(m/m0 )

(1)

where m0 and m are the masses of the solution before and after the distillation, A01 and A1 are the proportional analytical responses to the solute concentrations in the original solution and in the remainder, and psi are the pure component vapor pressures. With the nitrogen flow rates set between 4 and 12 mL/min and the extent of distillation chosen according to the error analysis [6] to minimize the effect of analytical errors, the distillation experiments for the present systems took from 10 to 25 h, depending on the system and temperature. Samples of the original solution and of the distillation remainder were analyzed in this work either by UV spectroscopy (for pyridine) or by gas chromatography (for piperidine). The spectroscopic analyses were carried out with a Varian spectrophotometer, Model Cary 50 Bio. The UV absorbances were determined at the maximum absorbance wavelength (252 nm), in the differential mode against pure water using closed quartz cells of 10 mm optical length. The GC analyses were performed using an Agilent 6890 Plus gas chromatograph and a 0.5-m-long stainless steel 1/8 o.d. column packed with Carbopack B coated with 4% Carbowax 20 M and 0.8% KOH from Supelco. Samples were dosed by an Agilent 7683 automatic sampler, typically with 12 replicates each.

In this method, a VLE circulation still operated at constant pressure is employed to provide samples of the vapor and liquid in equilibrium in the region of high dilution, no measurement of temperature being needed as the boiling temperature of the solution is effectively the same as that of the neat solvent water. Provided the samples are analyzed by a method responding proportionally to the solute concentration, the value of 1∞ is obtained from 1∞ =

ps2 ps1

AG 1 AL1

and AL1 are the responses for the samples of equilibwhere AG 1 rium vapor phase condensate and the corresponding liquid phase, respectively. Due to their rather poor boiling characteristics, the aqueous solutions studied were boiled for extended periods of time 24–30 h, to ensure the generation of truly representative equilibrium samples. UV spectrophotometry for pyridine and gas chromatography for NMP and piperidine were used to analyze the obtained samples. The mole fractions of the solutions ranged from 10−5 to 10−4 for the UV and from 10−4 to 10−3 for the GC analysis. The analyses were carried out in the same manner as in the case of the RDIST method. 2.5. Differential distillation (DDIST) method This technique is based on one-stage equilibrium flask-to-flask distillation in the course of which just a relatively small amount is distilled off from a batch of a highly dilute solution under study so that its composition remains effectively unchanged. In our implementation of DDIST, the stripping by an inert gas at isothermal conditions was used instead of heating to conduct the distillation as an equilibrium process. The distillation took typically 12 h. Samples of the collected distillate and the batch solution were analyzed by gas chromatography as in the case of the CIRC method. Since the GC response is proportional to the solute concentration, the ratio of the responses for the distillate and the batch solution, AG /AL1 , deter1 ∞ mines 1 exactly in the same way as in the case of the CIRC method (Eq. (2)). 2.6. Correction for solute hydrolysis Pyridine and piperidine are bases that in aqueous solutions partially hydrolyze according to B + H2 O  BH+ + OH−

(2)

(3)

which may appreciably affect thermodynamic behavior that these solutions exhibit at high dilutions. Hence, to treat properly the observed behavior of these solutions and, in particular, to evaluate true thermodynamic parameters corresponding to the neutral solute species, it is necessary to take into account the effect of the hydrolysis reaction. The equilibrium constants of solute hydrolysis Kb needed to establish the respective corrections can be obtained from more conventional dissociation constants Ka of respective protonated species and the ionic product of water Kw (Kb = Kw /Ka ). Values of these equilibrium constants at 298.15 K, together with the standard dissociation enthalpies are listed in Table 1. Calculations based on this data indicate that while for pyridine the degree of hydrolysis at conditions of our experiments is very small and the effect on the properties observed can be neglected, for piperidine, which is a much stronger base, the degree of hydrolysis is appreciable (from 0.13 to 0.15) and careful corrections are required. They were done as follows. The degree of hydrolysis  for a given total solute molality b1 was calculated from K =− + 2

2.4. Circulation still method (CIRC)

101



K2 +K 4

1/2

(4)

Table 1 Equilibrium constants pKb for the hydrolysis of pyridine and piperidine and the equi◦ librium constants pKa and standard enthalpy Ha changes for the dissociation of corresponding protonized species at 298.15 K.

