Page 155 - Essentials of physical chemistry

Gibbs’ Free Energy and Equilibria 117

TABLE 6.4
Selected Values of Alpha and Beta for Liquids at Temperatures in 8C
4
3
Compound Temperature (8C) Alpha (10 =8C) Beta (10 =MPa) Density (g=mL)
H 2 O 20 0.206 4.591 0.9982
CH 3 OH 20 1.49 12.14 0.7915
20 1.12 9.38 1.2632
CS 2
CH 3 CH 2 OH 20 1.40 11.19 0.7892
20 1.14 10.50 1.5844 (at 258C)
CCl 4
C 6 H 6 25 1.14 9.66 0.8783
25 1.16 12.82 0.7028
C 8 H 18

P tp 41570 J=mol 1 1 57090 J=mol 1 1
ln ¼ ¼
101, 325 8:314 J=mol K T tp 457:6 K 8:314 J=mol K T tp 443:913 K

After canceling the R value, this can be rearranged to isolate the value of T tp .
(57, 090 41, 570)
¼ 410:95 K. Then we use the liquid equation for the calculation of the

T tp ¼
57, 090 41, 570
443:9 457:6

P tp 41, 570 1 1
vapor pressure as ln ¼ ¼ 1:2322778.
101, 325 8:314 410:9 457:6
This leads to 29549.16 Pa for P tp , which converts to 221.6 mmHg. As calculated, we find the
triple point as 4118K, 222 mmHg, 4118K, 0.2916 atm, or 137.88C, 0.2955 bar. Both the
temperature and the vapor pressure we have calculated for the triple point are perhaps higher
than expected but the vapor pressure is certainly consistent with the idea that it is easy to obtain
a substantial vapor pressure for fingerprint enhancement at room temperature. In research
applications, it would be necessary to use 64 bit precision of about 14 significant figures in a
computer program to obtain more precise values due to the use of 1=T values numerous times
and we doubt that the calculated values are within 5% of experimental values because even
though the Clausius–Clapeyron equation is accurate, we are cautious rounding reciprocals. The
90th Edn. of the CRC Handbook does not give the temperature of the I 2 triple point but this
calculation has taught us about the existence of a triple point and provides information about the
vapor pressure of I 2 sublimation relative to the renewed use of iodine vapor fingerprint enhance-
ment (see Figure 6.6.)

(C P –C V ) FOR LIQUIDS AND SOLIDS
While we are discussing solids, liquids, and gases we can consider the difference in heat capacities
for solids and liquids. We will now need to use some of the information from the HUGA set of
equations. Along the way we will repeat the case for an ideal gas and show where the derivation
changes for the general case. We start from the definitions of C P and C V .

qH qU qU qV qP qU qP
þ P þ V , but ¼ 0:
C P C V ¼ ¼
qT qT qT qT qT qT qT
P V P P P V P