Physical Chemistry Third Edition

26.3 Chemical Equilibrium in Dilute Gases 1105

wherec◦is defined to equal to 1 mol m−^3. Equation (26.3-9) can be written

0 

∆ε 0

kBT

−ln

[c

∏

a 1

(

z′a

NAvVc◦

)νa]

+ln

[ c

∏

a 1

(c

a

c◦

)νa

]

(26.3-19)

so that

Kc

∏c

a 1

(ca

c◦

)νa

e−∆ε^0 /kBT

∏c

a 1

(

z′a

NAvVc◦

)νa

e−∆ε^0 /kBT

∏c

a 1

(

z′a

NAvc◦

)νa

(26.3-20)

Exercise 26.11

CalculateKcfor the reaction of Example 26.11.

PROBLEMS

Section 26.3: Chemical Equilibrium in Dilute Gases

26.19Calculate the equilibrium constant for the dissociation of
hydrogen at 5000 K.

26.20Find the value of the equilibrium constant at 298.15 K for
the reaction
Cl 2 (g)
2Cl(g)

Assume that the electronic partition functions can be

approximated as the degeneracy of the ground levels. The

dissociation energy at 0 K is equal to 239.242kJmol−^1.

26.21Calculate the value of the equilibrium constant at 900 K
for the reaction

CO 2 +H 2 
CO+H 2 O

Carbon dioxide is linear, with bond lengths of 1.161×

10 −^10 m. The vibrational frequencies are in Example

25.12. The bond distances in H 2 O are equal to 95.8 pm

and the bond angle is equal to 104. 45 ◦. The value of∆U 0

for the reaction is equal to 40.33 kJ mol−^1.^2 The

experimental value of the equilibrium constant is 0.46.

Calculate your percent error.

(^2) G. Herzberg,Molecular Spectra and Molecular Structure. Vol. II.
Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand
Reinhold, New York, 1945, p. 429.
26.22Calculate the value of the equilibrium constant at 750 K
for the reaction
H 2 +I 2
2HI
The value of∆U◦ 0 is equal to− 8 .461 k J mol−^1.^3
26.23Without doing any detailed calculations, estimate the
equilibrium constant for each of the following gas-phase
reactions; assume that∆ε 0 ≈0. Ignore differences in
masses and moments of inertia. Assume that all
vibrational partition functions≈1.
a.NH 3 +D 2 O
NH 2 D+HDO
b.^35 Cl 2 +^37 Cl
^35 Cl^37 Cl+^35 Cl
26.24Without doing any detailed calculations, estimate the
equilibrium constant for the gas-phase chemical reaction
at 298.15 K.
(^1) H (^35) Cl+ (^37) Cl 2
(^1) H (^37) Cl+ (^35) Cl (^37) Cl
State any assumptions. Does your result depend on
temperature? Why or why not?
26.25Without doing any detailed calculations, estimate the
equilibrium constant for each of the following gas-phase
reactions. Assume that∆ε 0 ≈0. Ignore differences in
masses and moments of inertia. Assume that all
(^3) K. P. Huber and G. Herzberg,Molecular Spectra and Molecular Struc-
ture. Vol. IV. Constants of Diatomic Molecules,Van Nostrand Reinhold,
New York, 1979, pp. 240, 330, 324.