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Thermal pressure and energy-volume coefficients for dimethyl sulfoxide + methanol
J. Chem. Thermodynamics 1976, 8,615-682
Thermal pressure and energy-volume coeffkients for dimethyl sulfoxide + methanol KAREN
M. CHAPMAN”
Department of Chemistry, New Zealand
and DIGBY Victoria
D. MACDONALDbsC
University of Wellington,
Wellington,
(Received 5 June 1975; in revised form I9 January 1976)
Density as a function of temperature and thermal-pressure coefficients for dimethyl sulfoxide+methanol are reported. The results are used to derive expansivities, energyvolume coefficients, cohesive energy densities, isothermal compressibilities, and the derivatives of entropy with respectto volume and pressureover the entire range of composition. The variation of these parameters with composition and temperature is briefly discussed.
1. Introduction The isothermal energy-volume coefficient (the “internal thermal pressure coefficient, j3 = (@+W),, by (W/8V),
= T/3-p.
pressure”) is related to the (1)
Extensive compilations of this quantity for pure liquids, including molten salts, are available in the literature,‘lV3’ but only a few studies on liquid mixtures have been reported. (4-1o) Previous work by one of the authors (s-1’) has shown that the energyvolume coefficient is sensitive to changes in liquid “structure” as the composition of a binary mixture is varied. The observed variation of (&Y/a& with composition has been interpreted in terms of the effect of volume on both attractive and repulsive interactions in the system, and it is believed that the composition dependence of this quantity reflects changes in the average intermolecular distance in the liquid.@* 9, In this paper we report the thermal-pressure and energy-volume coefficients of dimethyl sulfoxide (DMSO) + methanol (CH,OH). This pair was chosen for study since it is characterized by strong intercomponent interaction which results in large negative deviations from Raoult’s law and large negative values for the excess enthalpy over the entire range of composition.‘“* 12) a Present address: Department of Chemistry, University of Auckland, Auckland, New Zealand. b Present address: Department of Chemistry, The University of Calgary, Calgary, Alberta, Canada. c To whom correspondence should be sent.
676
K. M. CHAPMAN
AND D. D. MACDONALD
2. Experimental MATERIALS
Spectral grade DMSO was found to contain not more than 0.05 mass per cent of water by Karl Fischer titration, and was used without further purification. The refractive index was found to be 1.4778 at (293.65 + 0.05) K, which compares well with the following values quoted in the literature: n(293.15 K) = 1.477,‘r4) 1.4788,(12) 1.4783,‘r3) and n(298.15 K) = 1.476(14). The melting temperature was 291.6 to 291.7 K (lit., 291.7 K),(r3) and the density at 298.15 K was determined as 1095.3 kg me3 comparing favourably with values of 1095.8,(“) 1095.0,(r2) and 1095.7 kg m-3,W) quoted in the literature. Analar-grade methanol was dried over calcium oxide and distilled twice at atmospheric pressure. Karl Fischer titration indicated a water content of 0.05 to 0.06 mass per cent. The refractive index was found to be 1.3285 at (293.20 rt 0.05) K compared with literature values of n = 1.3287,‘12’ and 1.3288(16’ at 293.15 K and n = 1.326(‘@ at 298.15 K. The density at 298.15 K was found to be 787.0 kg mm3, comparing well with literature values of 786.9,“‘) and 787.0 kg mm3.(12) No impurities could be detected by g.1.c. APPARATUS
AND
METHOD
Densities of various mixtures at temperatures in the range 298.15 to 323.15 K were determined using Sprengel-type pyknometers which were thermostatted to better than +O.Ol K in a water bath. Each pyknometer was standardized using triply distilled water, and all weighings were reduced to masses. Thermal-pressure coefficients were measured using a constant-volume cell similar in design to that previously described.@* ‘) The constant-volume cell was contained in a pressure vessel which was agitated internally by a magnetic stirring bar. The pressure vessel was thermostatted to rtO.01 K in a 18 dm3 oil bath equipped with a Braun Thermomix II temperature controller. In the present work a pressure range of 0.1 to 70 MPa was employed, which is considerably greater than the 0.1 to 2 MPa range used in previous work.@* lo) Pressures were measured using a calibrated 0 to 150 MPa Heise-Bourdon gauge which could be read to better than kO.05 MPa. The temperature inside the pressure vessel was monitored by use of a calibrated platinum resistance thermometer. This thermometer also served to indicate thermal equilibration following pressurization.@“) 3. Results DENSITY