Pyridine Piperidine

◦

−1

pKb a

pKa

Ha /kJ mol

Ref.

8.79 2.88

5.21 11.123

20.08 52.96

[7] [8]

a pKb = pKw − pKa ; (Ref. [9]).

pKw = −408.174 + 15141.68/T − 0.09835T + 70.32965 ln T

102

M. Bernauer, V. Dohnal / Fluid Phase Equilibria 282 (2009) 100–107

where K = Kb /(b1 ±2 ) and  ± is the mean activity coefficient estimated from the Debye–Hückel equation. Considering that it is only the neutral species which undergoes the vapor–liquid partitioning, the following formula: 1∞

=

ps2

AG 1

ps1 AL (1 − ) 1

T/K

(5)

accounting for piperidine hydrolysis was used to calculate 1∞ from the CIRC measurements. Note that in contrast to Eq. (2), the application of Eq. (5) requires the composition of the equilibrium liquid phase to be known absolutely. For RDIST method, the evaluation of 1∞ accounting for piperidine hydrolysis was more complicated. The following equation [1]: ln

m − m0



b1

b0 1

db1 =0 b1 [˛∞ (1 − ) − 1] 12

Table 2 Experimental limiting activity coefficients 1∞ (this work and literature) for Nmethylpyrrolidone (NMP), pyridine, and piperidine in water along with their estimated uncertainties srel (1∞ )a and the method of measurement.

(6)

where b01 is the total solute molality in the original solution and b1 that in the remainder, was to be solved for the limiting relative volatility (˛∞ = 1∞ ps1 /ps2 ) iteratively with the involved integral 12 being evaluated numerically by the Simpson method. The first approximation of 1∞ for the iterative procedure was conveniently obtained from Eq. (1). 2.7. Calorimetry Reasonably accurate data on infinite dilution thermal properties for the aqueous solutes studied are available in the literature. Thus, the only calorimetric determination performed in this work was the heat capacity measurement for aqueous NMP to check an unpublished result of Cabani et al. for the NMP hydration heat capacity given in their database of hydration properties [10]. The heat capacities of dilute NMP solutions were determined at 298.15 K using a Picker differential flow microcalorimeter (SETARAM, France). The principle of the measurement and the procedure have been thoroughly described in the literature [11]. The measurements were carried out in duplicate for a series of six dilute solutions with the solute concentration varying in the range from 0.015 to 0.3 mol kg−1 . The limiting partial molar heat ∞ (=307 J K−1 mol−1 ) was obtained by linear extrapolacapacity C¯ p,1 tion of the apparent quantity to infinite dilution. The partial molar E,∞ excess heat capacity C¯ p,1 was then derived by subtracting the molar heat capacity of the pure solute.

NMP 333.15 343.15 353.15 372.85 298.80 308.40 318.00 328.40 337.90 351.01 380.24

1∞ 1.34 1.56 1.75 2.07 0.37 0.60 0.86 1.13 1.39 1.59 2.05

srel (1∞ )

Methodb

Ref.

0.03 0.03 0.03 0.05 0.2 0.2 0.2 0.1 0.2 0.05 0.05

DDIST DDIST DDIST CIRC DEWT DEWT DEWT DEWT DEWT TENS TENS

This work This work This work This work [12] [12] [12] [12] [12] [13] [13]

Pyridine 333.15 343.15 353.15 372.80 343.15 358.15 373.15 298.15 313.15 343.01 362.98 298.15 298 298.15 343.15 363.15 373.15 298.15 356.32 362.06 366.87 353.15

