J. CHEM. SOC. FARADAY TRANS., 1993, 89(12), 1969-1974 1969

Mutual Diffusion Coefficients for the Systems Water-Ethanol and Water-Propan-I -01 at 25 OC Kenneth R. Harris," Teresa Goscinska and Hanh Ngoc Lam Chemistry Department, University College, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2601, Australia

Mutual diffusion coefficients have been measured by the Taylor dispersion technique at 25 "C for aqueous solu- tions of ethanol and propan-1-01. The results for the ethanol system are in good agreement with the better diaphragm cell results in the literature. Those for the propanol system do not show the large maximum at high propanol concentrations reported by Pratt and Wakeham (Proc. R . SOC. London, Ser. A , 1975, 342, 401), and support the argument of Leaist and Deng (J. Phys. Chern., 1992, 96, 2016) that this maximum is an artifact. The quotient DE/41 $ 2 , t h e 'excess ' diffusion coefficient divided by t h e product of t h e volume fractions, is found to vary only slightly with composition and to take almost the same values for aqueous methanol, ethanol and propan-1-01. Similar behaviour is shown by reference systems also having positive excess Gibbs energies but containing non-associating components. However, it has been found that for t h e aqueous ethanol system the thermodynamically corrected diffusion coefficient, Ol2/(1 + a In f,/d In x ~ ) ~ , ~ , shows a minimum at low ethanol mole fraction, where some thermodynamic properties also show extrema or inflections. This effect is not shown by the reference systems.

The Taylor dispersion technique now provides a good alter- native to the classical methods for the determination of the mutual or inter-diffusion Coefficient (D12) in liquid systems, particularly where this quantity is strongly dependent on composition. The method is relatively fast, quite small con- centration gradients can be used and convective disturbances are negligible. By contrast, the classical interferometric and diaphragm cell techniques are slow and normally require the use of large concentration gradients. Where strongly composition-dependent D,, values are to be measured by one of the interferometric methods this results in the necessity for several experiments for each datum, carried out with dif- ferent initial gradients but at the same mean concentration, with extrapolation of the experimental apparent diffusion coefficients to a value at zero gradient. For the diaphragm cell method, the experimental diffusion coefficients are 'integral' quantities which must be numerically manipulated to yield D,, values. The accuracy with which this can be done can vary considerably from one system to another, depending on the form and strength of the concentration dependence. These difficulties are largely avoided in the Taylor method, which yields differential diffusion coefficients directly.'

We report here mutual diffusion coefficients for the systems water-ethanol and water-propan-1-01 at 25 "C, which are strongly composition dependent. The former are used for comparison with diaphragm cell results for this system obtained by several groups of workers, which show some scatter, and the latter for comparison with the results of Pratt and Wakeham,2 which show a large maximum at high alcohol concentrations (Fig. 1). This behaviour is quite unusual and is not accompanied by any corresponding minimum in the viscosity or any noticeable effect on the excess or partial molar volumes, which are smooth functions of composition in this region. It was therefore felt worthwhile to reinvestigate this system.

Experimental Our Taylor dispersion apparatus and technique have been described b e f ~ r e : ~ . ~ only a brief description need be given here.

The detector used in this study was an Optilab 5902 inter- ference refractometer (Tecator AB, Hoganas, Sweden) with

the refractometer cell holder placed in an air thermostat con- trolled to +50 mK. The temperature of the tubing joining the diffusion coil in the main water thermostat to the detector cell head was also maintained at the working value by sheathing it with insulated flexible bellows tubing through which thermostat water was drawn by a peristaltic pump. Temperatures in the waterbath were regulated to + 1 mK and were determined to k20 mK with a calibrated Pt resist- ance thermometer (Leeds and Northrup, Sydney, NSW, model 8926) by means of an a.c. resistance bridge (Leeds and Northrup, model 8078).

The mutual diffusion coefficients were calculated from the moments of the peak determined from a non-linear least- squares fit to a truncated Edgeworth-Cramer s e r i e ~ . ~ This has the form

4 y(t) = ; f ( t ) - - y 3 ' ( t ) + 5 ft4'(t) - - f '5 ' ( t ) "[ 3"! 4! 5 !