AND
THERMAL
EXPANSION
The densities of XDMSO + (1 -x)CH,OH at six temperatures in the range 298.15 to 323.15 K are given in table 1. The values listed are the averages of at least two determinations for each composition and temperature. Error analysis indicates that the accuracy of the density measurement is +0.2 kg rnm3, which is confirmed by comparison of the measured densities of the two pure components with data from the literature. The densities given in table 1 were used to calculate expansivities LXat
DIMETHYL TABLE
T/K
1. Densities
SULFOXIDE
p, expansivities tl, and values of (OS/&X for xDMSO+(~ as a function of temperature T and mole fraction x
298.15
303.15
308.15
0.7870 0.8342 0.8751 0.9310 0.9591 0.9965 1.0190 1.0372 1.0633 1.0810 1.0953
0.7821 0.8290 0.8699 0.9259 0.9539 0.9912 1.0138 1.0321 1.0583 1.0760 1.0904
0.7772 0.8242 0.8648 0.9205 0.9485 0.9858 1.0085 1.0269 1.0532 1.0710 1.0855
P/10‘ .3
X
0 0.088 0.175 0.309 0.391 0.512 0.599 0.679 0.807 0.902 1
T/K
298.15
K
0.088 0.175 0.309 0.391 0.512 0.599 0.679 0.807 0.902 1
318.15 a/10+
x
0
677
+ METHANOL
12.8OhO.25 12.5O~tO.24 11.55zt0.23 11.25zt0.23 11.07hO.22 10.75ztO.21 10.151tO.20 10.15+~0.20 9.4OIto.19 9.20rto.19 8.96kO.18
K
313.15
12.10&0.25 11.5010.25 11.40~0.25 ll.lOztO.25 11.20&0.25 11.25hO.25 11.15~tO.25 10.5OkO.20 10.10~0.20 9.75zto.20 9.40f0.18
318.15
323.15
0.7680 0.8149 0.8550 0.9103 0.9381 0.9748 0.9976 1.0163 1.0428 1.0608 1.0756
0.7628 0.8102 0.8501 0.9053 0.9328 0.9693 0.9921 1.0110 1.0375 1.0556 1.0703
kg m-3 0.7724 0.8196 0.8600 0.9153 0.9433 0.9803 1.0031 1.0216 1.0480 1.0659 1.0806 298.15
K
- - waPhllo
K-l
-x)CHsOH
5.21 +O.lO 5.41 i-o.10 5.29*0.10 5.59*0.11 5.78&0.11 6.OOztO.12 5.94kO.12 6.2OhO.12 6.12kO.12 6.2710.12 6.39hO.13
- ,8 J K-l
318.15
K
Pa-l
mol-’
5.05*0.10 5.09f0.10 5.35*0.10 5.64*0.11 5.98kO.12 6.42kO.13 6.67kO.14 6.54kO.14 6.71 rtO.14 6.77hO.14 6.83&-0.14
298.15 and 318.15 K. The method adopted for determining ct was to compute the mean coefficient (a) for the temperature interval TI to T2 according to (a> = -(In PZ - In ~dl(T2 - TA (2) and then to extrapolate this quantity against mean temperature to the temperature of interest. Numerical values for a at 298.15 and 3 18.15 K are listed in table 1. The estimated precision of a is +2 per cent. Lau, Malcolm, and Fenby, and Martin, Weise, and Niclaso3) report values of (9.9 + 0.6) x 10e4 K-’ and 8.8 x loo4 K-l, respectively, for pure DMSO at 298.15 K. Our value of (8.96 ) 0.18) x 10m4 K-l is in reasonable agreement. THERMAL
PRESSURE
COEFFICIENTS
Plots of pressure against temperature for apparent constant volume were found to be linear, and reproducible with respect to ascending and descending temperature changes. Accordingly, the results were fitted to the linear expression: P = A,,T+C, where A,, is the apparent thermal pressure coefficient. Each &,
(3) value was corrected
678
K. TABLE
-__
T/K
2. Thermal b/10”
Pa K-l
CHAPMAN
pressure
/I/lo6
322.65
295.05 298.55 306.35 313.15 320.65
x = 0.549 295.35 18.20 298.05 16.88 308.75 15.36 317.15 14.99
9. b From
T/K
-x)CH30H p/lo5
at various Pa K-l
320.65
T/K
15.34
313.15 317.15 322.55
13.76 13.38 12.91
reference
Pa K-l
x=1.000 297.15 17.30 298.65 16.96 b 17.06 = 309.45 16.49 310.95 16.59 b 16.05 c 322.65 15.13 324.95 15.45 330.65 14.63
x = 0.698 295.15 18.58 299.55 15.14 305.75 13.09 317.15 12.63
8. c From
jI/106
x = 0.890 294.95 18.10 299.15 17.29 301.65 16.29 309.65 16.11 311.35 16.08 314.15 15.38 321.15 15.11
x = 0.672 15.43 299.15 307.65 14.29 311.15 13.93
19.09 16.82 14.05 13.59 13.40
temperatures
x = 0.192 295.95 18.57 299.55 15.85 300.85 15.40 303.55 15.17 308.15 13.79 310.55 13.55
x = 0.497 294.35 17.62 298.65 17.04 16.07 311.15
16.44 15.66 15.25 15.11
reference
D. MACDONALD
x = 0.206 297.15 13.44 302.65 12.47 12.12 312.35 11.55 317.65
x = 0.596
12.68
reference
Pa K-l
x = 0.418 294.75 17.20 298.45 311.15 315.45 321.15
D.
for XDMSO+(~
x = 0.094 295.15 11.97 297.15 11.55 301.35 11.26 305.95 10.79 316.65 10.12 324.15 9.83
9.59 9.80 a 9.35 9.27 a 8.87 8.94” 8.48 8.44 a
x = 0.291 294.55 15.03 299.15 14.37 303.15 14.09 307.55 13.62 316.35 13.15
’ From
AND
coefficients
T/K -~-~__~__~-
x=0 294.15 296.15 302.15 303.65 309.75 313.45 321.45 324.45
M.
