Question

For Br₂(g), ∆H_fº = 30.9 kJ/mol and ∆G_fº = 3.1 kJ/mol at 298.15 K. Estimate the lowest temperature at which Br₂(g) will not spontaneously condense to Br₂(l).

A –10. ºC

B –59 ºC

C 59 ºC

D 332 ºC

E 10. ºC

Answer 1

Correct option: C. 59 ºC

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∆H_fº = 30.9 kJ/mol

∆G_fº = 3.1 kJ/mol

T = 298.15 K

Now,

∆G_fº = ∆H_fº - T∆S_fº

or, 3.1 = 30.9 - 298.15∆S_fº

or, - 27.8 = - 298.15∆S_fº

or, ∆S_fº = 0.0932 kJ/mol

Now, during phase transition,

∆G_fº = 0

or, ∆H_fº - T∆S_fº = 0

or, 30.9 - T x 0.0932 = 0

or, T x 0.0932 = 30.9

or, T = 332 K

        = (332 - 273) ^oC

        = 59 ^oC

Hence, the lowest temperature at which Br₂(g) will not spontaneously condense to Br₂(l) = 59 ^oC