1os2 35se 280s3 6! 7! 9!

+ - f '6 '( t) - - f"'(t) - - f'9'(t) + . ..I (1)

where f i t ) is the time-dependent output signal, corrected for linear baseline drift, and f ( t ) is the normalized Gaussian

with

t - € x=- 0

(3)

The differentials offare given by the recursive relation

f ' W + "(t) = -f(t)[tf'"'(t) + u p - (01 = ( - 1)"fut)f(t) (4)

where Hu(t) are successive Hermite polynomials. The first peak moment, or flow time, t; the peak area A, and the quan- tities CT, s, e and q are obtained from the fit.

The diffusion coefficient is then obtained as v2F I C D,, = -

24a2 where r is the internal radius of the diffusion tube and o2 is the variance of the temporal concentration distribution

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1970 J. CHEM. SOC. FARADAY TRANS., 1993, VOL. 89

Table 1 Coefficients of eqn. (2) for alcohol solution densities, di

C3H,0H

coefficient CH,OH C,H,OH x2 < 0.05 x2 > 0.05

102d,

10Sd, 1034

1054 1074 1054 106d, 108d, 10lOd, standard deviation/10P5 g cmP3 ref. M/g mol - p / g cmW3'

-0.598819 0.149443 0.356710

- 0.126666 0.742775 - - - -

3 12 32.0422 0.78635

- 0.897070 0.724780

4.99875

0.19 1925

0.502798

8

- 14.9759

- 139.144

-0.137848

-0.740886

10, 13 46.0697 0.7846

- 1.23908 7.3963 1

- 8 19.8 18 509.667

- 16951.7 27.6770

- 17.4956 -

-

3 9

~~~ ~~ ~~

- 2.68760 23.5523

- 1236.08 343.763

- 5777.26 6.05702

- 3.87987 13.9046

- 2 1.3772

10, 11 3

60.0958 0.79935

a Ref. 7.

observed at the detector, that is the second central moment of the peak. The main criteria for a good experiment are the linearity of the baseline, equal standard deviations for the fits of the peak and baseline, and invariance of the diffusion coef- ficient to the width of the signal treated as the peak (8, 10 or 12 times a). The skewness, s, excess, e, and the function q are also useful indicators of experimental quality. The corrections to eqn. (5) outlined by Alizadeh et aL5 were applied where necessary : however, experimental conditions were such that these corrections were generally negligible.

Ethanol and propan-1-01 (AR grade) were obtained from Rh8ne-Poulenc and used without further purification. Solu- tions were prepared gravimetrically from these materials using de-ionized water (resistivity 18 Mi2 cm), obtained by passing distilled water through a Milli-Q ion-exchange system (Millipore Pty Ltd.). The eluent solutions were out gassed by warming under the vacuum produced by a water pump and the compositions then checked by comparison of the density, determined by pycnometry, with literature data.

The densities (p/g cmP3) were determined with a set of matched pycnometers, with a precision of + lo pg cm-3, again using a thermostat controlled to & 1 mK. The liter- ature density data selected were fitted to polynomials in the molarity (clmol drnp3)

n

( p - 0.997 048) = C di ci (4) i = 1

and the sources and fitted coefficients, d i , are given in Table 1 : these polynomials were then used to obtain concentrations

7 1.0

0.6

a- 0.4

I I I I I

1 .o 0.0 ' 0.0 0.2 0.4 0.6 0.8

x(l -PrOH) Fig. 1 Mutual diffusion coefficients for water-propan-1-01 at 25 "C: 0, this work (the solid line represents the best fit to eqn. (8) using volume fractions; ., Pratt and Wakeham"

from the pycnometric analyses with an estimated accuracy of - +0.001 mol dm-3 (approximately +0.0001 in the mole fraction).