24.0 25.5 26.0 25.4 22.9 24.2 23.7 17.9 21.2 22.6 23.7 16.9 17.5 16.2 24.3 19.8 16.8 22.5 23.4 20.7 19.7 25.6

0.05 0.03 0.03 0.03 0.1 0.05 0.05 0.05 0.05 0.1 0.05 0.1 0.05 0.05 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.05

RDIST CIRC CIRC CIRC CIRC CIRC CIRC TRANS TRANS CIRC CIRC TRANS GLC GLC EBU EBU EBU GLC EBU EBU EBU EBU

This work This work This work This work [14] [14] [14] [15] [15] [16] [16] [17] [18] [19] [20] [20] [20] [21] [22] [22] [22] [23]

Piperidine 333.15 343.15 353.15 372.60 298.15 343.15 363.15 373.15

11.9 14.7 17.7 21.0 6.20 6.54 6.80 7.15

0.05 0.03 0.05 0.05 0.2 0.5 0.5 0.5

RDIST RDIST RDIST CIRC TENS EBU EBU EBU

This work This work This work This work [8] [20] [20] [20]

a

3. Results and discussion

Relative standard deviation. CIRC, circulation still; DEWT, dew temperature measurement; DDIST, differential distillation; EBU, comparative ebulliometry; GLC, gas–liquid chromatography; RDIST, Rayleigh distillation; TENS, tensimetry; TRANS, transpiration method.

The limiting activity coefficients determined in this work for NMP, pyridine, and piperidine in water are listed, along with results gathered from the literature, in Table 2. The uncertainties given (relative combined standard uncertainties srel (1∞ )) take into account all possible sources of error. We estimated these uncertainties in a consistent manner so that within their limits the statistical coher¯ E,∞ , and C¯ E,∞ for a given ence of all existing information on 1∞ , H 1 p,1 system was achieved. The 1∞ data are displayed in van’t Hoff coordinates in Figs. 1–3. Mutual comparison of these values based on their thermodynamically consistent fit with related thermal data will be discussed below. The saturated vapor pressures of pure solutes used in our calculations are given in Table 3. We selected these vapor pressure equations amongst other vapor pressure data and their representations available in the literature as the most reliable ones for the temperature range considered here. For piperidine, no suitable vapor pressure equation could be found in the literature; therefore it was obtained in this work by fitting the Wagner equation simultaneously to vapor pressure data of different authors. For pyri-

dine and piperidine these vapor pressure equations were proved to be consistent with independent calorimetric measurements of vaporization enthalpy, for NMP however this consistency check was not possible because the calorimetric information needed is not available. The equations from Table 3 are further compared to existing vapor pressure data in Figs. 4–6. As seen, their performance is quite good, even at subambient temperatures where the vapor pressures, in particular for NMP, are very low. Figs. 4–6 also give some idea about the level of uncertainty one should allow in the vapor pressure of the compounds studied, e.g. for NMP at subambient temperatures one should count with an uncertainty of at least 3%. Data on limiting partial molar excess enthalpies, which we collected from the literature, are listed in Table 4. Analogous collection for limiting partial molar excess heat capacities, involving also the result of our own measurement for NMP, is given in Table 5. As seen from these tables most calorimetric information refers to the ambi¯ E,∞ for pyridine in water ent temperature, the determination of H 1 receiving the greatest attention (seven literature sources). The tem-

b

M. Bernauer, V. Dohnal / Fluid Phase Equilibria 282 (2009) 100–107

103

Table 3 Constants of vapor pressure equations of pure solutesa . Solute NMP Pyridine Piperidine a b c d e f

Equation d

Riedel–Planck Wagnere Wagnerf

A

B

C

D

E

Rangeb

TNBP /Kc

Ref.

