The viscosity of mixtures of benzene and methanol

J. inorg,nucl.Chem.,1972,Vol.34, pp. 2241-2247. PergamonPress. Printedin GreatBritain

THE VISCOSITY OF MIXTURES OF BENZENE A N D METHANOL H. M. N. H. I R V I N G and R. B. SIMPSON Department of Inorganic and Structural Chemistry, University of Leeds, Leeds LS2 9JT

(Received 29 November 1971) A b s t r a c t - T h e densities and absolute viscosities of mixtures of methanol and benzene have been determined at 10°, 20 °, 30 °, 40 ° and 50°C. In each case the plot of viscosity against mole fraction is sigmoid and the maxima that occur with the methanol-rich (and the minima with the benzene-rich) mixtures become less pronounced as the temperature increases. The results are interpreted in terms of the various intermolecular attractions. INTRODUCTION

IN PREVIOUS papers [ 1] we have shown how viscosity measurements can be used to detect solute-solvent interactions between a variety o f formally uncharged inorganic or organic compounds or metal chelates and a series of organic solvents. In the present paper the use of viscometry to study interactions in a binary mixture of mutually soluble organic solvents is illustrated by measurements on mixtures of benzene and methanol over a range of temperatures. EXPERIMENTAL A suspended level viscometer of the Ubbelolde type was calibrated with benzene at 10°, 20 °, 30 °, 40 ° and 50°±0.005°C using the published kinematic viscosities v, at these temperatures[2]. The equation v = 0.005466t - 0.01957t -1 (t is the flow-time through the viscometer in sec) was found to hold with a standard deviation of ±O.O008cSt. Densities, d, of pure solvents and mixtures of accuratelyknown mole fraction were measured by standard procedures [3] and used to convert the measured kinematic viscosities into values of the absolute viscosity, "0. The composition of each mixture is given in Table 1 in terms of the mole fraction, xB, and the volume fraction ~bB,of benzene. In each case M is the molar wt. of the mixture and I'M is the molar volume. Table 1. Absolute viscosities of benzene-methanol mixtures

(i)

At 10°C

Mixture C6H6 1 2 3 4 5 6 CH3OH

~/cp

xB

dpB

M/g

d41°

VM/ml

t/sec ___0.05

v/cSt

1.00000 0.92849 0.78165 0-60296 0.42162 0-22164 0.04357 0.00000

1.00000 0.96608 0.88709 0.76927 0"61540 0.38463 0.09087 0.00000

78.115 74.820 68.055 59.822 51.467 42.254 34.049 32.042

0.88962 0.88660 0.87960 0"86920 0.85554 0-83508 0.80879 0.80065

87.807 84.390 77.370 68 "824 60.157 50.599 42.099 40.020

156.40 151'30 150.45 153.90 157'15 157.90 155.50 154.40

0.8547 0.8269 0.8222 0.8411 0-8588 0.8629 0.8498 0.8438

±0.0010 0.7604 0.7331 0.7232 0.7311 0.7348 0.7206 0.6873 0.6756

1. H. M. N. H. Irving, R. B. Simpson and J. S. Smith, J. inorg, nucl. chem. 32, 901 (1970) and Refs. therein. 2. J. Timmermans, Physico-Chemical Constants of Pure Organic Compounds. Elsevier, New York (1950). 3. R. B. Simpson. Ph.D. Thesis, University of Leeds, 1971. 2241

2242

H.M.N.H.

I R V I N G and R. B. SIMPSON Table 1. (Contd.)