There are recent sources of data in the literature6-' for water-propan-1-01 : these have been examined by plotting the excess volume function ( VE/xl x2) against composition. There is a deep minimum in this function at a propanol mole frac- tion, x2 , of ca. 0.05. The data of Dethlefsen et aL6 span the whole composition range, those of Kiyohara and Benson7 extend from pure propanol back to the position of the minimum, but no further, and those of Sakurai and Nakagawa' lie wholly above mole fraction 0.95. Our own data, and those of the two latter groups fit on a smooth curve: those of Dethlefsen et al. are consistently higher above mole fraction 0.3, but agree with the other data at lower com- positions, including the well of the minimum. Therefore, in our analyses, we have used Dethlefsen's data below this point (0.05) where other data are lacking, and the other two sets, combined, above it.

For the system water+thanol, the density data sets of Kiy- ohara and Benson7 and of Marsh and Richards' are in excel- lent agreement and have been combined.

Some viscosity measurements were made on the water- propan- 1-01 system for comparison with literature data and these measurements are reported in Table 2. They were carried out with a flared capillary Ubbelohde suspended-level viscometer immersed in the thermostat also used for pyc- nometry. The viscometer was calibrated in the manner recommended by James et a1."

Results Results for the alcohol systems are given in Tables 3 and 4. 'Excess' diffusion coefficients, DE, defined in analogy to ther- modynamic excess functions,

(7)

[where 2D12 and 'D,, are the limiting values at zero concen- tration of alcohol (2) and water (l), respectively], were fitted

Table 2 Viscosities for water-propan-1-01 at 25 "C

X q/mPa s

0.024 92 1.239 0.052 16 1.616 0.381 15 2.627 0.899 4 1 2.036 0.962 12 1.986

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Table 3 Mutual diffusion coefficients for water-ethanol at 25 "C ~~

X Ea/mol dm-3 Acb/mol dm-3 D/lOP9 m2 s - ' X E/mol dm-3 Ac/mol dm-3 D/lOP9 m2 s-'

0.00001 0.00001 0.oO001 o.Oooo1 0.000 01 0.049 85 0.050 66 0.050 68 0.073 32 0.073 32 0.099 68 0.099 68 0.147 67 0.147 67 0.14767 0.147 76 0.249 14 0.249 14 0.249 14 0.249 18 0.249 20 0.349 48 0.350 15 0.350 15 0.350 15 0.350 15 0.350 15

0.0003 0.0003 0.0005 0.0005 0.0005 2.5108 2.5480 2.5486 3.5457 3.5457 4.6 137 4.6139 6.3265 6.3265 6.3265 6.3294 9.1534 9.1534 9.1 534 9.1545 9.1549

1 1.202 11.214 11.214 11.214 111.214 11.214

0.026 0.026 0.030 0.030 0.030 0.060 0.032 0.083 0.025 0.025 0.049 0.067

- 0.093 - 0.093 - 0.093

0.240 -0.191 -0.191 -0.191

0.084 0.218 0.161 0.39 1 0.391 0.391 0.391 0.391

1.22 1.23 1.24 1.23 1.22 0.89 0.89 0.88 0.82 0.79 0.67 0.70 0.50 0.51 0.49 0.49 0.37 0.37 0.36 0.36 0.39 0.35 0.36 0.36 0.36 0.39 0.39

0.449 67 0.547 38 0.548 17 0.548 17 0.71499 0.714 99 0.71499 0.797 34 0.797 43 0.898 32 0.898 32 0.898 32 0.947 58 0.947 58 0.947 76 0.948 09 0.948 09 0.997 68 0.997 68 0.997 68 0.997 68 0.997 70 0.997 73 0.997 73 0.997 78 0.997 78

12.756 13.940 13.948 13.948 15.448 15.448 15.448 16.01 1 16.012 16.579 16.579 16.579 16.815 16.815 16.815 16.817 16.817 17.029 17.029 17.029 17.029 17.029 17.029 17.029 17.030 17.030

~~

0.360 - 1.983 - 1.Ooo - 1.Ooo

0.140 0.140 0.140

- 0.086 0.153 0.05 1 0.05 1 0.05 1

- 0.037 - 0.037

0.038 0.092 0.092

- 0.03 1 - 0.03 1 - 0.03 1 - 0.03 1 -0.014 - 0.007 - 0.007 - 0.006 - 0.006

0.45 0.58 0.54 0.55 0.79 0.77 0.76 0.87 0.90 1.06 1.07 1.06 1.13 1.13 1.10 1.08 1.10 1.22 1.20 1.18 1.19 1.19 1.20 1.18 1.17 1.19

~ ~ ~~~~~~