18.
for the finite expansion and compression of glass in the usual manner,@~g. I*) and the corrected values are given in table 2 as a function of temperature and composition. Values for j? taken from the literature for pure DMSO and CH30H are also given in table 2 for comparison. Plots of fl against T for various values of mole fraction x were found to be nonlinear, particularly for x = 0.549 to 0.792. Values of (@I/aT),, estimated by drawing tangents to the curves of /I against T are given in table 3. When /? varies nearly TABLE
T K X
:094 01206 0.291 0.418 0.497 0.549
3. Temperature
-mm-),
K
lo6 Pa KeZ 298.15 0.0410.02 0.11zt0.04 0.1510.05 0.12&0.04 0.14*0.05 0.12~0.04 0.25hO.15
derivatives XDMSC+
K
10e9 Pa-’ 298.15
K
1.36f0.04 1.05&0.03 0.87f0.03 0.77+0.03 0.66rf10.03 0.63f0.03 0.63 SO.03
318.15 1.40~0.04 1.15+0.03 0.98&0.03 0.85f0.03 0.73*0.03 0.72kO.03 0.74&0.03
K
of /I and isothermal (1 -x)CH,OH
T K _~-x 0.596 0.672 0.698 0.792 0.890 1
compressibilities
for
- WaT),
K
lo6 Pa Ke2 298.15
K
0.5610.16 0.60*0.20 0.7OkO.22 0.53f0.16 0.11 kO.03 0.08fO.02
10-O 298.15
K
0.61 zkO.03 0.65&0.03 0.63ztO.03 0.58 ~‘~0.03 0.53f0.03 0.5210.03
Pa-’ 318.15
K
0.82hO.03 0.81&0.03 0.84*0.03 0.75 zlcO.03 0.65ztO.02 0.6010.02
DIMETHYL
SULFOXIDE
679
+ METHANOL
linearly with temperature, (f@/ZYQ, could be estimated to within f0.005 MPa K- ‘. However, for x = 0.549 to 0.792, where fi exhibits a strong non-linear dependence upon temperature, a somewhat higher uncertainty of kO.02 MPa KS2 seems appropriate. ENERGY-VOLUME
COEFFICIENT
AND
COHESIVE
ENERGY
DENSITIES
The energy-volume coefficient is related to the cohesive energy AU,/V by(19’ W-J/W,
(4)
= nWv/V),
where AU, is the energy of vaporization of the mixture to the perfect-gas state and n is an empirical parameter. The energy of vaporization of a real liquid mixture to the perfect-gas state can be calculated using’*, 9, AU, =x~H~,,+x~H~,~--H~-RT, (5) where AH, 1 and AH, z are the enthalpies of vaporization of components 1 and 2 to the perfect-gas state, and HE is the molar excess enthalpy of the mixture. Values for AH, 1, AH, 2, and HE at 298.15 K were taken from the literature,‘20Y * ‘, ‘*I and combined with molar volumes (calculated from densities given in table 1) to yield the values for A&W listed in table 4. Values of the energy-volume coefficient, (W/l3V),, (calculated using equation 1) and the parameter n are also listed in table 4. TABLE
X
0 0.094 0.206
0.291 0.418 0.497
4. Energy-volume
coefficients and cohesive energy densities for at 298.15 K
(au/avh.
WJ,IV)T
lOa Jrne3
108 J me3
2.83&0.05 3.38&0.06 3.93-10.07 4.43f0.08 4.88&0.09 5.1O=kO.10
8.599;tO.O04 8.400f0.004 8.233&0.004 8.062~0.003 7.907~0.003 7.756~0.003
n
X
0.33f0.01 0.40f0.01
0.596 0.698
w/a VI,
--_
108Jm-3
4.99kO.10 4.68rtO.10
XDMSO+(~
WW% ___.
lOa J me3
7.6OlrtO.003 7.452&0.003
-x)CH30H
n 0.66f0.01 0.63&0.01
0.48&0.01
0.792
5.0110.10
7.309rtO.002
0.6910.01
0.551tO.01 0.62&0.01 0.66f0.01
0.890
5.16*0.10
7.174rtO.002
0.71i-0.01
1
5.16%0.10
7.041f0.002
0.73kO.02
4. Discussion THE
THERMAL
PRESSURE
AND
ENERGY-VOLUME
COEFFICIENTS
Thermal pressure coefficients for DMSO + CH,OH, interpolated from the values given in table 2, are plotted in figure 1 as a function of x. At all temperatures from 295.15 to 318.15 K, fl initially increases with the addition of DMSO to methanol, culminating in a maximum at about x = 0.5. Further addition of DMSO results in /I passing through a minimum (with a possible exception at 295.15 K) at x = 0.65 to 0.70. The minimum becomes more pronounced with increasing temperature. Maxima in plots of /I against x have been found for other binary mixtures, including methanol + water, (9) t-butanol + water ,(9) and DMSO + water.(*)
680
K. M. CHAPMAN
AND D. D. MACDONALD I
I
I
I
20
I&I
/I /
/I
I
‘I Gc/ I/
--
( 18
I
I/
318:15 K
1 16 l2 8
12
8 0
0.2
0.4
0.6
0.8
1
0
0.2
.0.4
X
FIGURE 1. Thermal pressure coefficients for 298.15, 308.15, and 318.15 K.
