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Enthalpies of mixing and excess Gibbs free energies of mixtures of octamethylcyclotetrasiloxane+cyclopentane at 291.15, 298.15, and 308.15 K
J. Chem. Thermocfvnamics 1970, 2. 359-365
Enthalpies of mixing and excess Gibbs free energies of mixtures octamethyIcyclotetrasiloxane+cycIopentane at 291.15, 298.15, and 308.15 K
of
K. N. MARSH Department of Physical and Inorganic Chemistry, The University of New England, Armidale, N.S. W., Australia (Received 20 November 1969) The enthalpies of mixing of octamethylcycIotetrasiloxane+cyclopentane have been measured at 291.15, 298.15, and 308.15 K with an isothermal displacement calorimeter. Vapour pressures of the mixtures have been measured at the same temperatures by a precision static vapour pressure method. The enthalpy of mixing has a maximum of 227 J mol-1 at 291.15 K and the enthalpies decrease with increase in temperature. The excess Gibbs free energy, calculated from the vapour pressures, has a minimum of - 199 J mol-l at 291.15 K. This function becomes more negative with increase in temperature. The excess volumes, measured previously, change sign with composition and are independent of temperature.
1. Introduction This paper is one of a series of papers reporting the thermodynamic properties of mixtures formed from small and large globular molecules. Such systems are of particular interest as they may give some guide to the form of the combining rules which are assumed in formulating theories of liquid mixtures. In previous papers”-3’ we presented some thermodynamic properties of mixtures of octamethylcyclotetrasiloxane with benzene and carbon tetrachloride. We present here vapour pressure measurements and enthalpy of mixing measurements for the system octamethylcyclotetrasiloxane + cyclopentane at 29 1.15, 298.15, and 308.15 K. 2. Experimental Octamethylcyclotetrasiloxane (OMCTS) and cyclopentane were purified as described previously.“# 4, The purity of the samples was determined by g.1.c. using a 10 m x 6 mm SE 30 column and a hydrogen flame ionization detector. Columns with a stationary phase of Apiezon L and Carbowax W were also used in order to guard against the possibility of the presence of impurities having the same retention time on the SE 30 column. We believe that both samples had a purity of at least 99.97 moles per cent. The density of cyclopentane at 298.15 K was found to be 0.74036 g cme3. This is in good agreement with the value of 0.74034 g cme3 obtained by Boubllk et al.“’ The A.P.I. Project 44 tablesc6) list a value of 0.74045 g cmm3. The precision static vapour
K. N. MARSH
360
pressure apparatus, described previously, (’ ’ has been modified by replacing the 10 mm “Veridia” precision bore manometer by a 19 mm “Corning” precision bore manometer. This change reduced the possibility of errors in the pressure measurements resulting from capillary effects. (I’ Also the mercury+ toluene regulator has been replaced by a thermistor control system capable of controlling the temperature in the thermostat to better than 0.001 K. (7) Enthalpy of mixing experiments were performed in an isothermal displacement calorimeter. The operation of this apparatus has been described in detail.“’ All temperatures were measured with a calibrated platinum resistance thermometer in terms of the International Practical Temperature Scale of 1948. 3. Results The activity coefficient of cyclopentane for a particular mixture was calculated from a knowledge of the total volume, the total amount of each component in the vapour pressure cell, and the total pressure. (I) Values for the vapour pressures, molar volumes, and second virial coefficients of cyclopentane and the molar volumes and vapour pressures of OMCTS which were used in the calculations are listed in table 1. The molar volumes of cyclopentane at 29 1.15 K and 308.15 K were calculated from the densities listed in the A.P.I. Project 44 tables. (6) The molar volume at 298.15 K was calculated from the density reported here. The molar volumes of OMCTS were calculated from previous density values. (I) The second virial coefficients of cyclopentane were calculated from the enthalpies of vaporization of McCullough et ~1.‘~’ Their values are in excellent agreement with those calculated by Hermsen and Prausnitz(g’ from critical constants and the Pitzer ascentric factor. TABLE
