1. Relationship between equilibrium constants and partition functions a) McQuarr

ID: 518862 • Letter: 1

Question

1. Relationship between equilibrium constants and partition functions a) McQuarrie and Simon problem 12-39 b) By defining in simple English what is represented by the partition functions for molecules and by the equilibrium constants for a reaction, explain why it is reasonable that one should be able to calculate equilibrium constants from partition functions. c) Explain (also in simple English) why the plotting procedure to extract AHxn from the temperature dependence of the equilibrium constant works.

Explanation / Answer

Prepare the table as below:

ln KP

T (K)

1/T (K-1)

3.05*10-5

-10.398

800

0.00125

3.94*10-4

-7.893

900

0.00111

3.08*10-3

-5.783

1000

0.00100

1.66*10-2

-4.098

1100

0.00091

6.79*10-2

-2.690

1200

0.00083

Plot the graph of ln KP vs 1/T.

The slope of the plot is -18471 K.

As per the Vant Hoff equation, the slope of the plot of ln KP vs 1/T is (-fH0/R). Therefore,

-fH0/R = (-18471 K)

===> fH0 = (18471 K)*R = (18471 K)*(8.314 J/mol.K) = 153567.894 J/mol = (153567.894 J)*(1 kJ/1000 J) = 153.568 kJ/mol 153.6 kJ/mol (ans).