Thermal Pressure Coefficient of 2,P-Dimethylpropane
1543
Thermal Pressure Coefficient and Internal Pressure of 2,2-Dimethylpropane George A. Few and Maurlce Rlgby* Chemistry Department, Queen Ellzabeth College, Campden Hi//,London W8 7AH, England (Received January 27, 1975)
Direct measurements have been made of the thermal pressure coefficient, (aP/aT)I/, for liquid 2,2-dimethylpropane (neopentane) at densities near to the coexistence curve in the temperature range from -15 to + 8 5 O . Other values of (aP/aT)vhave been derived from the P V T data of Dawson et al. from 65' to the critical temperature 160.6'. These data have been used to obtain the internal pressure ( a U l a V ) ~along , the coexistence curve from triple point to critical point. The results have been compared with those for other simple liquids using the principle of corresponding states. The thermal pressure coefficient, (aP/aT)v, and the internal pressure, ( a U / a v ) ~provide , a useful basis for understanding the nature of the liquid state.2 They are related by the thermodynamic equation of state
and may also be considered in terms of the van der Waals equation of state p=-- nRT V - nb
or its generalized form
P = Zf, V - f2
(+)
);(
(3)
Equations 2 and 3 both require that pressure-temperature isochores should be linear, Le., that the thermal pressure coefficient should be a function of density only. Although this is not precisely true, it proves to be a good approximation for most liquids at densities fairly near to the coexistence curve. The molecular interpretation3 of eq 2 and 3 associates the first term on the right-hand side, and hence the thermal pressure coefficient, with the effects of intermolecular repulsive interactions, as represented by a hard sphere model. The second term, corresponding to the internal pressure, describes the effects of intermolecular attractions, necessary to maintain the high density of the liquid state, but having little effect on the geometrical structure. In the original van der Waals equation the contribution due to the repulsive interactions was given by an inaccurate representation of the hard sphere equation of state. There have been several investigations4 using more accurate hard sphere expressions, together with the original attractive energy term, and these have proved to give remarkably good qualitative equations of state. An extension to mixed fluids5 has been particularly successful. The relationship between the thermal pressure coefficient and the hard sphere equation of state has been pointed out previously,6 but there seems to have been no systematic study for a variety of liquids over an extended range of temperature. Recently data have been presented for the thermal pressure coefficient of the heavier inert gases over most of the liquid range,7 and in this paper we supplement these results with measurements of the thermal pressure coefficient of 2,2-dimethylpropane (neopentane) a t densities near to the coexistence curve from -15 to + 8 5 O . These data have been combined with results derived from P V T studies by Dawson et a1.I to give the thermal pressure coefficient of neopentane from a temperature near
to the triple point up to the critical point. This then permits a comparison between the results for the inert gases and for the pseudospherical, globular molecule, neopentane, over the whole liquid range.
Experimental Section Direct measurements of thermal pressure coefficients may conveniently be made using an apparatus of the type described by Hildebrand8 and subsequently used by several other w o r k e r ~ . ~We J ~have used a glass cell of the general appearance shown in Figure 1. The sample liquid is confined to the cell by mercury and the presence of the mercury-liquid interface is established electrically using contacts sealed through the glass. By adjusting the pressure and temperature of the cell, the mercury surface can be brought to the pointer a t Q and sets of isochoric P-T data can be obtained. The cell is placed in a pressure vessel, and pressures up to about 35 atm were applied from a nitrogen cylinder. The pressures were measured using a Texas Instruments Model 44 Bourdon tube pressure gauge, with an estimated error not exceeding 0.002 atm. Temperatures were measured using a Hewlett-Packard 2801A quartz thermometer, with a Model 2850B sensor which was sealed through the lid of the pressure vessel. Most of the space in the pressure vessel was filled with liquid toluene, acting as a heat transfer fluid, and the thermometer probe was positioned in the toluene, close to the cell. The pressure vessel was placed in a thermostat tank which could operate over the temperature range -20 to $85'. Since neopentane is gaseous at room temperature, the sample cell was filled at a reduced temperature, and quickly transferred to the previously cooled pressure vessel, which was then closed. A moderate nitrogen pressure was then applied, after which the vessel could be stored at room temperature. A series of runs was made after a single filling. Each run consisted of a set of about six P-T points covering a rising pressure range of about 10-15 atm, followed by a similar set with the pressure being decreased. After changes in the pressure, suitable times were allowed to elapse for the avoidance of errors due to adiabatic heating or cooling. When a particular isochore had been studied, the temperature was raised by 10-15 K, without increasing the pressure. The liquid then expanded to an extent sufficient to displace some of the sample. On cooling, a new isochore could then be investigated. The sets of P-T data were always linear within the experimental error. No systematic changes were observed beThe Journal of Physical Chemistry, Vol. 79, No. 75, 1975
1543
George A. Few and Maurice Rigby TABLE I: Therm'al Pressure Coefficients for Benzene yv, bar
T , "C
22.8 32.9 42.3 48.3
K-'
12 .62 11.Q2 11.Z6 10.82
T , "C
yv, bar K-'
52.9 62.2 69.7 81.8
10 ,67 9 'g7 9.56 a .a4
xo A 0