1. Molar Volumes, second virial coefficients,and vapour pressures of the pure components. Cyclopentane
T/K -__. 291.15 298.15 308.15
V&m3 mol-l .-.~--~~.-~ 93.83 * 94.71 95.98
&/cm3
mol-l
-1122 -106 4 -991
OMCTS p/kN me2
v,/cm3 mol-’
___ .p/kN m-2
,31.892 42.339 61.847
309.52 312.12 315.94
0.079 0.133 0.269
The vapour pressures of cyclopentane reported here are approximately 15 N me2 above the values calculated from the Antoine equation quoted by the Bureau of Standards.(6’ Boublik et aLc7) have measured the vapour pressure of cyclopentane at 298.15, 308.15, and 318.15 K using an equilibrium still. Their value at 298.15 K, 42.265 kN me2, is considerably lower than our value. However their value at 308.15 K, 61.866 kN m-‘, is in good agreement with that reported here. Scatchard et ai. have noted that there are difficulties in designing a recirculating still which operates satisfactorily at low pressures when temperatures are close to room temperature. Generally at these temperatures the recirculating still gives lower values of the vapour pressure compared with those obtained from static measurements.(” 1‘) The total vapour pressures and activity coefficientsf, of cyclopentane, expressed as In I., of mixtures of OMCTS(l)+cyclopentane(2) are listed in table 2. together with
rABLE
K:
K:
K:
298.15
308.15
y ) {-0.34698-0.006 2. I
{-0.33589-0.006
RTxlxz 1-0.2(1-2x,)
=
( -0.32804-0.004
4716(1
-22.~I)-0.00
554(1-2x1)-0.00
-2.~~)-0.00
6697(1-2.~~)~};
standard
standard
standard
0.80057 0.81982 0.88018
0.79771 0.81529 0.87906
0.79617 0.81315 0.87834
Xl
(I)+cyclopentane
-2.~~)~:; 2765(1--2~~)~);
2449(1
-0.05832 -0.09571 -0.1226 -0.1578
308.15 K 37.877 29.546 24.350 18.201
0.34540 0.46898 0.55025 0.65212
254(1
-0.05561 -0.09163 -0.1177 -0.1514
298.15 K 26.167 20.465 16.916 12.712
0.34152 0.46425 0.54483 0.64601
0.34251 0.46622 0.54696 0.64805
m-”
of OMCTS
-0.05349 -0.08861 -0.1136 -0.1467
p/kN
in mixtures
291.15 K 19.808 15.541 12.872 9.689
.Vl
of cyclopentane
zzz -.__-~ RTX& 1-0.2(1-2x1)
-0.00360 -0.01353 -0.02463 -0.02569
-0.00301 -0.01256 -0.02257 -0.02428
GE = 1 -oRl:T
G”
G”
57.034 51.710 47.591 47.168
0.07277 0.14926 0.20715 0.21325
291.15
39.129 35.489 32.855 32.419
0.07178 0.14878 0.20323 0.21233
lnfi
coefficientsfi
-0.00270 -0.01240 -0.02095 -0.02347
and activity
mm2
29.503 26.762 24.902 24.477
p/kN
Xl
0.07140 0.14845 0.20021 0.21174
pressuresp
2. Vapour
deviation
deviation
deviation
9.993 8.978 5.899
6.971 6.341 4.102
in lnfi
in lnfi
in In,fL
m-a
5.320 4.850 3.114
p/kN
(2) at 291.15,
and 308.15
= 0.00018
= 0.00009
z 0.00013
-0.‘097 --0.2180 -0.2447
-0.2043 -0.2098 -0.2325
-0.1987 -0.2053 -0.2275
In fa
298.15,
K
0.10655 0.11857 0.13024 0.15271 0.17405 0.19433 0.21365 0.25288
0.09741 0.10973 0.12479 0.15265 0.17444 0.19406 0.21293
-0.1 -0.0 -0.1 -0.1 -0.1 -0.0 -0.0 : 0.0
-to.0 -0.0 -0.0 -0.1 -0.1 -0.1 -0.0
6.5 15.8 33.6 50.0 64.9 78.8 91.4 103.1
6.6 15.7 32.6 48.4 62.6 76.1 88.1
0.00506 0.01240 0.02705 0.04127 0.05509 0.06853 0.08154 0.09422
0.005 27 0.012 78 0.027 28 0.041 66 0.055 36 0.069 04 0.082 01
98.9 109.9 126.7 142.2 155.3 165.8 174.8
113.8 123.6 132.6 148.5 161.9 173.3 182.8 198.9
110.9 126.9 141.0 153.3 164.1 176.3 186.4 195.2
HE J mol-1 6HE
+0.2 $0.3 +0.4
f0.1
-0.0 $0.0
-0.0
fO.0 to.0 i-o.0 +o.o -t 0.0 f0.3
-i-o.1 +0.1
-0.2 -0.4 +0.6
-0.1
-to.0
10.1 f0.1 $0.1
J mol-’
308.15
298.15
291.15
-0.1
-0.2 -0.2 -0.2 -0.2
-0.1 -0.1
-0.1
-0.2 -0.3 -0.3 -0.2
+0.1 -t 0.0 -0.1
-0.2 -0.2 -0.2
$0.0 -0.0
-0.6 +0.4 -10.2
0.55485 0.61093 0.67963 0.76574 0.87683 0.94541
0.50819
0.55393 0.61090 0.67879 0.76511 0.80594 0.87734 0.90103 0.92717 0.94842
0.48953 0.53534 0.59062 0.65862 0.74432 0.85566 0.92484 0.97198
standard deviation = 0.3 J mol-I. standard deviation = 0.2 J mol-I. standard deviation = 0.2 J mol-I.