(ii)

At 20°C

Mixture CoH6 1

2 3 4 5 6 CH3OH

xB I '00000 0"92849 0"78165 0"60296 0"42162 0.22164 0.04357 0"00000

CoB

M/g

1"00000 78"115 0"96600 74"820 0'8869568"055 0"76921 59"822 0'61558 51'467 0.38474 42.254 0.09091 34.049 0"00000 32'042

"tl/cp

d4z°

Vu/ml

t/sec +0.05

v/cSt

_0.0010

0'87900 0"87593 0"86897 0"85876 0"84556 0.82536 0.79941 0"79139

88"868 85"418 78"317 69"661 60'867 51.195 42.593 40"488

135"00 130"60 129"25 131"35 134"10 135.95 135.05 134'60

0'7378 0"7137 0"7063 0"7178 0"7328 0'7430 0.7380 0"7356

0"6485 0"6252 0"6138 0"6164 0"6197 0.6132 0.5900 0'5821

(iii) At 30°C

CoH6 1

2 3 4

5 6 CHaOH

"O/cp

xB

CoB

M/g

d4a°

VM/ml

t/sec +0.05

v/cSt

+0.0010

1.00000 0.92849 0.78165 0.60296 0.42162 0.22164 0.04357 0"00000

1.00000 0.96582 0.88684 0.76913 0.61553 0.38479 0.09092 0"00000

78.115 74.820 68.055 59.822 51.467 42.254 34.049 32"042

0.86830 0.86511 0.85828 0"84822 0.83520 0"81542 0.78979 0"78184

89.963 86.486 79.292 70.527 61.622 51.819 43. l II 40"983

118.20 114.20 112.55 114.25 116.45 118.50 118"65 118"30

0.6459 0.6240 0.6150 0.6243 0'6363 0.6476 0.6484 0"6465

0.5608 0.5399 0.5278 0.5296 0.5315 0.5280 0.5121 0"5054

M/g

d44°

Vu/ml

t/sec _.+0.05

v/cSt

_0.0010

1-00000 0.96572 0.88684 0.76901 0.61551 0.38474 0.09095 0-00000

78.115 74.820 68"055 59.822 51.467 42.254 34.049 32"042

0.85755 0"85431 0.84766 0-83753 0-82483 0.80521 0"78030 0"77247

91.091 87.579 80"286 71.422 62.397 52"476 43"636 41"480

105.05 I0!'45 99"55 100.35 102"35 104.20 104-90 104"80

0.5740 0-5543 0.5439 0.5483 0.5592 0.5694 0.5732 0"5726

0.4922 0.4736 0.4611 0"4593 0.4613 0-4585 0.4473 0"4423

CoB

Mlg

Vu/ml

t/sec ___0.05

v/cSt

_0.0010

92"254 88.708 81"334 72"342 63"214 53"142 44"202 42'013

94"30 91.10 89-10 89"30 90"80 92"45 93"50 93"75

0"5152 0.4977 0.4868 0"4879 0"4961 0"5051 0'5109 0"5122

0"4363 0.4198 0"4073 0"4034 0.4039 0-4016 0.3935 0.3907

Mixture

(iv) At 40°C

xB

Mixture Cell6 1

2 3 4

5 6 CHsOH

1.00000 0.92849 0.78165 0.60296 0.42162 0.22164 0.04357 0"00000

CoB

~/cp

(v) At 50°C Mixture

xB

CsH6 1 2 3 4 5 6 CHaOH

1-00000 0.92849 0"78165 0"60296 0-42162 0.22164 0.04357 0.00000

1.00000 0.96561 0.88660 0"76892 0.61531 0"38476 0.09093 0.00000

78"115 74.820 68"055 59"822 51"467 42"254 34"049 32"042

d45° 0.84674 0.84344 0"83673 0"82693 0.81417 0"79511 0"77030 0"76267

*?/cp

Mixtures of benzene and methanol

2243

RESULTS AND DISCUSSION

The results of the present measurements are shown in Fig. 1 as plots of absolute viscosity, rl, against mole fraction, x. For each temperature the thin line connecting the points for the pure solvents represents the situation that would exist if the viscosity of a binary mixture were a linear function of mole fraction. In many binary mixtures a single maximum (or minimum) is seen in the experimental curves [4, 5] but with the present system there is clearly an anomalous increase in viscosity on adding benzene to methanol and an anomalous decrease on adding methanol to benzene. The effects tend to compensate as the mole fractions of the components become more nearly the same and are less marked as the temperature rises.