' E is the mean concentration calculated from eqn. (109) of ref. 14: it is flow rate dependent. x is the corresponding mole fraction. * Ac is the difference between the concentration of the injected solution and that of the flowing stream.

to an orthogonal polynomial series :11-13 n

DE = 1 a, P i ( X l X2) i = 2

with

P, = X l X Z ( 9 4

and

P" = [(2n - 1)(1 - 2X,)P,-, - (n - 3)P,-,]/(n + 2) (94

The calculated limiting values of the diffusion coefficients and the coefficients, ai are given in Table 5. Some improvement to

the fit was found when the volume fraction was used in place of the mole fraction, especially for the propanol system. Fits to a classical Meyers-Scott (Redlich-Kister) function' were much inferior.

Note that DE is not a true excess function: even for almost

is not a linear function of mole fraction, DE being slightly negative in both cases. Nevertheless, it is a useful function for dealing with a strong composition dependence.

Eqn. (8) has been used to provide a comparison of our results with those of others. Fig. 2 shows residuals for the fit of the ethanol data together with differences between the experimental values of Hammond and Stokes16 (diaphragm cell, experimental error, & 1 %), Dullien and Shemilt " v l

(diaphragm cell, f 2%), Calus and Tyn' (diaphragm cell,

ideal mixtures, such as H,O-D,O l4 and C,&-C&6 ,15 DI2

Table 4 Mutual diffusion coefficients for water-propan-1-01 at 25 "C

X Fa/mol dm-3 Acb/mol dm- j D/10-9 m2 s - ' Y F/mol dm-3 Ac/mol dmP3 D/lOP9 m2 s- '

O.OO0 28 O.oO0 28 0.000 28 0.024 92 0.024 92 0.024 92 0.052 16 0.052 16 0.099 67 0.099 67 0.14748 0.14748 0.196 17 0.196 17 0.221 44 0.221 48 0.381 15 0.381 15 0.501 90

0.00016 0.000 16 0.00016 1.2876 12876 12876 2.5144 2.5144 4.2770 4.2770 5.68 12 5.6812 6.8379 6.8379 7.3540 7.3458 9.7305 9.7305

10.98 1

0.013 0.013 0.013

-0.016 -0.016 -0.016 - 0.006 - 0.006

0.025 0.025 0.050 0.050

- 0.038 - 0.038

0.036 0.036

- 0.023 - 0.023

0.079

1.07 1.05 1.07 0.794 0.784 0.775 0.485 0.489 0.162 0.162 0.113 0.113 0.129 0.127 0.126 0.139 0.214 0.219 0.265

0.501 88 0.700 64 0.798 53 0.889 65 0.889 65 0.890 76 0.899 85 0.899 85 0.900 33 0.900 33 0.920 80 0.920 80 0.920 80 0.973 63 0.973 63 0.973 9 1 0.977 03 0.997 94

10.891 12.173 12.623 12.967 12.967 12.971 13.001 13.001 13.003 13.003 13.070 13.070 13.070 13.230 13.230 13.23 1 13.240 13.298

0.047 0.320

-0.125 - 0.470 - 0.470

0.292 0.152 0.152 0.262 0.262

- 0.58 1 -0.581 -0.581 - 1.006 - 1.006 - 1.006 - 0.294 -0.358

0.293 0.438 0.55 1 0.625 0.622 0.657 0.635 0.638 0.629 0.639 0.669 0.635 0.651 0.689 0.686 0.702 0.699 0.736

and ', as for Table 3.

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Table 5 Limiting diffusion coefficients and coefficients of eqn. (8), t i

CH,OHb C2H,0H C,H,OH

coefficients" XC @ X 4 X 4

'0 1 ZC 1.555 1.563 1.232 1.223 1.107 ID,* 2.187 2.191 1.192 1.192 0.758 5 1 - 3.240 76 - 3.663 61 -3.103 15 - 3.331 63 - 3.043 74 5 2 -0.964 627 1.913 65 - 2.618 06 1.103 76 - 3.346 29 53 0.186 776 -0.767 348 - 1.520 76 0.141 775 - 3.499 87 r4 - 0.676 774 -0.569 838 -0.567 394 0.323 562 - 3.674 07 5 5 -4.015 61 standard deviation 0.02 0.003 0.02 0.01 0.03

' Units for the coefficients and the standard deviations are m2 s-'. * Data from ref. 4. x, mole fraction; 4, volume fraction.