189.4 196.2 202.5 207.6 210.7 209.4 206.1
206.0 212.6 218.2 221.5 221.6 220.2 216.8 210.6
202.8 210.7 217.9 222.5 225.8 226.9 224.4
194.8
HE J mol-’
(2) at 291.15, 298.15, and 308.15 K.
J molwl; J mol-I; J mol-I;
0.25275 0.27579 0.30352 0.33684 0.37910 0.43441 0.46802
K
0.27599 0.30375 0.33771 0.38023 0.40528 0.43505 0.46881 0.50821
K
0.27653 0.30613 0.33285 0.36469 0.40325 0.45094
0.25188
0.23367
K
Xl
(l)+cyclopentane
291.15 K: 6HE = HE-x1x2(1332.5-1128.7xl+410.7x:) 298.15 K: SHE = HE-~I~a(1310.2-l128.0x1+410.4x~) 308.15 K: SHE = HE-x&1259.2-l116.6x1+418.4x~)
0.13809 0.15564 0.17249 0.19394 0.21431 0.23172
0.11980
0.10071
10.1 io.l
+0.2
+0.1 -i-O.1
-t 0.0 10.0 -i- 0.1
3.4 9.8 19.9 38.7 55.8 71.5 85.8 98.9
Xl
0.00257 0.00743 0.01529 0.03063 0.04551 0.05993 0.07393 0.08752
-..
&HE J mol-1
~- HE J mol-’
3. Enthalpies of mixing of OMCTS
.Yl
TABLE
199.9 190.0 174.6 151.4 116.4 64.7 29.6
104.6 68.5 55.5 41.4 29.3
184.3 160.3 123.8
200.5
16.7
44.1
219.3 210.4 195.8 172.9 137.4 82.1
__-HE J mol-1
-0.3 -0.2
-0.1
t 0.0 -t 0.2 i 0.3 f0.3
-m0.3 :ro.3 -0.2 -0.0 -0.4 -0.3 -0.5
0.1 0.2
-0.2 0.0 t 0.2 -1-0.4 y-o.4 -0.3 -0.4 -0.3
.__SHE ~. J mol-’
-86.4 - 145.9 - 182.4 -199.1 - 198.5
-91.0 -153.5 -191.7 - 209.0 -208.1
-97.8 - 164.5 -205.0 -223.2 -222.2
0.1 0.2 0.3 0.4 0.5
0.1 0.2 0.3 0.4 0.5
0.1 0.2 0.3 0.4 0.5
103.7 168.4 202.0 211.1 201.4
108.1 176.2 211.8 221.9 212.2
110.1 179.7 216.5 227.2 217.7
HE J___mol-’
-0.0078 0.0072 0.0257 0.0394 0.0461
-0.0078 0.0072 0.0257 0.0394 0.0461
-0.0078 0.0072 0.0257 0.0394 0.0461
308.15
298.15
291.15
OMCTS
____ VE cm3 mol - 1
for the system
The excess volumes were calculated from the equation? VE =1x~x~(O.l84l-O.O64(1-2x~)-O.14o(l-2x~)~-O.168(1-2x~)~-O.1O6(1-2x~)*}
GE J mol-’
4. Excess functions
Xl
TABLE
K
K
K
0.6 0.7 0.8 0.9
0.6 0.7 0.8 0.9
0.6 0.7 0.8 0.9
Xl
(I)+cyclopentane
cm3 mol-’
-204.5 -172.1 ~~ 126.4 -68.8
-191.4 -160.8 -117.8 -63.9
- 182.8 -153.8 -112.8 -61.3
GE J mol-’
(2) at rounded
177.6 143.4 101.4 53.4
187.5 151.5 107.3 56.5
192.8 156.2 110.8 58.4
HE J mol-’
mole
0.0462 0.0410 0.0306 0.0170
0.0462 0.0410 0.0306 0.0170
0.0462 0.0410 0.0306 0.0170
VE cm3 mol-’
fractions.
