CHEMISTRY TEXTBOOK

Problem 4.19 : Calculate ∆Stotal and state

whether the reaction is spontaneous or

nonspontaneous at 25^0 C.

HgS(s) + O 2 (g) Hg(l) + SO 2 (g),

∆H^0 = -238.6 kJ, ∆S^0 = +36.7 J K-1

Solution :

∆Ssurr = - ∆H

0

T

=

(-238.6 kJ)

298 K

= +0.8007 kJ K-1 = +800.7 J K-1

∆Stotal = ∆Ssys + ∆Ssurr

= +36.7 JK-1 + 800.7 JK-1^

= +837.4 J K-1

∆Stotal > 0, the reaction is spontaneous at

25 0 C.

Problem 4.20 : Calculate ∆G for the

reaction at 25^0 C

CO(g) + 2 H 2 (g) CH 3 OH(g), ∆G^0

= -24.8 kJ mol-1 The partial pressures of

gases are PCO = 4 bar, PH 2 = 2 bar and

PCH 3 OH = 2 bar

Solution : ∆G = ∆G^0 + RT ln Qp

= ∆G^0 + 2.303 RT log 10

PCH 3 OH

PCO×P^2 H 2

∆G^0 = -24.8 kJ mol-1, R =8.314 ×10-3 kJ

K-1 mol-1, T = 298 K

Calculate Qp,

Qp =

PCH 3 OH

PCo×P^2 H 2 =

2

4 × 4 =

1

8 = 0.125

∆G = -24.8 kJ mol-1 +2.303 ×8.314× 10-3

kJ K-1 mol-1 × 298 K × log 10 0.125^

= -24.8 kJ mol-1 + 5.706 × (-0.903) kJ

mol-1

= -24.8 kJ mol-1 - 5.153 kJ mol-1

= -29.953 kJ mol-1

Exercises

1. Select the most apropriate option.

i. The correct thermodynamic

conditions for the spontaneous

reaction at all temperatures are

a. ∆H < 0 and ∆S > 0

b. ∆H > 0 and ∆S < 0

c. ∆H < 0 and ∆S < 0

d. ∆H < 0 and ∆S = 0

ii. A gas is allowed to expand in a

well insulated container against a

constant external pressure of 2.5 bar

from an initial volume of 2.5 L to a

final volume of 4.5 L. The change in

internal energy, ∆U of the gas will

be

a. -500 J b. + 500 J

c. -1013 J d. + 1013 J

iii. In which of the following, entropy of

the system decreases?

a. Crystallization of liquid into

solid

b. Temperature of crystalline solid is

increased from 0 K to 115 K

c. H 2 (g) 2H(g)

d. 2 NaHCO 3 (s)

Na 2 CO 3 (s) + CO 2 (g) + H 2 O(g)