61.568 −6.82447 −8.07628

−8467.9 0.47569 3.98133

−6.3622 0.02974 −4.73013

3.2235E−18 −4.19797 −2.93838

6.0

249–722 310–426 283–417

477.14 388.36 379.32

[24] [25] This work

Vapor pressures of solvent water were obtained from equation given by Wagner and Pruss [26]. K. Normal boiling temperature. ln(ps /kPa) = A + B/T + C ln T + DTE . ln(ps /pc ) = (Tc /T)(AF + BF1.5 + CF1.5 + CF2 + DF4 ); F = 1 − T/Tc ; Tc = 620 K; Tc = 620 K; pc = 5650 kPa. ln(ps /pc ) = (Tc /T)(AF + BF1.5 + CF2.5 + DF5 ); F = 1 − T/Tc ; Tc = 594 K; pc = 4650 kPa.

Fig. 1. Limiting activity coefficient ln 1∞ of NMP (1) in water (2) as a function of temperature. Experimental values are from Table 2: , Trampe and Eckert [12]; , Noll et al. [13]; 䊉, this work (DDIST); , this work (CIRC). The solid line indicates the ¯ E,∞ , recommended temperature dependence obtained by simultaneous fit of 1∞ , H 1 E,∞ ¯ and C and data by Eq. (7). p,1

E,∞ perature dependence of C¯ p,1 studied for aqueous piperidine proved to be non-monotonous and relatively weak compared to experiE,∞ mental errors. Therefore, C¯ p,1 (T ) was not explicitly considered in our data treatment (see Eq. (7)).

Fig. 2. Limiting activity coefficient ln 1∞ of pyridine (1) in water (2) as a function of temperature. Experimental values are from Table 2: , Andon et al. [14]; , Andon et al. [15]; , Andon et al. [16]; , Bjerrum [17]; ♦, Pemberton and Mash [18]; , Mash , Moore and Pemberton [19]; , Lobien and Prausnitz [20]; Φ, Yaws et al. [21]; et al. [22]; ×, Gierycz [23]; , this work (RDIST); , this work (CIRC). The solid line indicates the recommended temperature dependence obtained by simultaneous fit ¯ E,∞ , and C¯ E,∞ data by Eq. (7). of 1∞ , H 1 p,1

Fig. 3. Limiting activity coefficient ln 1∞ of piperidine (1) in water (2) as a function of temperature. Experimental values are from Table 2: , Cabani et al. [8]; , Lobien and Prausnitz [20]; , this work (RDIST); , this work (CIRC). The solid line indicates ¯ E,∞ the recommended temperature dependence obtained by simultaneous fit of  ∞ H E,∞ and C¯ p,1 data by Eq. (7).

1

1

For each of the systems studied, the thermodynamic information gathered above was processed by a simultaneous correlation to establish reliable temperature dependence of 1∞ . The following equation was used for representing the temperature dependence

Fig. 4. Comparison of the selected vapor pressure equation for NMP (Table 3) to experimental data: , Aim [27]; , Linek et al. [28]; , Kneisl and Zondlo [29]; , Palczewska-Tulinska and Oraz [30]; ♦, Gierycz et al. [31]; , Fulem [32].

104

M. Bernauer, V. Dohnal / Fluid Phase Equilibria 282 (2009) 100–107 Table 4 ¯ E,∞ (literature) for NExperimental limiting partial molar excess enthalpies H 1 methylpyrrolidone (NMP), pyridine, and piperidine in water along with their E,∞ a ¯ ) . estimated uncertainties s(H 1

Fig. 5. Comparison of the selected vapor pressure equation for pyridine (Table 3) to experimental data: , Weclawski and Bylicki [33]; , Chan and van Hook [34]; , Chirico et al. [25]; ♦, McCullough et al. [35]; —, Das et al. [36].

B = A + + C ln  

(7)

¯ E,∞ )/kJ mol s(H 1

−1

Techniqueb

Ref.