364
K. N. MARSH
the smoothing equations and the standard deviations cyclopentane was calculated from the total pressure approximations for the partial pressure of OMCTS. previously. (I) The smoothing equation used was Scott:“2’
in lnfi. The partial pressure of by using a method of successive This method has been described that suggested by Myers and
GE =
(1)
where k is a skewing factor. From equation (1) we deduce for In fi the relation: m “x’t1-2x1)“-’ Inf2 =nzo [l-k(l-2X,)]2
{2n+1-2x,(l+n)-k[2n-1-2x,(3n-l)+4nx:]).
(2)
The coefficients A,, Ai, and A, and the skewing factor k were determined by a least squares fit of equation (2) to the experimental results after introducing a weighting function proportional to x2. (i) The smoothing equations listed in table 2 are expressed in terms of equation (1) from which GE can be calculated directly. The enthalpies of mixing at the three temperatures are listed in table 3, together with the smoothing equations and the standard deviations from the smoothing equations.
4. Discussion The excess functions GE, HE, and VE at rounded mole fractions are listed in table 4. The excess volumes were calculated from results reported previously.(3’ An indication of the accuracy of the vapour pressure measurements can be obtained from the value of HE calculated from the variation of GE with temperature according to the equation HE = GE- T(8GE/i3Tjp.
(3)
The excess Gibbs energy varies linearly with temperature, within experimental limits, over the whole composition range, leading to a value of HE = 206 J mol-’ for the equimolar mixture at a temperature close to 298.15 K. This compares more than favourably with the directly determined value of 212 J mol- ’ at 298.15 K. We have previously estimated (2) that values of HE calculated from our vapour pressure measurements should be accurate to +25 J mol-‘. The excess Gibbs free energy was found to have its minimum value at a mole fraction of OMCTS of 0.44 at all temperatures. The enthalpy of mixing showed a maximum at a mole fraction of OMCTS of 0.41 and decreased linearly (to within 5 1 J mol-l) with temperature. At mole fractions close to that at which HE has its maximum value, the temperature coefficient aH E/aT is - 0.9 J K- i mol- ‘. The excess volumes were found to be independent of temperature and to change sign with composition. @)At mole fractions of OMCTS less at 0.15 the excess volume is negative.
This work was supported by a grant from the Australian Research Grants Committee. I am grateful to Miss Barbara J. Levien for measuring the density of cyclopentane.
THERMODYNAMICS
OF MIXTURES
365
REFERENCES I. Marsh, K. N. Trans. Furudav Sot. 1968, 64, 883. 2. Marsh, K. N.; Tomlins, R. P. Trans. Far&y Sot. 1970, 66, 783. 3. Levien, B. J.; Marsh, K. N. J. Chem. Thermodynamics 1970, 2, 227. 4. Stokes, R. H.; Marsh, K. N.; Tomlins, R. P. J. Chem. Thermodynamics 1969, 1, 377. 5. Boublik, J.; Lam, V. T.; Murakami, S.; Benson, G. C. J. Phys. Chem. 1969,73,2356. 6. Rossini, F. D.; editor. Amer. Petrol. Inst. Project 44 Tables 1967. 7. Stokes, R. H.; Marsh, K. N.; Tomlins, R. P. J. Chem. Thermodynamics 1969, 1, 211. 8. McCullough, J. P.; Pennington, R. E.; Smith, J. C.; Hossenlopp, I. A.; Waddington, G. J. Amer. Chem. Sac. 1959, 81, 5880. 9. Hermsen, R. W.; Prausnitz, J. M. Chem. Eng. Sci. 1963, 18, 485. 10. Scatchard, G.; Ticknor, L. B. J. Amer. Chem. Sot. 1952, 74, 3124. 11. Baxendale, J. H.; Eniisttin, B. V. ; Stern, J. Phil. Trans. Roy. Sot. London, Ser. A. 1951, 243, 169. 12. Myers, D. B.; Scott, R. L. Znd. Eng. Chem. 1963, 55, 43.