0.5-3%), Pratt and Wakeham,' (Taylor dispersion, + 2.5%), Kircher et (dual bellows diaphragm cell, f 3%), a i d those predicted from our equation of best fit. With the exception of some of the points of Kircher, obtained with an awkward dual-bellows cell intended for high-pressure mea- surements, and of Pratt and Wakeham at mole fraction 0.44 and their highest concentration, the agreement between these sets of data and ours is very good. The interferometric values reported by Yarnauchi2, differ widely from the other data sets and must be regarded as unreliable. The diaphragm-cell tracer diffusion coefficient for l4C-labe1led ethanol in water of Easteal and W00lf,,~ (1.224 & 0.006) lo-' m2 s- ' , is in excel- lent agreement with the corresponding limiting mutual value, (1.23 f 0.01) lo-' m2 s-'.

Note that the limiting values obtained from the diaphragm cell data have higher uncertainties than the experimental points: the strength of the composition dependence of D , , is such that it is difficult to carry out extrapolations accurately when results are not available at high dilution.

Fig. 3 shows residuals for the propanol system using the volume fraction fit: the results of Pratt and Wakeham* differ greatly at high concentrations. On the other hand, Woolfs value24 for the tracer diffusion coefficient of H, "0 in propan-1-01, 0.75, m2 s-I, is in good agreement with our limiting mutual value, (0.72 & 0.03) m2 s-'.

Discussion Pratt and Wakeham have reported results for water-ethanol mixtures" as well as the systems water-propan-1-01 and water-propan-2-01.~ Those for the ethanol-containing system show a deep minimum similar to that found for water- methanol,, but those for the two propanol-containing

0.1 0

0.05 r I v)

N E 0.00 cn I 0 > -0.05 F

c

2 -0.1 0

-0.1 5

T 00

4

v

0.0 0.2 0.4 0.6 0.8 1 .o x(Et0H)

Fig. 2 Deviation graph for water-ethanol at 25 "C. Note, the points at mole fractions 0 and 1 for the diaphragm cell data are extrapo- lated, not experimental, values: 0, this work; 0, Hammond and Stokes;I6 A, Dullien er ~ 1 . ; " * ' ~ V, Kircher et al.;" ., Pratt and Wakeham;" +, Calus and Tyn."

1.064 0.721

- 3.221 93 - 0.384 224 -0.368 274

1.882 83 1.330 77 0.01

systems exhibit, in addition, a large maximum at high alcohol concentrations, the diffusion coefficient at the maximum being approximately twice that obtained by interpolation between the minimum and the limiting value at the concen- tration of the pure alcohol (Fig. 1). As stated above there is no corresponding feature in the excess or partial molar

nor any minimum in the viscosity26-28 (see Fig. 4).

Like ourselves, Pratt and Wakeham used a refractive index detector in their studies. Aqueous alcohol systems commonly exhibit maxima in their refractive index-composition curves,29 and care must be taken when working in the neigh- bourhood of such regions, as the sign of the refractive index gradient determines whether a positive or a negative peak is observed. Indeed, a non-Gaussian peak with a high kurtosis results if the compositions of the eluent and of the injected solution lie too close to that of the maximum, and split peaks result if the two solution compositions are separated by that of the maximum. The propanol-water systems show a very flat refractive index-composition curve at high mole fraction and we have found this to be a difficult region in which to work. Our results, obtained with a very sensitive interfero- metric refractometer, show that the refractive index does, in fact, pass through a maximum at 25°C at about that com- position where Pratt and Wakeham reported their anom- alously high diffusion coefficients (0.95). This was observed as a change in the sign of the eluted peaks at this point; there- fore measurements were carried out by approaching the maximum from below on either side (see Table 4) and our results show a smooth monotonic increase above the low concentration minimum (Fig. l), similar to that exhibited by the systems containing methanol and ethanol.