NMP 298.15 296.15 298.15 298.15 308.15 318.15

−21.22 −21.13 −21.30 −21.30 −20.11 −18.73

0.3 0.3 0.2 0.07 0.06 0.04

FLOW BATCH FLOW FLOW FLOW FLOW

[40] [41] [42] [43] [43] [43]

Pyridine 298.15 298.15 298.15 296 300 300 307 307 298.15 298.15 298.15

−9.76 −9.59 −9.58 −9.73 −9.14 −9.19 −7.96 −8.16 −9.54 −9.71 −9.74

0.1 0.05 0.1 0.1 0.09 0.09 0.08 0.08 0.3 0.1 0.03

FLOW BATCH TITR TITR TITR TITR TITR TITR BATCH BATCH

[40] [8] [44] [45] [45] [45] [45] [45] [46] [47] [48]

−25.94 −26.14

0.4 0.03

FLOW BATCH

[40] [8]

a

Combined standard uncertainty. BATCH, batch dissolution calorimetry; FLOW, flow mixing calorimetry; TITR, titration calorimetry. b

giving ¯ E,∞ = RT0 (B − C) H 1

E,∞ and C¯ p,1 = −RC,

where A, B, and C are adjustable parameters,  = T/T0 and T0 = 298.15 K. All measured and literature data were treated together using the weighted least-squares method to evaluate the parameters of Eq. (7). In the objective function: S =

¯ E,∞ /kJ mol−1 H 1

Piperidine 298.15 298.15

of 1∞ : ln 1∞

T/K

nG ∞ (exp) − ln  ∞ (calc)]2  [ln 1,i 1,i i=1

∞) s2 (ln 1,i

2 nH ¯ E,∞ (exp) − H ¯ E,∞ (calc)]  [H 1,i 1,i

+

i=1

¯ E,∞ ) s2 (H 1,i

nC E,∞ E,∞  [C¯ p,1,i (exp) − C¯ p,1,i (calc)]

+

i=1

E,∞ s2 (C¯ p,1,i )

2

the data were weighted according to their uncertainties (standard deviations) which we assigned on the basis of our critical evaluation. All possible sources of error were considered and the contributions were combined according to the error propagation law. For literature data, the first estimates of the uncertainties were based on information given in the original source from which the data were extracted. When necessary, the uncertainties were readjusted by trail and error to obtain the coherence of all data in the statistical sense. The goodness-of-fit test (2 ) for the standard deviation of fit was used to indicate the coherence. Statistically reasonable sizes of individual residuals (checked by the t-test) and their distribution amongst the three properties were considered as additional constraints.

(8) Table 5 E,∞ (this work and literature) Values of limiting partial molar excess heat capacities C¯ p,1 of N-methylpyrrolidone (NMP), pyridine, and piperidine in water along with their E,∞ a ) . estimated uncertainties s(C¯ p,1 −1 E,∞ C¯ p,1 /J K−1 mol b

E,∞ s(C¯ p,1 )/J K−1 mol

Techniquec

Ref.

NMP 298.15 298.15

131 131d

1 3

FLOW Unknown

This work [10]

Pyridine 298.15

173

1

FLOW

[49]

Piperidine 293.15 313.15 333.15

247 238 244

9 9 9

ADIAB ADIAB ADIAB

[50] [50] [50]

T/K

a b

−1

Combined standard uncertainty. ∞ Calculated from partial molar heat capacity at infinite dilution (C¯ p,1 ) given in

L,• the cited source and molar heat capacity of pure liquid solute (Cp,1 ) taken from [51] (C¯ E,∞ = C¯ ∞ − C L,• ). p,1 c

d

Fig. 6. Comparison of the selected vapor pressure equation for piperidine (Table 3) to experimental data: , Osborn and Douslin [37]; , Blanco et al. [38]; , Cabani et al. [8]; —, Das et al. [36].

p,1

p,1

ADIAB, adiabatic calorimetry; FLOW, flow calorimetry. ∞ Calculated from hydration heat capacity (hyd Cp,1 ) given in the cited source and

L,• the pure solute heat capacities at the liquid state (Cp,1 ) and the ideal gas standard G,◦ E,∞ G,◦ L,• ∞ state (Cp,1 ), taken from [51,52], respectively (C¯ p,1 = hyd Cp,1 + Cp,1 − Cp,1 ).