Enthalpies of mixing and excess Gibbs free energies of mixtures octamethyIcyclotetrasiloxane+cycIopentane at 291.15, 298.15, and 308.15 K
of
K. N. MARSH Department of Physical and Inorganic Chemistry, The University of New England, Armidale, N.S. W., Australia (Received 20 November 1969) The enthalpies of mixing of octamethylcycIotetrasiloxane+cyclopentane have been measured at 291.15, 298.15, and 308.15 K with an isothermal displacement calorimeter. Vapour pressures of the mixtures have been measured at the same temperatures by a precision static vapour pressure method. The enthalpy of mixing has a maximum of 227 J mol-1 at 291.15 K and the enthalpies decrease with increase in temperature. The excess Gibbs free energy, calculated from the vapour pressures, has a minimum of - 199 J mol-l at 291.15 K. This function becomes more negative with increase in temperature. The excess volumes, measured previously, change sign with composition and are independent of temperature.
1. Introduction This paper is one of a series of papers reporting the thermodynamic properties of mixtures formed from small and large globular molecules. Such systems are of particular interest as they may give some guide to the form of the combining rules which are assumed in formulating theories of liquid mixtures. In previous papers”-3’ we presented some thermodynamic properties of mixtures of octamethylcyclotetrasiloxane with benzene and carbon tetrachloride. We present here vapour pressure measurements and enthalpy of mixing measurements for the system octamethylcyclotetrasiloxane + cyclopentane at 29 1.15, 298.15, and 308.15 K. 2. Experimental Octamethylcyclotetrasiloxane (OMCTS) and cyclopentane were purified as described previously.“# 4, The purity of the samples was determined by g.1.c. using a 10 m x 6 mm SE 30 column and a hydrogen flame ionization detector. Columns with a stationary phase of Apiezon L and Carbowax W were also used in order to guard against the possibility of the presence of impurities having the same retention time on the SE 30 column. We believe that both samples had a purity of at least 99.97 moles per cent. The density of cyclopentane at 298.15 K was found to be 0.74036 g cme3. This is in good agreement with the value of 0.74034 g cme3 obtained by Boubllk et al.“’ The A.P.I. Project 44 tablesc6) list a value of 0.74045 g cmm3. The precision static vapour
K. N. MARSH
360
pressure apparatus, described previously, (’ ’ has been modified by replacing the 10 mm “Veridia” precision bore manometer by a 19 mm “Corning” precision bore manometer. This change reduced the possibility of errors in the pressure measurements resulting from capillary effects. (I’ Also the mercury+ toluene regulator has been replaced by a thermistor control system capable of controlling the temperature in the thermostat to better than 0.001 K. (7) Enthalpy of mixing experiments were performed in an isothermal displacement calorimeter. The operation of this apparatus has been described in detail.“’ All temperatures were measured with a calibrated platinum resistance thermometer in terms of the International Practical Temperature Scale of 1948. 3. Results The activity coefficient of cyclopentane for a particular mixture was calculated from a knowledge of the total volume, the total amount of each component in the vapour pressure cell, and the total pressure. (I) Values for the vapour pressures, molar volumes, and second virial coefficients of cyclopentane and the molar volumes and vapour pressures of OMCTS which were used in the calculations are listed in table 1. The molar volumes of cyclopentane at 29 1.15 K and 308.15 K were calculated from the densities listed in the A.P.I. Project 44 tables. (6) The molar volume at 298.15 K was calculated from the density reported here. The molar volumes of OMCTS were calculated from previous density values. (I) The second virial coefficients of cyclopentane were calculated from the enthalpies of vaporization of McCullough et ~1.‘~’ Their values are in excellent agreement with those calculated by Hermsen and Prausnitz(g’ from critical constants and the Pitzer ascentric factor. TABLE