Since our experimental work was completed, another Taylor study of the two aqueous propanol systems has been reported by Leaist and Deng3' from which they draw similar

0.1 5

0.1 0

," 0.05 E

m

I-

I

0 0.00

5 -0.05

%

-0.1 0

-0.1 5

W

0.0 0.2 0.4 0.6 0.8 1 .o x(1 -PrOH)

Deviation graph for water-propan-1-01 at 25°C: a, this Fig. 3 work; ., Pratt and Wakeham'

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3.0 r o r

-s l.Y 1 .o

0.5 I I I I 1 I I

0.0 0.2 0.4 0.6 0.8 1 .o x(1 -PrOH)

Fig. 4 Viscosity of water-propan-1-01 at 25°C: a, this work; D, Dunstan;26 A, D’Aprano et al.;27 +, Soliman and Marschal12*

conclusions. They attribute the Pratt and Wakeham result to a second-order effect: the refractive index gradient can be expanded as a Taylor series in the concentration gradient AC, and the first coefficient of this series vanishes at the maximum. Consequently, the second term is the leading one, that in (AC),: this leads then to a Gaussian peak with a variance corresponding to an apparent diffusion coefficient of twice the real value. They provide experimental evidence to support this argument.

Our results support the conclusions of Leaist and Deng. However, they did not publish numerical data, or report measurements over the full concentration range, and this was a further impetus to report our own results.

We turn now to a comparison of the three alcohol systems. In an analysis of mutual diffusion coefficients, it is sometimes helpful3 to calculate resistance coefficients,

the values of which are frame of reference independent. In this expression is the total molar volume, T the tem- perature, R the gas constant,

B , = (1 + a lnf,/d In x l ) T , p

andf i s the mole fraction scale activity coefficient. Much of the composition dependence of D , , is contained in the activ- ity term: as is well known, D,, becomes zero at a consolute point where this term is also zero, whereas the frictional coef- ficient remains finites3’ To first order, the excess diffusion coefficient DE varies as (a lnf,/d In x ’ ) ~ , ~ , that is as -xl x,(i?’GE/dx:),, p .

For the alcohol--water systems the excess Gibbs energy, GE, is a large, positive quantity and the activity coefficient factor is therefore large and negative. GE is commonly obtainable from vapour pressure measurements and can be expressed in various polynomial forms, such as that used above for the excess diffusion coefficient. However, with the exception of ethanol solutions, dealt with below, the vapour pressure data in the literature are either too sparse, or of insufficient preci- sion, to give really reliable values for the second derivative of GE. The number of coefficients needed to fit the data tends to be large, and unless the data are both precise and closely spaced in composition, this leads to second derivatives with spurious extrema and which vary with the form of the fitting equation used.? We have, therefore, left the comparison of resistance coefficients to a time when more extensitve and better quality activity coefficients are available.

t See, for example, the discussion by Marsh32 on the difficulties of extracting accurate activity Coefficients from vapour pressures by the Barker method of least-squares fits of GE(x).