0.6
0.8
1
X XDMSO+(~
--x)CH30H
plotted against x at 295.15,
The derivatives @S/al’), and @Slap), are equal to j? and -crV, respectively, where V is the molar volume of the mixture. Values for these two derivatives are given in figure 1 and table 1, and are found to be positive, and negative, respectively, for all values of X. It is of interest that @S/aV), passes through a positive maximum at x = 0.5, demonstrating that at this composition the entropy of the system is most susceptible to isothermal expansion. This is the same composition at which the excess volume(12S13) passes through a negative maximum, thereby lending support to the hypothesis (& ‘) that the variation of /I with x reflects, at least to some extent, changes in intermolecular distance. In contrast to the behaviour of jI, @S/~p), varies monotonically with x at both temperatures considered. The general features exhibited by the plots of fi against x are also shown by the plots of @U/aV), against x as dictated by equation (1). For this reason, the curves of (aU/aV), against x for all temperatures are not presented. However, values for @U/a&, AUJV, and n at 298.15 K are plotted as a function of composition in figure 2. The cohesive energy density, A&/V, exhibits an almost monotonic variation with x. On the other hand, the parameter n reflects, to a large extent, the dependence of /I and (aU/aV), on x. Previous work (‘Lo’) has shown that for non-polar liquids n x 1, as predicted for a van der Waals fluid. For strongly associated liquids, and in particular those which are hydrogen bonded, n 4 1. This observation is supported by the present work in that n is found to increase from 0.33 for x = 0 to 0.73 for x = 1. The values of (@I/87’), given in table 3 shows that for all values of x this quantity is negative, i.e. the entropy of the system is less susceptible to isothermal expansion at higher temperatures. Negative values for (@I/aT), have been reported for many other organic liquids.“, ‘* ‘* 18) Pl o t s of (ag/aT), against x show that (ag/aT), is nearly independent of composition for x < 0.5. At higher values of x, (@/CC), passes through a negative maximum, which corresponds well with the temperature dependent minimum in a plot of /I against x (figure 1).
DIMETHYL
SULFOXIDE
+ METHANOL
681
0.8 0.7 0.6 0.5 0.4
0
0.2
0.4
0.6
0.8
0.3
x FIGURE 2. Energy-volume coefficients, cohesive energy densities, and values of n for (1 -x)CH30H at 298.15 K. A, (ACry/V)T/10-8 J mbs; B, (W/aV),/108 J m-9; C, n. ISOTHERMAL
XDMSO+
COMPRESSIBILITY
Isothermal compressibility expansivity by
is related
to the thermal-pressure
Ic = a//l.
coefficient
and (6)
Numerical values for K for XDMSO+ (I- x)CH30H at 298.15 and 3 18.15 K are given in table 3. For an ideal mixture, the molar volume of the system is given by v;d = xY,“+(l -x>v;, where I/” is the molar volume of the pure component. to pressure, and defining rcid as Kid = -(av;d/apyv;d, yields for the compressibility of an ideal mixture: lcid = xqv,o/v;q-(1 -X)KZV;/V;d. The excess compressibility of the system is, therefore ,p = K-Ki* ,
Differentiation
(7) with respect (8)
(9) (10)
682
K. M. CHAPMAN
AND D. D. MACDONALD
t P w‘ Y
P -0.3 L-I---.__1 0 0.2
0.4
0.6
0.8
1
.Y FIGURE 3. Excessisothermal compressibility, K~, of .,318.15 K.
XDMSO+(~--x)CH&H.
0, 298.15 K;
and is plotted as a function of composition in figure 3 for temperatures of 298.15 and 318.15 K. At 298.15 K the excess compressibility is found to be negative for all values of x with an extremum at x = 0.3 to 0.5. At 318.15 K, however, the excess compressibility appears to pass through a positive maximum at x = 0.7 and 0.75. This is the same region of composition at which plots of /3 against x pass through a minimum. REFERENCES 1. 2. 3. 4. 5. 6. I. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Barton, A. F. M. J. Chem. Ed. 1971,48, 156.
Hildebrand, J. H.; Scott, R. L. Solubility of Non-electrolytes, 3rd ed. Reinhold, New York 1950. Hildebrand, J. H. ; Scott, R. L. Regulur Solutions. Prentice-Hall: New Jersey1962. Gibson, R. E.; Loeffler, 0. H. J. Amer. Chem. Sot. 1939,61,2515. Gibson, R. E.; Loeffler, 0. H. J. Amer. Chem. Sot. 1941, 63, 898. Staveley, L. A. K.; Tupman, W. I.; Hart, K. R. Disc. Faraday Sot. 1954, 15, 130. Dunlap, R. D.; Scott, R. L. J. Phys. Chem. 1%2, 66, 631. Macdonald, D. D. ; Hyne, J. B. Can. J. Chem. 1971,49, 611. Macdonald, D. D.; Hyne, J. B. Can. J. Chem. 1971,49,2636. Macdonald, D. D.; Hyne, J. B.; Swinton, F. L. J. Amer. Chem. Sot. 1970,92,6355. Quitzsch, K.; Prinz, H. ; Suehnel, K. ; Pham Van Sun; Geiseler, G. 2. Phys. Chem. 1969,241,273. Quitzsch, K.; Ulbrecht, H.; Geiseler, G. Z. Phys. Chem. 1967,234, 33. Martin, D. ; Weise, A.; Niclas, H. J. Angew. Chem. Znt. Ed. Engl. 1967, 6, 318. Handbook of Chemistry and Physics, The Chemical Rubber Publishing Co.: Cleveland, Ohio. 1970,51st-. ed. Lindberg, J. J. Finska Kemistsamjimdets Medd. l%l, 70, 33. Fort. R. J.: Moore. W. R. Trans. Furu& Sot. 1965.61,2102. Milkail, S. ‘Z.; Kiiel, W. R. J. Chem. Z&g. Data l%l, 6, 533. Lau, C. F.; Malcolm, G. N.; Fenby, D. V. Aust. J. Chem. 1%9,22, 855. Frank, H. S. J. Chem. Phys. 1945, 13,493. Stull, D. R.; Westrum Jr., E. F.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds. John Wiley. New.York 1969. Hildebrand. J. H. Phvs. Rev. 1929. 34. 984. Allen, G. ; &e, G. ; Wilson, G. J.Po&mer 1960, 1.456.
