Concise Physical Chemistry

c09 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

140 THE PHASE RULE

-1/T (K-1)

-0.0037 -0.0036 -0.0035 -0.0034 -0.0033 -0.0032 -0.0031 -0.0030

Vapor Pressure (kPa)

0

2

4

6

8

10

12

14

FIGURE 9.13 The liquid–vapor coexistence curve of water leading to
vapH(H 2 O)=

44 .90 kJ mol−^1.

The vapor pressures over pure water were selected at 10 K intervals

from 273 to 323 K, plotted, and submitted to a standard curve-fitting rou-

tine (SigmaPlot 11.0). A two-parameter exponential curve fit of pvap vs.

− 1 /T(Statistics → Nonlinear → Regression Wizard→ Ex-

ponential Growth → Single, 2-Parameter) gave the empirical con-

stantb(Outputb 5400.6916) K, where the unit of the empirical constant is kelvins

in order to make the exponent−b/Tunitless. The curve fit is good, having a mean

residual (difference between calculated and experimental values) of 1 part per thou-

sand or 0.1% over a range of about 12 kPa. We have the relationship between the

parameterband
vapH:

b=

vapH

R

which gives us

vapH=R(b)= 8. 314

(

5. 401 × 103

)

= 44. 90 × 103 = 44 .90 kJ mol−^1

This value is “averaged out” by the curve fitting technique over the temperatures

symmetrically distributed around 298 K. The handbook value of
vapHof water at

298 K is 43.99 kJ mol−^1.

Example 9.2 Ternary Phase Diagrams

The ternary phase diagram ABC in which A is completely miscible with B and C but

B and C are only partially miscible in each other looks like a combination of Figs.

9.9 and 9.12 except that the tie lines are not horizontal.