&a Figure 1. The thermal pressure cell. Q is the position of the liquid/ mercury interface. tween the sets obtained with rising and falling temperatures. The slopes of the experimental P-T data were obtained by a least-squares analysis. This "experimental" value of the thermal pressure coefficient, yexpt,was then corrected to allow for the compressibility and thermal expansivity of the glass, using the equationg
0
11
41
-
0
8v bar K - l
0 X
lot
where yv is the corrected value, a and ag are the thermal expansivities of the sample liquid and of the glass, and & is the compressibility of glass. The isochoric P-T line was extrapolated back to the saturated vapor pressure curve. The intersection temperature was then used to determine the density of the sample, from a knowledge of the molar volume of the liquid on the coexistence curve. The latter data were not available for neopentane below 65O, except for a single value a t Oo.l1 We have confirmed the latter value, and have measured the coefficient of thermal expansion, 1/V(aV/aT)p, directly in the temperature range from -10 to +30°. The dilatometer used was closely based on that described by Orwoll and F l ~ r y and , ~ operated under a constant total pressure of about 2 atm. Data could thus be obtained at temperatures above the normal boiling point. The method of operation was very similar to that described by the previous workers. The observed values of the coefficient of expansion are believed to be accurate to about 0.5-1%. Material. The 2,2-dimethylpropane was of commercial grade, supplied by the Matheson Co. Its purity was stated to be better than 9996, with n-butane as the principal impurity. In view of the similarity between the physical properties of n-butane and 2,2-dimethylpropane it seems unlikely that the impurity would have a detectable effect on the results. The samples were carefully degassed before use, by means of two or three freeze-pump-thaw cycles. Results a n d Discussion Some preliminary results were first obtained using benzene. In these experiments a slightly different cell was used, and the total volume of benzene and the confining mercury was held constant. The benzene used was supplied by British Drug Houses Ltd. with a purity not less than 99.8%. The sample was carefully dried and degassed before use. The results of these measurements are shown in Table I. The thermal pressure coefficients are quoted for the temThe Journal of Physical Chemistry, Vo/. 79, No. 15, 1975
X
9-
X
81
0
I
I
I
10
20
30
1
40
50
60
70
80
T "C
Figure 2. Thermal pressure coefficient results for benzene: ( X ) this work; (A)ref 8; (0)ref 8; (0)ref 10. peratures on the coexistence curve corresponding to the density studied. The results are compared with those of previous workersal0 in Figure 2. I t may be seen that the available data are somewhat scattered, with a spread of around 2%, and that the results obtained in this work lie within the range of values found previously. We have found no data above 60° to permit comparison a t the higher temperatures. In Table I1 we summarize the thermal pressure results obtained for 2,2-dimethylpropane. In Table I11 results are given at regular temperature intervals, and include values obtained by graphical interpolation of the P V T data in ref 1. In addition we have reported the measured coefficients of thermal expansion, and the derived values of the molar volumes. The molar volumes between 30 and 65" are based on a corresponding states correlation. They are believed to be accurate to 0.3%.The thermal pressure coefficients are shown in Figure 3, where it may be seen that our directly measured values are in good agreement with the indirect values from ref 1. In the region of overlap, our results lie within about 0.1 bar K-l of the other data. Using the results in Table I11 the internal pressure, (aU/ a v ) ~of, neopentane along the coexistence curve for most of
1545
Thermal Pressure Coefflclent of 2,2-Dimethylpropane 9-
TABLE 11: Thermal Pressure Coefficients for 2.2-Dimethsl~ro~ane
0 S-
T , "C
yV, bar K-'
T , "C
yv, bar Kmi
-16.0 -2.7 8.0 99.3 17.1 30 .O 38.8
8 .54 7.65 7 .04 7 .02 6.54 5 .87 5 '41
39.4 49.8 59.5 62.5 71.4 84.1
5.39 4.89 4 '48 4.34 3 'g7 3 .44
0
6
7-
0 6-
0
0
'6v
0
5-
bar K-'
%P
4-
3-
TABLE 111: Smoothed Data for 2,%-Dimethylpropane YV
T , "C
,
0,
0 0
bar K-i
lo3,bar-'
7, cm3 mol-'
8 .47 8 .13 7 .50 6 .g2 6.39 5 .87 5 .36 4.88 4 .44 4.01 3.63 3.43 4.12 3 .29 2.9, 2.1; 1 .63 1 .lo .4g3
1 .80 1 .83 1 ,89 1 .g6 2 '05 2.17
114.4 115.4 117.2 119.9 122.3 124.9 127.2' 130.0 132.8 136.4 140.1 142.1 136.4 144.2 149.2 161.3 175.1 199.8 311.3
0
1-
0
-1 5 -1 0 0 10 20 30 40 50 60 70 80 85 70b gob lOOb 12Ob 135b 150b 160.6b
=Data between 30 and 70" from corresponding states interpolation. Above 70" from ref 1. Values from ref 1. the liquid range was calculated. These data are shown as a function of molar volume in Figure 4, and it is seen that the internal pressure decreases with increasing molar volume. The relationship between the configurational internal energy and the internal pressure2 implies that, throughout the liquid range, neopentane has a structure which is sufficiently expanded that the attractive intermolecular forces are dominant. This behavior seems to be typical of most simple fluids. The reverse situation has been reported for only a few liquids,2 at densities near to the triple point. It seems probable that this behavior is found only in liquids which have an extended liquid range, such as the normal alkanes, but there do not seem to be sufficient data available to test this hypothesis thoroughly. A convenient basis for a corresponding states comparison of thermal pressure coefficient data may be achieved using the quantity V'yvlR, as a function of reduced temperature or density. As may be seen from a comparison of eq 1 and 2 this term is the equivalent of the van der Waals hard sphere compressibility factor, and so may perhaps be associated with the repulsive intermolecular forces. In Figure 5 we show the results for the heavier inert gases, together with our results for neopentane, as a function of the reduced temperature. In addition we have included values for
1
1
1
1
Flgure 3. Thermal pressure coefficients of 2,2dimethylpropane: (0) this work; (0)from PVTdata of ref 1.