M. Bernauer, V. Dohnal / Fluid Phase Equilibria 282 (2009) 100–107

105

Table 6 ¯ E,∞ and C¯ E,∞ data, number of respective underlying data points nG , nH , nC , standard deviation of fit s, and weighted Parameters of Eq. (7)a obtained by simultaneous fit of 1∞ , H p,1 1 root-mean-square deviations (WRMSD) of individual properties. Solute

A

N-methylpyrrolidone Pyridine Piperidine a b c

B

C

−24.3629 −24.6628 −39.6760

23.7865 27.5628 41.2590

nG /nH /nC

−15.7507 −20.7947 −29.1331

11/6/2 22/11/1 8/2/3

sb

WRMSDc

1.29 1.01 1.24

1∞

¯ E,∞ H 1

E,∞ C¯ p,1

1.41 0.91 1.35

0.88 1.14 0.36

0.04 0.16 0.45

Recommended temperature dependence for limiting activity coefficient (273–373 K). s = (Smin /n − p)1/2 ; S is given by Eq. (8), p is the number of adjustable parameters.



nY

WRMSD = (1/nY )

i=1

2

1/2

[Yi (exp) − Yi (calc)] /s2 (Yi )

¯ E,∞ , C¯ E,∞ . , Y = ln 1∞ , H 1 p,1

For each of the systems studied, the calculated parameters of Eq. (7) are given together with the standard deviation of fit, the number of underlying experimental data points, and the weighted root-mean-square deviations (WRMSDs) in the individual properties in Table 6. The recommended temperature dependences of 1∞ established by the fits are plotted in the van’t Hoff coordinates in Figs. 1–3. The probable data uncertainties are those listed in Tables 2, 4 and 5. Before discussing the 1∞ (T ) fits for individual solutes, we should point out that compared to the measurements of limiting activity coefficients, the calorimetric measurements are in general considerably less scattered and therefore they almost entirely determine the shape of the recommended 1∞ (T ) dependences. Thus, as more credit is placed in calorimetric information than in 1∞ (T ) measurements, if an inconsistency of 1∞ data with the calculated 1∞ (T ) shape is encountered, it indicates an error in the 1∞ data. For NMP in Fig. 1 the limiting activity coefficients measured in this work (DDIST and CIRC) and taken from literature are seen to follow the recommended line quite well except of those by Trampe and Eckert [12] at temperatures approaching ambient. The results of these authors are systematically lower than the fit and the disproportion gets bigger as the temperature decreases, a situation which might suggest that incorrect NMP ps1 values were used in the calculation of limiting activity coefficients. Note that the vapor pressures of NMP at ambient temperatures are very low and an extrapolation by a vapor pressure equation towards ambient temperatures can easily give progressively incorrect ps1 values. Although quite probable, this speculation can hardly be proved because Trampe and Eckert gave no information on vapor pressure data they used. For pyridine (Fig. 2) one can see also a very good mutual agreement between the present measurements carried out by RDIST and CIRC techniques as well as their reasonable accord with most existing literature data. Exceptions are the GLC value of Yaws et al. [21] which is an apparent outlier (too high) and the ebulliometric measurements of Lobien and Prausnitz [20] and Moore et al. [22] which exhibit an inconsistent temperature trend and diverge with increasing temperature to systematically lower values. Note that the ebulliometric method is well suited for systems having relative volatility close to unity, so for pyridine in water, exhibiting in the temperature range in question ˛∞ > 15, the measurement is 12 expected to be rather inaccurate. The recommended 1∞ (T ) depen¯ E,∞ , and dence obtained by simultaneous fit of all available  ∞ , H 1

Table 7 Parameters of Eq. (9)a . Solute

AH

BH

CH

N-methylpyrrolidone Pyridine Piperidine

48.9642 50.7195 65.8177

−52.6210 −46.7951 −62.8464

−21.9565 −26.6745 −36.3248

a

Recommended temperature dependence for Henry’s law constant (273–373 K).

