Question

Classify each of the following reactions as one of these four types:

• spontaneous at all temperatures • not spontaneous at any temperature • spontaneous below a certain temperature but not above

• spontaneous above a certain temperature but not below

(a) PbS (s) + Mg (s) → Mg (s) + Pb (s); ∆H = 66 kJ; ∆S = -9 J/K

(b) 2 SO2 (g) + O2 (g) → 2 SO3 (g); ∆H = -197.8 kJ; ∆S = -188.1 J/K

(c) 2 N2O (g) + O2 (g) → 4 NO (g); ∆H = 199.5 kJ; ∆S = 198.2 J/K

(d) 2 C8H18 (l) + 25 O2 (g) → 16 CO2 (g) + 18 H2O (g); ∆H = -10139 kJ; ∆S = 977 J/K

Answer 1

From the second law of thermodynamics,

∆G = ∆H - T∆S

The criteria of spontaneity of a reaction is ∆G < 0.

For reaction (a)

∆H > 0

∆S < 0

Temperature, T is always > 0.

Hence, ∆G > 0 at all temperature.

Hence, the reaction (a) can be classified as not spontaneous at any temperature.

For reaction (b)

∆H < 0

∆S < 0

Temperature, T is always > 0.

Hence, ∆G < 0 when |∆H| > |T∆S| which is possible below certain T.

Hence, the reaction (b) can be classified as spontaneous below a certain temperature but not above.

For reaction (c)

∆H > 0

∆S > 0

Temperature, T is always > 0.

Hence, ∆G < 0 when |∆H| < |T∆S| which is possible above certain T.

Hence, the reaction (c) can be classified as spontaneous above a certain temperature but not below.

For reaction (d)

∆H < 0

∆S > 0

Temperature, T is always > 0.

Hence, ∆G < 0 at all temperature.

Hence, the reaction (d) can be classified as spontaneous at all temperatures​​​​​​​​​​​​​​.