1. Molar Volumes, second virial coefficients,and vapour pressures of the pure components. Cyclopentane
T/K -__. 291.15 298.15 308.15
V&m3 mol-l .-.~--~~.-~ 93.83 * 94.71 95.98
&/cm3
mol-l
-1122 -106 4 -991
OMCTS p/kN me2
v,/cm3 mol-’
___ .p/kN m-2
,31.892 42.339 61.847
309.52 312.12 315.94
0.079 0.133 0.269
The vapour pressures of cyclopentane reported here are approximately 15 N me2 above the values calculated from the Antoine equation quoted by the Bureau of Standards.(6’ Boublik et aLc7) have measured the vapour pressure of cyclopentane at 298.15, 308.15, and 318.15 K using an equilibrium still. Their value at 298.15 K, 42.265 kN me2, is considerably lower than our value. However their value at 308.15 K, 61.866 kN m-‘, is in good agreement with that reported here. Scatchard et ai. have noted that there are difficulties in designing a recirculating still which operates satisfactorily at low pressures when temperatures are close to room temperature. Generally at these temperatures the recirculating still gives lower values of the vapour pressure compared with those obtained from static measurements.(” 1‘) The total vapour pressures and activity coefficientsf, of cyclopentane, expressed as In I., of mixtures of OMCTS(l)+cyclopentane(2) are listed in table 2. together with
rABLE
K:
K:
K:
298.15
308.15
y ) {-0.34698-0.006 2. I
{-0.33589-0.006
RTxlxz 1-0.2(1-2x,)
=
( -0.32804-0.004
4716(1
-22.~I)-0.00
554(1-2x1)-0.00
-2.~~)-0.00
6697(1-2.~~)~};
standard
standard
standard
0.80057 0.81982 0.88018
0.79771 0.81529 0.87906
0.79617 0.81315 0.87834
Xl
(I)+cyclopentane
-2.~~)~:; 2765(1--2~~)~);
2449(1
-0.05832 -0.09571 -0.1226 -0.1578
308.15 K 37.877 29.546 24.350 18.201
0.34540 0.46898 0.55025 0.65212
254(1
-0.05561 -0.09163 -0.1177 -0.1514
298.15 K 26.167 20.465 16.916 12.712
0.34152 0.46425 0.54483 0.64601
0.34251 0.46622 0.54696 0.64805
m-”
of OMCTS
-0.05349 -0.08861 -0.1136 -0.1467
p/kN
in mixtures
291.15 K 19.808 15.541 12.872 9.689
.Vl
of cyclopentane
zzz -.__-~ RTX& 1-0.2(1-2x1)
-0.00360 -0.01353 -0.02463 -0.02569
-0.00301 -0.01256 -0.02257 -0.02428
GE = 1 -oRl:T
G”
G”
57.034 51.710 47.591 47.168
0.07277 0.14926 0.20715 0.21325
291.15
39.129 35.489 32.855 32.419
0.07178 0.14878 0.20323 0.21233
lnfi
coefficientsfi
-0.00270 -0.01240 -0.02095 -0.02347
and activity
mm2
29.503 26.762 24.902 24.477
p/kN
Xl
0.07140 0.14845 0.20021 0.21174
pressuresp
2. Vapour
deviation
deviation
deviation
9.993 8.978 5.899
6.971 6.341 4.102
in lnfi
in lnfi
in In,fL
m-a
5.320 4.850 3.114
p/kN
(2) at 291.15,
and 308.15
= 0.00018
= 0.00009
z 0.00013
-0.‘097 --0.2180 -0.2447
-0.2043 -0.2098 -0.2325
-0.1987 -0.2053 -0.2275
In fa
298.15,
K
0.10655 0.11857 0.13024 0.15271 0.17405 0.19433 0.21365 0.25288
0.09741 0.10973 0.12479 0.15265 0.17444 0.19406 0.21293
-0.1 -0.0 -0.1 -0.1 -0.1 -0.0 -0.0 : 0.0
-to.0 -0.0 -0.0 -0.1 -0.1 -0.1 -0.0
6.5 15.8 33.6 50.0 64.9 78.8 91.4 103.1
6.6 15.7 32.6 48.4 62.6 76.1 88.1
0.00506 0.01240 0.02705 0.04127 0.05509 0.06853 0.08154 0.09422
0.005 27 0.012 78 0.027 28 0.041 66 0.055 36 0.069 04 0.082 01
98.9 109.9 126.7 142.2 155.3 165.8 174.8
113.8 123.6 132.6 148.5 161.9 173.3 182.8 198.9
110.9 126.9 141.0 153.3 164.1 176.3 186.4 195.2
HE J mol-1 6HE
+0.2 $0.3 +0.4
f0.1
-0.0 $0.0
-0.0
fO.0 to.0 i-o.0 +o.o -t 0.0 f0.3
-i-o.1 +0.1
-0.2 -0.4 +0.6
-0.1
-to.0
10.1 f0.1 $0.1
J mol-’
308.15
298.15
291.15
-0.1
-0.2 -0.2 -0.2 -0.2
-0.1 -0.1
-0.1
-0.2 -0.3 -0.3 -0.2
+0.1 -t 0.0 -0.1
-0.2 -0.2 -0.2
$0.0 -0.0
-0.6 +0.4 -10.2
0.55485 0.61093 0.67963 0.76574 0.87683 0.94541
0.50819
0.55393 0.61090 0.67879 0.76511 0.80594 0.87734 0.90103 0.92717 0.94842
0.48953 0.53534 0.59062 0.65862 0.74432 0.85566 0.92484 0.97198
standard deviation = 0.3 J mol-I. standard deviation = 0.2 J mol-I. standard deviation = 0.2 J mol-I.