not considered to be a suitable experimental technique here and the data were as unreliable essentially disregarded when establishing the recommendation for 1∞ (T ). Furthermore, in addition to the recommended temperature dependences of the limiting activity coefficients, analogous recommendations were derived for the temperature dependences of the Henry’s law constants kH (T), combining the 1∞ (T ) results from Table 6 with ps1 (T ) from Table 3 (kH = 1∞ ps1 ). In order to obtain an analytical expression for the temperature dependence of the Henry’s law constant, kH values were generated at 21 equidistant temperatures (5 K increment) covering the temperature range from 273.15 K to 373.15 K and fitted with the following equation: ln(kH /kPa) = AH +

BH + CH ln  

(9)

The calculated parameters of Eq. (9) are given in Table 7 and the respective temperature dependences of kH are plotted in the van’t Hoff coordinates in Fig. 7. NMP exhibits the lowest volatility from the dilute aqueous solutions being two to three orders of magnitude smaller than those for piperidine or pyridine. Piperidine is retained by water somewhat more than pyridine, but the difference with

1

E,∞ C¯ p,1 data shows a maximum at about 353 K and is seen to approximate well the temperature course of results from the present VLE measurements. For piperidine, the consistency within experimental errors of our equilibrium measurements with calorimetric information is demonstrated in Fig. 3. Only very few literature 1∞ values are available for this system. The result of Cabani et al. [8] at 298.15 K is seen to be in fair agreement with the recommended 1∞ (T ) line, but the ebulliometric measurements of Lobien and Prausnitz [20] are apparent outliers. Like for pyridine in water, ebulliometry was

Fig. 7. Henry’s law constants kH of NMP (––), pyridine (––), and piperidine (––) in water as a function of temperature.

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M. Bernauer, V. Dohnal / Fluid Phase Equilibria 282 (2009) 100–107

Table 8 Recommended values of limiting activity coefficients 1∞ and Henry’s law constants kH along with their relative standard uncertainties. T/K

1∞

srel (1∞ )

kH /kPa

srel (kH )