200c
($1, bar
100c
20c
1
0
v
t
300
200 cm3 mol-'
Figure 4. The internal pressure of liquid 2,24imethylpropane along the coexistence curve: ( 0 )triple point; (X) critical point.
another globular molecule, carbon tetrachloride, for which there are data at lower reduced temperatures. I t is seen that the inert gases are in good corresponding states with each other, and that the results for neopentane and carbon tetrachloride lie significantly above the inert gas values. The two globular molecules show similar behavior, as might be expected from their acentric factors, which are almost identical. Thus despite the approximately spherical shape of the globular molecules there is a marked difference in the effect of the repulsive interactions. This preThe Journal of Physical Chemistryv Voi. 79, No. 15, 1975
1546 18
George A. Few and Maurice Rigby
Q
16
I
14
I
12
9
10
I
e Q
Q Q
-vJ l l
Q QQ
Q 0
8 9
Q
aA 6 -
Q
4p A
4
9
a
Q x
a
Q
#a0
2 -
Q
I
I
I
1
I
J
*5
.6
-7
.8
.9
1.0
Figure 5. Reduced thermal pressure coefficients for the heavier inert gases and for 2.2-dimethylpropane: (0)C(CH& 7; (A)Xe ref 7; (4) CCi4 from ref 12.
sumably reflects the nonconformality of the intermolecular potential energy functions for the inert gases and the globular molecules, with a consequently different dependence of density on reduced temperature. If the corresponding states comparison is made as a function of reduced density, a similar distinction is again seen between the inert gases and the globular molecules. This suggests that the relationship between the critical volume and the hard core molecular volume is different for the two classes of molecules. This again implies nonconformality of the intermolecular potential functions. A more detailed analysis of the role of molecular shape and intermolecular repulsive forces on the thermal pressure coefficient will be presented subsequently.
Acknowledgment. We thank the Science Research Council for the award of a research studentship to G.A.F., and
The Jwmal of Physical Chemistry, Vol. 79, No. 15, 1975
(X) Ar ref 7; (0) Kr ref
for an equipment grant for the purchase of the pressure gauge.
References and Notes (1) P. P. Dawson, I. H. Sllberberg, and J. J. McKetta, J. Chem. Eng. Data, 10, 7 (1973). (2) J. H. Hlldebrand and R. L. Scott, "The Solubility of Nonelectrolytes", 3rd
ed, Dover Publications, New York, N.Y., 1964, Chapter 5. (3) M. Rlgby, Quart. Rev. Chem. Soc., 24, 416 (1970). (4) E. A. Guggenhelm, Mol. fhys., 9, 199 (1965); H. C. Longuet-Hlgglns and B. Wldorn, /bid., 8, 549 (1964). (5) N. S. Snider and T. M.Herrington, J. Chem. fhys., 47, 2248 (1967). (6) E. B. Smith, J. Chem. Phys., 38, 1404 (1962). (7) W. B. Streett and L. A. K. Staveley, J. Chem. fhys., 50, 2302 (1969). (8) W. Westwater, H. W. Frantz, and J. H. Hlldebrand, fhys. Rev., 31, 135 (1928). (9) R. A. Orwoll and P. J. Flory, J. Am. Chem. SOC.,89,6814 (1967). (IO) G. A. Allen, 0. Gee, D. Mangaraj, D. Slrns, and G. J. Wilson, Polymer, 1, 467 (1960); U. Blanchi, G. Agablo, and A. Turturro, J. Phys. Chem., 89, 4392 (1965). (11) V. Mathot and A. Desmyter, J. Chem. Phys., 21, 782 (1953). (12) H. Bennlnga and R. L. Scott, J. Chem. Phys., 23, 1911 (1955).