189.4 196.2 202.5 207.6 210.7 209.4 206.1
206.0 212.6 218.2 221.5 221.6 220.2 216.8 210.6
202.8 210.7 217.9 222.5 225.8 226.9 224.4
194.8
HE J mol-’
(2) at 291.15, 298.15, and 308.15 K.
J molwl; J mol-I; J mol-I;
0.25275 0.27579 0.30352 0.33684 0.37910 0.43441 0.46802
K
0.27599 0.30375 0.33771 0.38023 0.40528 0.43505 0.46881 0.50821
K
0.27653 0.30613 0.33285 0.36469 0.40325 0.45094
0.25188
0.23367
K
Xl
(l)+cyclopentane
291.15 K: 6HE = HE-x1x2(1332.5-1128.7xl+410.7x:) 298.15 K: SHE = HE-~I~a(1310.2-l128.0x1+410.4x~) 308.15 K: SHE = HE-x&1259.2-l116.6x1+418.4x~)
0.13809 0.15564 0.17249 0.19394 0.21431 0.23172
0.11980
0.10071
10.1 io.l
+0.2
+0.1 -i-O.1
-t 0.0 10.0 -i- 0.1
3.4 9.8 19.9 38.7 55.8 71.5 85.8 98.9
Xl
0.00257 0.00743 0.01529 0.03063 0.04551 0.05993 0.07393 0.08752
-..
&HE J mol-1
~- HE J mol-’
3. Enthalpies of mixing of OMCTS
.Yl
TABLE
199.9 190.0 174.6 151.4 116.4 64.7 29.6
104.6 68.5 55.5 41.4 29.3
184.3 160.3 123.8
200.5
16.7
44.1
219.3 210.4 195.8 172.9 137.4 82.1
__-HE J mol-1
-0.3 -0.2
-0.1
t 0.0 -t 0.2 i 0.3 f0.3
-m0.3 :ro.3 -0.2 -0.0 -0.4 -0.3 -0.5
0.1 0.2
-0.2 0.0 t 0.2 -1-0.4 y-o.4 -0.3 -0.4 -0.3
.__SHE ~. J mol-’
-86.4 - 145.9 - 182.4 -199.1 - 198.5
-91.0 -153.5 -191.7 - 209.0 -208.1
-97.8 - 164.5 -205.0 -223.2 -222.2
0.1 0.2 0.3 0.4 0.5
0.1 0.2 0.3 0.4 0.5
0.1 0.2 0.3 0.4 0.5
103.7 168.4 202.0 211.1 201.4
108.1 176.2 211.8 221.9 212.2
110.1 179.7 216.5 227.2 217.7
HE J___mol-’
-0.0078 0.0072 0.0257 0.0394 0.0461
-0.0078 0.0072 0.0257 0.0394 0.0461
-0.0078 0.0072 0.0257 0.0394 0.0461
308.15
298.15
291.15
OMCTS
____ VE cm3 mol - 1
for the system
The excess volumes were calculated from the equation? VE =1x~x~(O.l84l-O.O64(1-2x~)-O.14o(l-2x~)~-O.168(1-2x~)~-O.1O6(1-2x~)*}
GE J mol-’
4. Excess functions
Xl
TABLE
K
K
K
0.6 0.7 0.8 0.9
0.6 0.7 0.8 0.9
0.6 0.7 0.8 0.9
Xl
(I)+cyclopentane
cm3 mol-’
-204.5 -172.1 ~~ 126.4 -68.8
-191.4 -160.8 -117.8 -63.9
- 182.8 -153.8 -112.8 -61.3
GE J mol-’
(2) at rounded
177.6 143.4 101.4 53.4
187.5 151.5 107.3 56.5
192.8 156.2 110.8 58.4
HE J mol-’
mole
0.0462 0.0410 0.0306 0.0170
0.0462 0.0410 0.0306 0.0170
0.0462 0.0410 0.0306 0.0170
VE cm3 mol-’
fractions.