Thermal pressure and energy-volume coeffkients for dimethyl sulfoxide + methanol KAREN
M. CHAPMAN”
Department of Chemistry, New Zealand
and DIGBY Victoria
D. MACDONALDbsC
University of Wellington,
Wellington,
(Received 5 June 1975; in revised form I9 January 1976)
Density as a function of temperature and thermal-pressure coefficients for dimethyl sulfoxide+methanol are reported. The results are used to derive expansivities, energyvolume coefficients, cohesive energy densities, isothermal compressibilities, and the derivatives of entropy with respectto volume and pressureover the entire range of composition. The variation of these parameters with composition and temperature is briefly discussed.
1. Introduction The isothermal energy-volume coefficient (the “internal thermal pressure coefficient, j3 = (@+W),, by (W/8V),
= T/3-p.
pressure”) is related to the (1)
Extensive compilations of this quantity for pure liquids, including molten salts, are available in the literature,‘lV3’ but only a few studies on liquid mixtures have been reported. (4-1o) Previous work by one of the authors (s-1’) has shown that the energyvolume coefficient is sensitive to changes in liquid “structure” as the composition of a binary mixture is varied. The observed variation of (&Y/a& with composition has been interpreted in terms of the effect of volume on both attractive and repulsive interactions in the system, and it is believed that the composition dependence of this quantity reflects changes in the average intermolecular distance in the liquid.@* 9, In this paper we report the thermal-pressure and energy-volume coefficients of dimethyl sulfoxide (DMSO) + methanol (CH,OH). This pair was chosen for study since it is characterized by strong intercomponent interaction which results in large negative deviations from Raoult’s law and large negative values for the excess enthalpy over the entire range of composition.‘“* 12) a Present address: Department of Chemistry, University of Auckland, Auckland, New Zealand. b Present address: Department of Chemistry, The University of Calgary, Calgary, Alberta, Canada. c To whom correspondence should be sent.
676
K. M. CHAPMAN
AND D. D. MACDONALD
2. Experimental MATERIALS
Spectral grade DMSO was found to contain not more than 0.05 mass per cent of water by Karl Fischer titration, and was used without further purification. The refractive index was found to be 1.4778 at (293.65 + 0.05) K, which compares well with the following values quoted in the literature: n(293.15 K) = 1.477,‘r4) 1.4788,(12) 1.4783,‘r3) and n(298.15 K) = 1.476(14). The melting temperature was 291.6 to 291.7 K (lit., 291.7 K),(r3) and the density at 298.15 K was determined as 1095.3 kg me3 comparing favourably with values of 1095.8,(“) 1095.0,(r2) and 1095.7 kg m-3,W) quoted in the literature. Analar-grade methanol was dried over calcium oxide and distilled twice at atmospheric pressure. Karl Fischer titration indicated a water content of 0.05 to 0.06 mass per cent. The refractive index was found to be 1.3285 at (293.20 rt 0.05) K compared with literature values of n = 1.3287,‘12’ and 1.3288(16’ at 293.15 K and n = 1.326(‘@ at 298.15 K. The density at 298.15 K was found to be 787.0 kg mm3, comparing well with literature values of 786.9,“‘) and 787.0 kg mm3.(12) No impurities could be detected by g.1.c. APPARATUS
AND
METHOD
Densities of various mixtures at temperatures in the range 298.15 to 323.15 K were determined using Sprengel-type pyknometers which were thermostatted to better than +O.Ol K in a water bath. Each pyknometer was standardized using triply distilled water, and all weighings were reduced to masses. Thermal-pressure coefficients were measured using a constant-volume cell similar in design to that previously described.@* ‘) The constant-volume cell was contained in a pressure vessel which was agitated internally by a magnetic stirring bar. The pressure vessel was thermostatted to rtO.01 K in a 18 dm3 oil bath equipped with a Braun Thermomix II temperature controller. In the present work a pressure range of 0.1 to 70 MPa was employed, which is considerably greater than the 0.1 to 2 MPa range used in previous work.@* lo) Pressures were measured using a calibrated 0 to 150 MPa Heise-Bourdon gauge which could be read to better than kO.05 MPa. The temperature inside the pressure vessel was monitored by use of a calibrated platinum resistance thermometer. This thermometer also served to indicate thermal equilibration following pressurization.@“) 3. Results DENSITY