30"Cl

0.5C

×

×

×

O.4(:

--7----I--

I

t

I

x C6H6 I i 0"5

0 I I-0

I

I

I 0"5

I

I

t

I 10

I

I

i

I

i

ICH3CH Fig. 1. The viscosity of methanol-benzene mixtures at various temperatures. Data from Mato and Hermlndez (Ref. [5]) are shown as crosses. The broken lines are the viscosities calculated according to their Equation (2).

Fig. 1 also shows data (as crosses) reported by Mato and Hernfindez[5] for the four highest temperatures. They used a falling sphere viscometer thermostatted at _+0.05°C and claim a precision better than ___0-2%. Although the agreement with our measurements is poor, especially at the higher temperatures and with methanol-rich mixtures, there can be no doubt that their data confirm the sigmoid nature of the curves. Their data for the system methanol-trichloroethylene show the same behaviour but, possibly because their results were not displayed 4. J. Kendall and K. P. Monroe,J. Am. chem. Soc. 39, 1787 (1917). 5. F. Mato and J, L. H e r n ~ d e z , A n a l e s de Fisica y Quimica 65(/1), 9 (1969).

2244

H.M.N.H.

I R V I N G and R. B. S I M P S O N

graphically, Mato and Hernfindez chose to interpret these on the same terms as the other systems they had investigated (viz. benzene-cyclohexane, acetonebenzene, chloroform-benzene, acetone-methanol, acetone-water, methanolwater, acetonitrile-water, and ethyl acetate-methanol), where plots of T against x present a single extremum. Tamura and Kurata [6] proposed the equation 7] ~- XA~A~A "Jr-XBI#BTB "q- 2 (XAXB¢#A~B ) 112 TAB

( 1)

for the viscosity of binary mixtures. Here A and B are the two components and the parameter TaB, introduced by Dolezalek[7] and used later by Wijk[8] in their treatments of this subject, is termed the 'mutual viscosity' and is intended to account for interactions between unlike molecules. Mato and Hernfindez[9] deduced a new semi-empirical equation involving the same mutual viscosity parameter, viz. T~ "= ~A2TA "~- ¢~B2TB "~- 2~AeB~AB. (2) To calculate the best value for the parameter ~,~B it would be preferable to use results covering the full range of mole fractions (or volume fractions) and to choose that value which minimises the sum X(~ca~c-Texp) 2. The authors prefer to calculate TAB from the viscosity of the mixture of equimolecular composition and claim that this leads to almoat as satisfactory agreement between calculated and experimental data. This would not be surprising if the maximum anomaly in viscosity happened to occur with an equimolecular mixture of A and B. The effect of applying the Equation (2) of Mato and Hermlndez in this way to the present data leads to the curves shown as dotted lines in Fig. 1, which are poor representations of the actual results. The reason is not far to seek. If we introduce the identity ~bB= (1 --4~A) into Equation (2) and differentiate, it will be clear that a single extremum will be found when ~A ~----(TB - - T A B ) / ( ~ A "JI-TB --2TAB)

with an inflexion if TAB = (~A + TB)/2 and a maximum (or minimum) if TAB is greater (or less) than this mean value. This treatment cannot possibly be validly appiied to systems where both maxima and minima occur, and it cannot fully account for systems in which one of the components is an associated liquid such as methanol. Satchard et al. have carried out many detailed studies of vapour pressures of binary systems including that of benzene-methanol[10, 11, 12], which have been supplemented, but not effectively superceded, by later work in the same field [13, 14]. 6. 7. 8. 9. 10. 11. 12. 13. 14.