L I 0 A=

0 I ,

w -

/IW

.* 0 0

0.0 0.2 0.4 0.6 0.8 1 .o x(alcoho1)

Fig. 5 DE/(x1x2) as a function of alcohol mole fraction, x l : a, water-methanol ; a, water-ethanol ; +, water-propan- 1-01

As an alternative approach, we have calculated the excess diffusion coefficient functions, DE/(x x 2 ) , for aqueous mix- tures of methanol, ethanol and propan-1-01 and these are plotted in Fig. 5. For none of the three alcohol systems do there seem to be any extrema of the form observed with the excess volume function, VE/(xl x ~ ) . ~ - ’ The excess diffusion coefficient function takes almost identical values for the three systems above mole fraction 0.2, but is composition depen- dent below this point, especially for mixtures containing propan-1-01. This effect seems to be largely due to the differ- ence in size of solute and solvent, which produces skewness in GE.33 Fig. 6 shows a plot of the excess diffusion coefficient function, $,), calculated using volume fractions, & i .

The values of this function for the three systems fall on almost the same curve, with a much weaker composition dependence. Indeed, the behaviour is not unlike that of simple hydrocarbon mixtures which also have large positive GE values and which serve as reference systems of non- associating components. Fig. 6 includes values of the same function for mixtures of n-alkanes with benzene:34 a similar lack of feature is observed.

In the case of water-ethanol, good-quality GE data are available at 30°C and above.35 Using HE results from the same l a b ~ r a t o r y , ~ ~ tables of vapour pressures, GE and activ- ity coefficients at 25 “C have been computed.37 We have used these to calculate the activity factor, B, , obtaining similar results from both a Meyers-Scott function and the orthog- onal polynomial series. Nevertheless, these deviate by as

-10 I I I I I

0.0 0.2 0.4 0.6 0.8 1 .o

9 Fig. 6 DE/(dl #2) for water-methanol (a), water-ethanol (D), water-propan-1-01 (+), as a function of alcohol volume fraction, and for benzene-n-hexane (O), benzene-n-heptane (a), as a function of alkane volume fraction. Note; (a) the values for the benzene- alkane systems are offset by the addition of 5 x lo-’ m2 s-’ to each point for clarity of presentation; (b) the experimental error increases a s x + O a n d x + 1.

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1974 J. CHEM. SOC. FARADAY TRANS., 1993, VOL. 89

7 8

0. Kiyohara and G. C. Benson, J. Solution Chem., 1980,9, 791. M. Sakurai and T. Nakagawa, J. Chem. Thermodyn., 1984, 16, 171. K. N. Marsh and A. E. Richards, Aust. J. Chem., 1980,33,2121. C. J. James, D. E. Mulcahy and B. J. Steel, J. Phys. D : Appl. Phys., 1984, 17, 225. R. L. Klaus and H. C. Van Ness, Chem. Eng. Prog., Symp. Ser., 1967,63, 88. L. J. Christiansen and A. Fredenslund, AlChE J., 1975, 21,49. J. S. Rowlinson and F. L. Swinton, Liquids and Liquid Mixtures, Butterworth, London, 3rd edn., 1982, ch. 5. L. G. Longsworth, J . Phys. Chem., 1960,64,1914. I. R. Shankland and P. J. Dunlop, J. Phys. Chem., 1975, 79, 1319. B. R. Hammond and R. H. Stokes, Trans Faraduy SOC., 1953,49, 890. F. A. L. Dullien and L. W. Shemilt, Can. J. Chem. Eng., 1961, 39, 242. R. K. Ghai, H. Ertl and F. A. L. Dullien, AIChE J., 1973, 19, 881, supplement. W. F. Calus and M. Tyn, J. Phys. E, 1974,7, 561. K. C. Pratt and W. A. Wakeham, Proc. R. SOC. London Ser. A, 1974,336,393. K. Kircher, A. Schaber and E. Obermeier, in Proc. 8th Symp. Thermophysical. Properties, Am. SOC. Mech. Eng., New York, 1982, p. 660; K. Kircher, Doctoral Dissertation, Universitat- Gesamthochschule Siegen, 1983. A. Yamauchi, Kenkyu Hokoku-Sasebo Kogyo Kotosenmon Gakka, 1984,21,57; Chem Abstr., 1985,102,155144~. A. J. Easteal and L. A. Woolf, J. Phys. Chem., 1985,89, 1066. L. A. Woolf, personal communication. 