For the reaction : C(s) + H2O(g) → CO(g) + H2(g) , ΔH° = 133 kJ/mol and ΔS° = 133 J/Kmol at 298 K. The minimum temperature above which this reaction is spontaneous is
Question
For the reaction : C(s) + H2O(g) → CO(g) + H2(g) , ΔH° = 133 kJ/mol and ΔS° = 133 J/Kmol at 298 K. The minimum temperature above which this reaction is spontaneous is
Solution
The spontaneity of a reaction can be determined by the sign of the Gibbs free energy change (ΔG). If ΔG is negative, the reaction is spontaneous. The formula for Gibbs free energy change is:
ΔG = ΔH - TΔS
Where: ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, ΔS is the change in entropy.
We are given that ΔH = 133 kJ/mol = 133,000 J/mol and ΔS = 133 J/Kmol. We are asked to find the minimum temperature (T) at which the reaction is spontaneous, i.e., when ΔG < 0.
Setting ΔG = 0 and solving for T, we get:
0 = ΔH - TΔS T = ΔH / ΔS T = 133,000 J/mol / 133 J/Kmol T = 1000 K
Therefore, the reaction is spontaneous at temperatures above 1000 K.
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