AND
THERMAL
EXPANSION
The densities of XDMSO + (1 -x)CH,OH at six temperatures in the range 298.15 to 323.15 K are given in table 1. The values listed are the averages of at least two determinations for each composition and temperature. Error analysis indicates that the accuracy of the density measurement is +0.2 kg rnm3, which is confirmed by comparison of the measured densities of the two pure components with data from the literature. The densities given in table 1 were used to calculate expansivities LXat
DIMETHYL TABLE
T/K
1. Densities
SULFOXIDE
p, expansivities tl, and values of (OS/&X for xDMSO+(~ as a function of temperature T and mole fraction x
298.15
303.15
308.15
0.7870 0.8342 0.8751 0.9310 0.9591 0.9965 1.0190 1.0372 1.0633 1.0810 1.0953
0.7821 0.8290 0.8699 0.9259 0.9539 0.9912 1.0138 1.0321 1.0583 1.0760 1.0904
0.7772 0.8242 0.8648 0.9205 0.9485 0.9858 1.0085 1.0269 1.0532 1.0710 1.0855
P/10‘ .3
X
0 0.088 0.175 0.309 0.391 0.512 0.599 0.679 0.807 0.902 1
T/K
298.15
K
0.088 0.175 0.309 0.391 0.512 0.599 0.679 0.807 0.902 1
318.15 a/10+
x
0
677
+ METHANOL
12.8OhO.25 12.5O~tO.24 11.55zt0.23 11.25zt0.23 11.07hO.22 10.75ztO.21 10.151tO.20 10.15+~0.20 9.4OIto.19 9.20rto.19 8.96kO.18
K
313.15
12.10&0.25 11.5010.25 11.40~0.25 ll.lOztO.25 11.20&0.25 11.25hO.25 11.15~tO.25 10.5OkO.20 10.10~0.20 9.75zto.20 9.40f0.18
318.15
323.15
0.7680 0.8149 0.8550 0.9103 0.9381 0.9748 0.9976 1.0163 1.0428 1.0608 1.0756
0.7628 0.8102 0.8501 0.9053 0.9328 0.9693 0.9921 1.0110 1.0375 1.0556 1.0703
kg m-3 0.7724 0.8196 0.8600 0.9153 0.9433 0.9803 1.0031 1.0216 1.0480 1.0659 1.0806 298.15
K
- - waPhllo
K-l
-x)CHsOH
5.21 +O.lO 5.41 i-o.10 5.29*0.10 5.59*0.11 5.78&0.11 6.OOztO.12 5.94kO.12 6.2OhO.12 6.12kO.12 6.2710.12 6.39hO.13
- ,8 J K-l
318.15
K
Pa-l
mol-’
5.05*0.10 5.09f0.10 5.35*0.10 5.64*0.11 5.98kO.12 6.42kO.13 6.67kO.14 6.54kO.14 6.71 rtO.14 6.77hO.14 6.83&-0.14
298.15 and 318.15 K. The method adopted for determining ct was to compute the mean coefficient (a) for the temperature interval TI to T2 according to (a> = -(In PZ - In ~dl(T2 - TA (2) and then to extrapolate this quantity against mean temperature to the temperature of interest. Numerical values for a at 298.15 and 3 18.15 K are listed in table 1. The estimated precision of a is +2 per cent. Lau, Malcolm, and Fenby, and Martin, Weise, and Niclaso3) report values of (9.9 + 0.6) x 10e4 K-’ and 8.8 x loo4 K-l, respectively, for pure DMSO at 298.15 K. Our value of (8.96 ) 0.18) x 10m4 K-l is in reasonable agreement. THERMAL
PRESSURE
COEFFICIENTS
Plots of pressure against temperature for apparent constant volume were found to be linear, and reproducible with respect to ascending and descending temperature changes. Accordingly, the results were fitted to the linear expression: P = A,,T+C, where A,, is the apparent thermal pressure coefficient. Each &,
(3) value was corrected
678
K. TABLE
-__
T/K
2. Thermal b/10”
Pa K-l
CHAPMAN
pressure
/I/lo6
322.65
295.05 298.55 306.35 313.15 320.65
x = 0.549 295.35 18.20 298.05 16.88 308.75 15.36 317.15 14.99
9. b From
T/K
-x)CH30H p/lo5
at various Pa K-l
320.65
T/K
15.34
313.15 317.15 322.55
13.76 13.38 12.91
reference
Pa K-l
x=1.000 297.15 17.30 298.65 16.96 b 17.06 = 309.45 16.49 310.95 16.59 b 16.05 c 322.65 15.13 324.95 15.45 330.65 14.63
x = 0.698 295.15 18.58 299.55 15.14 305.75 13.09 317.15 12.63
8. c From
jI/106
x = 0.890 294.95 18.10 299.15 17.29 301.65 16.29 309.65 16.11 311.35 16.08 314.15 15.38 321.15 15.11
x = 0.672 15.43 299.15 307.65 14.29 311.15 13.93
19.09 16.82 14.05 13.59 13.40
temperatures
x = 0.192 295.95 18.57 299.55 15.85 300.85 15.40 303.55 15.17 308.15 13.79 310.55 13.55
x = 0.497 294.35 17.62 298.65 17.04 16.07 311.15
16.44 15.66 15.25 15.11
reference
D. MACDONALD
x = 0.206 297.15 13.44 302.65 12.47 12.12 312.35 11.55 317.65
x = 0.596
12.68
reference
Pa K-l
x = 0.418 294.75 17.20 298.45 311.15 315.45 321.15
D.
for XDMSO+(~
x = 0.094 295.15 11.97 297.15 11.55 301.35 11.26 305.95 10.79 316.65 10.12 324.15 9.83
9.59 9.80 a 9.35 9.27 a 8.87 8.94” 8.48 8.44 a
x = 0.291 294.55 15.03 299.15 14.37 303.15 14.09 307.55 13.62 316.35 13.15
’ From
AND
coefficients
T/K -~-~__~__~-
x=0 294.15 296.15 302.15 303.65 309.75 313.45 321.45 324.45
M.
