When is the reaction spontaneous?

Question

For a given reaction, ΔH = -26.6 kJ/mol and ΔS = 77.0 J/Kmol. The reaction is spontaneous at ________. Assume that ΔH and ΔS do not vary with temperature.

Answer 1

For a reaction to be spontaneous, ∆G must be less than zero, i.e. ∆G must be negative.

∆G = ∆H - T∆S

To be spontaneous, ∆G < 0

∆H - T∆S > 0 and solve for T

-26.6 - T(0.077) > 0 (note to change 77 J/Kmol to kJ/Kmol)

-0.077T > 26.6

T > -345K

Check:

∆G = -26.6 - (-345)(0.077) = -26.6 + 26.6 = 0 so if T > -345K, ∆G will be negative and the rx is spontaneous.