M. Tamura and M. Kurata, Bull. chem. Soc. Japan 25, 32 (1952). F. Dolezalek, Z. Phy. Chem. 83, 73 (1913). A . J . A . van der Wijk, Nature 138, 845 (1936). F. Mato andJ. L. Hernfindez,Anales de Fisicay Quimica 63(B), 13 (1967). G. Scatchard, J. R. Goates and E. R. McCartney, J. A m. chem. Soc. 74, 3721 (1952). G. Scatchard and L. B. Ticknor, J. Am. chem. Soc. 74, 3724 (152). G. Scatchard and F. G. Satkiewicz, J. Am. chem. Soc. 86, 130 (1964). J. R. Goates, R. L. Snow and M. R. James, J. phys. Chem. 65, 335 (1961). A. G. Williamson and R. L. Scott, J. Phys. Chem. 64, 440 (1960).

Mixtures of benzene and methanol

2245

Figure 2 gives a qualitative picture of the excess thermodynamic functions for binary mixtures of methanol with (i) carbon tetrachloride and (ii) benzene at 35°C. It is clear that the benzene-methanol system produces greater positive excess heats (AH e) and entropies (T~LSe) and lower excess free energies (AG E) than mixtures of methanol with carbon tetrachloride. This suggests a more favourable energy of interaction between an hydroxyl group and the ~r-electrons of an aromatic molecule than with the less polarisable electrons of a saturated molecule. Such an interaction, though weaker than an ordinary hydrogen bond, is less demanding in its spatial requirements, and accounts for the greater miscibility of all highly polar liquids with aromatic hydrocarbons than with aliphatic hydrocarbons.

['01

o

-'._.e + ~ 0 E

.cH oH/°°

.-)

1.0

1.0 CH3OHICCL 4

CH3OHIC6H 6

Fig. 2. Excess functions for the system m e t h a n o l - c a r b o n tetrachloride and methanolbenzene reproduced from work by Scatchard et al. (Refs. [10-12]).

If the variation of molar volume and entropy of activation with temperature is ignored, the viscosity of a liquid can be represented by the equation "O= ( h N / V ) exp ( A G * / R T ) = ( h N / V ) exp { ( A H * / R T ) -- (AS*/R)}

(3)

so that a plot of log 7/against (l/T) should be linear with a slope of (AG*/2.303 R). This was found to be true for the present results, and values of AE*ls(-- AH*ls) and o f ASvl*s are collected in Table 2 and shown plotted in Fig. 3. Although the plots of AHv*~ and AS*t~ individually show gross-composition dependence, they compensate most effectively to give a graph for AGvi~* in which (on the same scale) the variations with mole fraction are just perceptibly sigmoid. Table 2. Thermodynamic data for 298.2 K

xB ~S~cal/K M/*l, kcal/mole-1 AGv*~kcal/mole-1

Pure benzene

1

2

Mixture 3

4

5

6

Pure Methanol

1.00 --2.05 2.30 2.91

0.93 --1.87 2.31 2.86

0.78 -1.41 2.38 2.80

0-60 --0.88 2.47 2.73

0"42 --0.56 2.49 2.65

0"22 -0.38 2.43 2.55

0.04 --0.35 2.31 2.42

0.00 --0.32 2.28 2.38

2246

'H. M. N. H. I R V I N G and R. B. S I M P S O N

2.7

0.4

2',=

)

I

I

I

I

0

I

I

I

I

1

I

l

i

I

05

i,O

% l bO

I

I

1

I

I 05

l 0

Fig. 3. Values of AG*,. and AH*ts(lefthand ordinate) and --TAS*t, (right-hand ordinate) in kcal. mole -1.

The divergence from a strictly linear behaviour is emphasised in Table 3, which shows that the negative anomaly caused by small additions of methanol to benzene increases slightly with rise of temperature whereas the positive anomaly due to small additions of benzene to methanol decreases. The most striking feature is the negative sign of AS*is(Table 2), for it is commonly stated [ 15] that it will be larger and positive for associated liquids. However, whereas the plot of log ~ against (l/T) for w a t e r - t h e typical example of an associated liquid-is not linear, implying that AE*vls is not constant, the corres, ponding graph for methanol is strictly linear and leads to AE*ls= 2.28 kcal/mole -1, a value comparable to that of benzene but much smaller than the values reported Table 3. Deviations of AG*~ from linearity XB =