18.
for the finite expansion and compression of glass in the usual manner,@~g. I*) and the corrected values are given in table 2 as a function of temperature and composition. Values for j? taken from the literature for pure DMSO and CH30H are also given in table 2 for comparison. Plots of fl against T for various values of mole fraction x were found to be nonlinear, particularly for x = 0.549 to 0.792. Values of (@I/aT),, estimated by drawing tangents to the curves of /I against T are given in table 3. When /? varies nearly TABLE
T K X
:094 01206 0.291 0.418 0.497 0.549
3. Temperature
-mm-),
K
lo6 Pa KeZ 298.15 0.0410.02 0.11zt0.04 0.1510.05 0.12&0.04 0.14*0.05 0.12~0.04 0.25hO.15
derivatives XDMSC+
K
10e9 Pa-’ 298.15
K
1.36f0.04 1.05&0.03 0.87f0.03 0.77+0.03 0.66rf10.03 0.63f0.03 0.63 SO.03
318.15 1.40~0.04 1.15+0.03 0.98&0.03 0.85f0.03 0.73*0.03 0.72kO.03 0.74&0.03
K
of /I and isothermal (1 -x)CH,OH
T K _~-x 0.596 0.672 0.698 0.792 0.890 1
compressibilities
for
- WaT),
K
lo6 Pa Ke2 298.15
K
0.5610.16 0.60*0.20 0.7OkO.22 0.53f0.16 0.11 kO.03 0.08fO.02
10-O 298.15
K
0.61 zkO.03 0.65&0.03 0.63ztO.03 0.58 ~‘~0.03 0.53f0.03 0.5210.03
Pa-’ 318.15
K
0.82hO.03 0.81&0.03 0.84*0.03 0.75 zlcO.03 0.65ztO.02 0.6010.02
DIMETHYL
SULFOXIDE
679
+ METHANOL
linearly with temperature, (f@/ZYQ, could be estimated to within f0.005 MPa K- ‘. However, for x = 0.549 to 0.792, where fi exhibits a strong non-linear dependence upon temperature, a somewhat higher uncertainty of kO.02 MPa KS2 seems appropriate. ENERGY-VOLUME
COEFFICIENT
AND
COHESIVE
ENERGY
DENSITIES
The energy-volume coefficient is related to the cohesive energy AU,/V by(19’ W-J/W,
(4)
= nWv/V),
where AU, is the energy of vaporization of the mixture to the perfect-gas state and n is an empirical parameter. The energy of vaporization of a real liquid mixture to the perfect-gas state can be calculated using’*, 9, AU, =x~H~,,+x~H~,~--H~-RT, (5) where AH, 1 and AH, z are the enthalpies of vaporization of components 1 and 2 to the perfect-gas state, and HE is the molar excess enthalpy of the mixture. Values for AH, 1, AH, 2, and HE at 298.15 K were taken from the literature,‘20Y * ‘, ‘*I and combined with molar volumes (calculated from densities given in table 1) to yield the values for A&W listed in table 4. Values of the energy-volume coefficient, (W/l3V),, (calculated using equation 1) and the parameter n are also listed in table 4. TABLE
X
0 0.094 0.206
0.291 0.418 0.497
4. Energy-volume
coefficients and cohesive energy densities for at 298.15 K
(au/avh.
WJ,IV)T
lOa Jrne3
108 J me3
2.83&0.05 3.38&0.06 3.93-10.07 4.43f0.08 4.88&0.09 5.1O=kO.10
8.599;tO.O04 8.400f0.004 8.233&0.004 8.062~0.003 7.907~0.003 7.756~0.003
n
X
0.33f0.01 0.40f0.01
0.596 0.698
w/a VI,
--_
108Jm-3
4.99kO.10 4.68rtO.10
XDMSO+(~
WW% ___.
lOa J me3
7.6OlrtO.003 7.452&0.003
-x)CH30H
n 0.66f0.01 0.63&0.01
0.48&0.01
0.792
5.0110.10
7.309rtO.002
0.6910.01
0.551tO.01 0.62&0.01 0.66f0.01
0.890
5.16*0.10
7.174rtO.002
0.71i-0.01
1
5.16%0.10
7.041f0.002
0.73kO.02
4. Discussion THE
THERMAL
PRESSURE
AND
ENERGY-VOLUME
COEFFICIENTS
Thermal pressure coefficients for DMSO + CH,OH, interpolated from the values given in table 2, are plotted in figure 1 as a function of x. At all temperatures from 295.15 to 318.15 K, fl initially increases with the addition of DMSO to methanol, culminating in a maximum at about x = 0.5. Further addition of DMSO results in /I passing through a minimum (with a possible exception at 295.15 K) at x = 0.65 to 0.70. The minimum becomes more pronounced with increasing temperature. Maxima in plots of /I against x have been found for other binary mixtures, including methanol + water, (9) t-butanol + water ,(9) and DMSO + water.(*)
680
K. M. CHAPMAN
AND D. D. MACDONALD I
I
I
I
20
I&I
/I /
/I
I
‘I Gc/ I/
--
( 18
I
I/
318:15 K
1 16 l2 8
12
8 0
0.2
0.4
0.6
0.8
1
0
0.2
.0.4
X
FIGURE 1. Thermal pressure coefficients for 298.15, 308.15, and 318.15 K.