364
K. N. MARSH
the smoothing equations and the standard deviations cyclopentane was calculated from the total pressure approximations for the partial pressure of OMCTS. previously. (I) The smoothing equation used was Scott:“2’
in lnfi. The partial pressure of by using a method of successive This method has been described that suggested by Myers and
GE =
(1)
where k is a skewing factor. From equation (1) we deduce for In fi the relation: m “x’t1-2x1)“-’ Inf2 =nzo [l-k(l-2X,)]2
{2n+1-2x,(l+n)-k[2n-1-2x,(3n-l)+4nx:]).
(2)
The coefficients A,, Ai, and A, and the skewing factor k were determined by a least squares fit of equation (2) to the experimental results after introducing a weighting function proportional to x2. (i) The smoothing equations listed in table 2 are expressed in terms of equation (1) from which GE can be calculated directly. The enthalpies of mixing at the three temperatures are listed in table 3, together with the smoothing equations and the standard deviations from the smoothing equations.
4. Discussion The excess functions GE, HE, and VE at rounded mole fractions are listed in table 4. The excess volumes were calculated from results reported previously.(3’ An indication of the accuracy of the vapour pressure measurements can be obtained from the value of HE calculated from the variation of GE with temperature according to the equation HE = GE- T(8GE/i3Tjp.
(3)
The excess Gibbs energy varies linearly with temperature, within experimental limits, over the whole composition range, leading to a value of HE = 206 J mol-’ for the equimolar mixture at a temperature close to 298.15 K. This compares more than favourably with the directly determined value of 212 J mol- ’ at 298.15 K. We have previously estimated (2) that values of HE calculated from our vapour pressure measurements should be accurate to +25 J mol-‘. The excess Gibbs free energy was found to have its minimum value at a mole fraction of OMCTS of 0.44 at all temperatures. The enthalpy of mixing showed a maximum at a mole fraction of OMCTS of 0.41 and decreased linearly (to within 5 1 J mol-l) with temperature. At mole fractions close to that at which HE has its maximum value, the temperature coefficient aH E/aT is - 0.9 J K- i mol- ‘. The excess volumes were found to be independent of temperature and to change sign with composition. @)At mole fractions of OMCTS less at 0.15 the excess volume is negative.
This work was supported by a grant from the Australian Research Grants Committee. I am grateful to Miss Barbara J. Levien for measuring the density of cyclopentane.
THERMODYNAMICS
OF MIXTURES
365
REFERENCES I. Marsh, K. N. Trans. Furudav Sot. 1968, 64, 883. 2. Marsh, K. N.; Tomlins, R. P. Trans. Far&y Sot. 1970, 66, 783. 3. Levien, B. J.; Marsh, K. N. J. Chem. Thermodynamics 1970, 2, 227. 4. Stokes, R. H.; Marsh, K. N.; Tomlins, R. P. J. Chem. Thermodynamics 1969, 1, 377. 5. Boublik, J.; Lam, V. T.; Murakami, S.; Benson, G. C. J. Phys. Chem. 1969,73,2356. 6. Rossini, F. D.; editor. Amer. Petrol. Inst. Project 44 Tables 1967. 7. Stokes, R. H.; Marsh, K. N.; Tomlins, R. P. J. Chem. Thermodynamics 1969, 1, 211. 8. McCullough, J. P.; Pennington, R. E.; Smith, J. C.; Hossenlopp, I. A.; Waddington, G. J. Amer. Chem. Sac. 1959, 81, 5880. 9. Hermsen, R. W.; Prausnitz, J. M. Chem. Eng. Sci. 1963, 18, 485. 10. Scatchard, G.; Ticknor, L. B. J. Amer. Chem. Sot. 1952, 74, 3124. 11. Baxendale, J. H.; Eniisttin, B. V. ; Stern, J. Phil. Trans. Roy. Sot. London, Ser. A. 1951, 243, 169. 12. Myers, D. B.; Scott, R. L. Znd. Eng. Chem. 1963, 55, 43.