2. J. Derlacki, A. J. Easteal, A. V. J. Edge, L. A. Woolf and Z. Roksandic, J. Phys. Chem., 1985,89, 5318. A. E. Dunstan, J. Chem. SOC., 1904,87,11. A. DAprano, I. D. Donato, E. Caponetti and V. Agrigento, J. Solution Chem., 1979,8, 793. K. Soliman and E. Marschall, J. Chem. Eng. Data, 1990,35, 375. K-Y. Chu and A. R. Thompson, J. Chem. Eng. Data, 1962, 7, 359. D. G. Leaist and Z. Deng, J. Phys. Chem., 1992,96,2016. Ref. 1, ch. 2, 4, 7. K. N. Marsh, Annu. Rep. Prog. Chem., Sect. C, 1984,81,209. J. M. Prausnitz, R. N. Lichtenthaler and E. Gomez de Azevedo, Molecular Thermodynamics of Fluid Phase Equilibria, Prentice- Hall, Englewood Cliffs, NJ, 2nd edn., 1986, ch. 6.10. K. R. Harris, C. K. N. Pua and P. J. Dunlop, J. Phys. Chem., 1970,74,3518. R. C. Pemberton and C. J. Mash, J. Chem. Thermodyn., 1978,10, 867. J. A. Larkin, J. Chem. Thermodyn., 1975,7, 137. J. A. Larkin and R. C. Pemberton, Natl. Phys. Lab. (U.K.), Rep. Chem., 1976,43. L. Nord, E. E. Tucker and S. D. Christian, J. Solution Chem., 1984, 13, 849. G. C. Benson, P. J. DArcy and 0. Kiyohara, J. Solution Chem., 1980,9, 931. J. B. Ott, J. R. Goates and B. A. Waite, J. Chem. Thermodyn., 1979, 11, 739.

9 10

11

4 1 i 12 13

14 15

01 I I I 1 I 0.0 0.2 0.4 0.6 0.8 1 .o

Fig. 7 Thermodynamically corrected diffusion coefficients for (a) water-ethanol and (b) benzene-n-heptane: (-) D,, , (---) D12,idea,, (- - .) (D12/Bl), note the overcorrection effect of the ther- modynamic factor for ben~ene-n-heptane.~~

X

16

17

18

19 20

much as 10% from values derived from equations given by Nord et ~ 1 . ~ ~ based on their extensive vapour pressure mea- surements for dilute solutions (x < 0.235): this is again indic- ative of the error magnification inherent in calculations of d2GE/ax:.

Fig. 7 is a plot of the thermodynamically corrected diffu- sion coefficient (D12/Bl) for this system, which in contrast to the excess function, shows quite different behaviour to that for benzene-n-heptane, also illustrated. The minimum in dilute ethanol solution may be associated with the extrema observed in the partial molar excess and heat c a p a c i t i e ~ , ~ ~ and the inflection reported in the solid-liquid equilibrium line4' Further work is required to investigate this interplay between the thermodynamic and transport properties of aqueous alcohol solutions.

21

22

23 24 25

26 27

28 29

30 31 32 33 We are grateful to Dr. M. Sakurai of Hokkaido University

for kindly making available raw density data for the alcohol systems, to Dr. Lawrie Woolf for access to his unpublished diffusion data, and to the Australian Research Council for a 34 grant in support of this work.

35

References 1 H. J. V. Tyrrell and K. R. Harris, Diflusion in Liquids, Butter-

worth, London, 1984, ch. 5. 2 K. C. Pratt and W. A. Wakeham, Proc. R. SOC. London Ser. A,

1975, 342,401. 3 W. E. Price, K. A. Trickett and K. R. Harris, J. Chem. SOC.,

Faraday Trans. 1,1989,85,3281. 4 K. R. Harris, J. Solution Chem., 1991, 20, 595. 5 A. Alizadeh, C. A. Nieto de Castro and W. A. Wakeham, in t . J.

Thermophys., 1980, 1,243. 6 C. Dethlefsen, P. G. Srarenson and A. Huidt, J. Solution Chem.,

1984, 13, 191.

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