Temp./K

1.00

0.93

0.78

0.60

0.42

0.22

0.04

0.00

283.2 293-2 303.2 313'2 323.2

0 0 0 0 0

--7.8 --8-4 --9.0 --9.6 --10"3

+10.1 +7.5 +4.8 +2.2 --0.5

+40.9 +36.1 +31.3 +26.4 +21.6

+60.0 +55.1 +50.2 +45.3 +40.4

+54"3 +51.2 +47.7 +44.7 +41.4

+15.2 +14.7 -:. !4-3 +13.6 +13.5

0 0 0 0 0

Values of AG*~ (expt.)-AG*l, (calc.) given above in calories have not been rounded off so that trends are more obvious. The actual precision will not be better than__+5 cais. 15. S. Glasstone, K. J. Laldler and H. Eyring, The Theory of Rate Processes, pp. 505-6. McGrawHill, New York (1941).

Mixtures of benzene and methanol

• 2247

for water (5.06 kcal at 0°C, 3.42 kcal at 50°C). Hence AS*+ is still negative, though much smaller than the value for benzene, since the degree of association between molecules of this solvent lies somewhere between those of water and benzene. The viscometric behaviour of the methanol-benzene system can now be interpreted as follows. The addition of a small amount of benzene to pure methanol will not break many hydrogen bonds, and most of this diluent will be accommodated interstitially in a matrix of associated methanol molecules. Interactions between hydroxy groups and the ~r-electrons of the aromatic hydrocarbon give rise to the observed sharp increase in viscosity. At first, as the benzene/methanol ratio is increased (xB increasing), the viscosity will rise, since additional molecules of benzene tend to saturate all interstitial sites and increase the net total intermolecular bonding. When these are saturated, additional benzene molecules breakdown the hydrogen bonding between methanol molecules; although the methanol-benzene interactions become more numerous the net number of interactions will decrease, with a concomitant decrease in the observed viscosity. The excess heat of mixing is therefore large in mixtures low in methanol content, since an addition of a small quantity of this to a large amount of a non-polar liquid must break all the hydrogen bonds in the alcohol, leading to the observed sharp decrease in viscosity. The addition of methanol to benzene thus gives rise initially to a solution of monomeric alcohol. The viscosity of a solution is a measure of the internal friction of a liquid in laminar flow. Dullien[16] has recently calculated values of the Lamm frictional coefficients ~b00,th~1 and 4~m characteristic of the "equivalent random solution" for the system benzene-methanol, and has compared these with the experimental frictional coefficients per mole, 4)00, +11 and 4~m- Here the subscripts refer to interactions between molecules of pure benzene (00), of pure methanol (1 1), and of benzene with methanol (01). As methanol (component 1) is added to benzene 4)11 increases very much more rapidly than the1, and 4~1odecreases more rapidly than +~0- There are therefore more alcohol-alcohol neighbours and fewer benzenealcohol neighbours than would be expected from the 'equivalent random solution'. In these dilute solutions of methanol in benzene 4~00is almost identical with 4~o0, implying that the number of benzene-benzene neighbours is essentially that predicted by the model. The almost constant value of 4)11 found in methanol-rich mixtures implies that any additional alcohol goes into existing large clusters. Deviations of ~b00from tb00 in this region were found to be in the same sense but occurred to a lesser extent, indicating that the benzene molecules are forced to cluster together in consequence of the tendency of the methanol molecules to associate. Measurements of thermal diffusion coefficients by Farsang and Tyrrell[17] provide a striking confirmation of the transition which occurs with increasing mole fraction of benzene, from the situation when benzene is dissolved in an associated alcoholic solvent to one comprising mainly monomeric methanol dissolved in benzene. Acknowledgement-One of us (R.B.S.) is indebted to the Science Research Council for a research studentship and we wish to thank Prof. V. Tyrrell for helpful comments. 16. F. A. L. Dullien, Trans. Faraday Soc. 59, 856 (I 963). 17. G. Farsang and H . J . V . Tyrrell,J. chem. Soc.(A) 1839 (1969).