0.6
0.8
1
X XDMSO+(~
--x)CH30H
plotted against x at 295.15,
The derivatives @S/al’), and @Slap), are equal to j? and -crV, respectively, where V is the molar volume of the mixture. Values for these two derivatives are given in figure 1 and table 1, and are found to be positive, and negative, respectively, for all values of X. It is of interest that @S/aV), passes through a positive maximum at x = 0.5, demonstrating that at this composition the entropy of the system is most susceptible to isothermal expansion. This is the same composition at which the excess volume(12S13) passes through a negative maximum, thereby lending support to the hypothesis (& ‘) that the variation of /I with x reflects, at least to some extent, changes in intermolecular distance. In contrast to the behaviour of jI, @S/~p), varies monotonically with x at both temperatures considered. The general features exhibited by the plots of fi against x are also shown by the plots of @U/aV), against x as dictated by equation (1). For this reason, the curves of (aU/aV), against x for all temperatures are not presented. However, values for @U/a&, AUJV, and n at 298.15 K are plotted as a function of composition in figure 2. The cohesive energy density, A&/V, exhibits an almost monotonic variation with x. On the other hand, the parameter n reflects, to a large extent, the dependence of /I and (aU/aV), on x. Previous work (‘Lo’) has shown that for non-polar liquids n x 1, as predicted for a van der Waals fluid. For strongly associated liquids, and in particular those which are hydrogen bonded, n 4 1. This observation is supported by the present work in that n is found to increase from 0.33 for x = 0 to 0.73 for x = 1. The values of (@I/87’), given in table 3 shows that for all values of x this quantity is negative, i.e. the entropy of the system is less susceptible to isothermal expansion at higher temperatures. Negative values for (@I/aT), have been reported for many other organic liquids.“, ‘* ‘* 18) Pl o t s of (ag/aT), against x show that (ag/aT), is nearly independent of composition for x < 0.5. At higher values of x, (@/CC), passes through a negative maximum, which corresponds well with the temperature dependent minimum in a plot of /I against x (figure 1).
DIMETHYL
SULFOXIDE
+ METHANOL
681
0.8 0.7 0.6 0.5 0.4
0
0.2
0.4
0.6
0.8
0.3
x FIGURE 2. Energy-volume coefficients, cohesive energy densities, and values of n for (1 -x)CH30H at 298.15 K. A, (ACry/V)T/10-8 J mbs; B, (W/aV),/108 J m-9; C, n. ISOTHERMAL
XDMSO+
COMPRESSIBILITY
Isothermal compressibility expansivity by
is related
to the thermal-pressure
Ic = a//l.
coefficient
and (6)
Numerical values for K for XDMSO+ (I- x)CH30H at 298.15 and 3 18.15 K are given in table 3. For an ideal mixture, the molar volume of the system is given by v;d = xY,“+(l -x>v;, where I/” is the molar volume of the pure component. to pressure, and defining rcid as Kid = -(av;d/apyv;d, yields for the compressibility of an ideal mixture: lcid = xqv,o/v;q-(1 -X)KZV;/V;d. The excess compressibility of the system is, therefore ,p = K-Ki* ,
Differentiation
(7) with respect (8)
(9) (10)
682
K. M. CHAPMAN
AND D. D. MACDONALD
t P w‘ Y
P -0.3 L-I---.__1 0 0.2
0.4
0.6
0.8
1
.Y FIGURE 3. Excessisothermal compressibility, K~, of .,318.15 K.
XDMSO+(~--x)CH&H.
0, 298.15 K;
and is plotted as a function of composition in figure 3 for temperatures of 298.15 and 318.15 K. At 298.15 K the excess compressibility is found to be negative for all values of x with an extremum at x = 0.3 to 0.5. At 318.15 K, however, the excess compressibility appears to pass through a positive maximum at x = 0.7 and 0.75. This is the same region of composition at which plots of /3 against x pass through a minimum. REFERENCES 1. 2. 3. 4. 5. 6. I. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Barton, A. F. M. J. Chem. Ed. 1971,48, 156.
Hildebrand, J. H.; Scott, R. L. Solubility of Non-electrolytes, 3rd ed. Reinhold, New York 1950. Hildebrand, J. H. ; Scott, R. L. Regulur Solutions. Prentice-Hall: New Jersey1962. Gibson, R. E.; Loeffler, 0. H. J. Amer. Chem. Sot. 1939,61,2515. Gibson, R. E.; Loeffler, 0. H. J. Amer. Chem. Sot. 1941, 63, 898. Staveley, L. A. K.; Tupman, W. I.; Hart, K. R. Disc. Faraday Sot. 1954, 15, 130. Dunlap, R. D.; Scott, R. L. J. Phys. Chem. 1%2, 66, 631. Macdonald, D. D. ; Hyne, J. B. Can. J. Chem. 1971,49, 611. Macdonald, D. D.; Hyne, J. B. Can. J. Chem. 1971,49,2636. Macdonald, D. D.; Hyne, J. B.; Swinton, F. L. J. Amer. Chem. Sot. 1970,92,6355. Quitzsch, K.; Prinz, H. ; Suehnel, K. ; Pham Van Sun; Geiseler, G. 2. Phys. Chem. 1969,241,273. Quitzsch, K.; Ulbrecht, H.; Geiseler, G. Z. Phys. Chem. 1967,234, 33. Martin, D. ; Weise, A.; Niclas, H. J. Angew. Chem. Znt. Ed. Engl. 1967, 6, 318. Handbook of Chemistry and Physics, The Chemical Rubber Publishing Co.: Cleveland, Ohio. 1970,51st-. ed. Lindberg, J. J. Finska Kemistsamjimdets Medd. l%l, 70, 33. Fort. R. J.: Moore. W. R. Trans. Furu& Sot. 1965.61,2102. Milkail, S. ‘Z.; Kiiel, W. R. J. Chem. Z&g. Data l%l, 6, 533. Lau, C. F.; Malcolm, G. N.; Fenby, D. V. Aust. J. Chem. 1%9,22, 855. Frank, H. S. J. Chem. Phys. 1945, 13,493. Stull, D. R.; Westrum Jr., E. F.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds. John Wiley. New.York 1969. Hildebrand. J. H. Phvs. Rev. 1929. 34. 984. Allen, G. ; &e, G. ; Wilson, G. J.Po&mer 1960, 1.456.