N-methylpyrrolidone 273.15 0.240 298.15 0.562 323.15 1.04 373.15 2.20

0.05 0.03 0.02 0.02

Pyridine 273.15 298.15 323.15 373.15

11.8 18.2 23.0 24.3

0.03 0.02 0.02 0.02

7.23 50.6 221 1550

0.03 0.02 0.02 0.02

Piperidine 273.15 298.15 323.15 373.15

1.65 4.87 10.05 20.5

0.05 0.03 0.02 0.02

1.49 19.5 135.5 1725

0.05 0.03 0.03 0.03

0.00143 0.0258 0.258 7.34

0.05 0.03 0.03 0.03

temperature diminishes and when approaching the normal boiling point of water the volatility of the two solutes from aqueous solution are very close. Recommended values of 1∞ and kH , along with their relative combined standard uncertainties calculated by the error propagation law, are given at several representative temperatures in Table 8. These uncertainties are typically within 2% or 3%, except for NMP and piperidine at subambient temperatures where one should expect the standard uncertainty as high as 5% due to the uncertainty of pure solute vapor pressure data. The heterocyclic nitrogen compounds studied in this work are efficient proton acceptors and the thermodynamic behavior of their aqueous solutions is greatly affected by hydrogen bonding with water. This complex formation has been proved by theoretical calculations and spectroscopic studies [53–56]. The complexation appears to be strongest for NMP which forms in dilute solutions with water complexes of 1:2 stoichiometry [57–59] and behaves as a quite hydrophilic solute. Amongst the three solutes studied here, NMP exhibits by far the lowest volatility from the aqueous solution, the lowest values of limiting activity coefficients, which at T < 323 K are even below unity, and the most exothermic hydration. Comparing the thermodynamic behavior for the other two solutes, one can see the complex formation for piperidine to be stronger than that for pyridine. The non-monotonous 1∞ (T ) course with a maximum around 353 K observed for pyridine is typical for semihydrophobic solutes. Note that it is only at higher temperatures where the thermodynamic properties of aqueous piperidine and pyridine converge as a consequence of the considerably diminished extent of hydrogen bonding. As a part of this work, the performance of two predictive approaches, namely the modified UNIFAC and the LFER correlation of Abraham [39], to estimate the limiting activity coefficients of the studied solutes was also examined. The leading group contribution method, modified UNIFAC (Dortmund), was applied with the latest parameter values published in the open literature (fourth [60] and fifth revision [61]) to predict 1∞ (T ) dependences. The results of the prediction are shown in the form of a deviation plot in Fig. 8. As concerns the Abraham LFER correlation, the calculated 1∞ (T ) dependence was obtained from that of the air–water partition coefficient Kaw (T ) constructed using the predicted values of air–water partition coefficient, hydration enthalpy, and hydration heat capacity at 298.15 K. Both forms, L and V, of the Abraham LFER correlation were applied, but results are given only for the L form because of its considerably better performance for the solutes studied. As seen from Fig. 8, the results of predictions for NMP and piperidine by the modified UNIFAC and for pyridine by the Abraham LFER

Fig. 8. Deviation ı ln 1∞ = ln 1∞ (predicted) − ln 1∞ (recommended) as a function of temperature for the modified UNIFAC (Dortmund); ––, NMP; ––, pyridine; ––, piperidine; and the LFER correlation (L) of Abraham [39]: ––, NMP; –䊉–, pyridine;– –, piperidine.

correlation are very good, being mostly within 10% of recommended 1∞ values. The deviations of the LFER prediction for NMP are of the same level at T > 333 K, but at lower temperatures the prediction systematically diverges. The slope of the deviation plot is an indication of incorrectly predicted hydration enthalpy. Completely unsatisfactory are seen the LFER prediction for piperidine and the prediction by the modified UNIFAC for pyridine which are both considerably in error. In the latter case the calculated values of 1∞ are lower than the recommended ones by even more than a factor of 2. 4. Conclusion Recommendations were established for the temperature dependences of limiting activity coefficients and Henry’s law constants of three heterocyclic nitrogen compounds, namely NMP, pyridine, and piperidine, in water. The temperature dependences reliable in the range from 273 K to 373 K are based on new measurements of limiting activity coefficients carried out in this work and other existing equilibrium and calorimetric data from literature which were all processed simultaneously by a thermodynamically consistent treatment. The results are of practical use for design and optimization of thermal separation processes and of theoretical interest for testing solution theories and improving prediction methods. List of symbols Ai analytical response to component i A, B, C parameters of Eq. (7) A, B, C, D, E parameters of vapor pressure equations in Table 3 AH , BH , CH parameters of Eq. (9) b molality ∞ hyd Cp,1 hydration heat capacity

CpG,,1◦ CpL ,, 1• C¯ ∞ p,1

E,∞ C¯ p,1

F Ha◦ ¯ E,∞ H 1

molar heat capacity of solute in the ideal gas standard state molar heat capacity of pure liquid solute partial molar heat capacity of solute at infinite dilution partial molar excess heat capacity of solute at infinite dilution dimensionless variable (F = 1 − T/Tc ) standard enthalpy of dissociation partial molar excess enthalpy of solute at infinite dilution

M. Bernauer, V. Dohnal / Fluid Phase Equilibria 282 (2009) 100–107

variable in Eq. (4) where K = Kb /(b1 ±2 ) equilibrium constant of solute dissociation equilibrium constant of solute hydrolysis equilibrium constant of water dissociation (ionic product of water) Kaw air–water partition coefficient Henry’s law constant kH m mass nG , nH , nC number of data in Eq. (8) pc critical pressure saturated vapor pressure ps R universal gas constant s(X) standard uncertainty of quantity X T temperature Tc critical temperature x molar fraction K Ka Kb Kw

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