Question

For the reaction

C(s) + H2O(g) ? CO(g) + H2 (g) ΔH∘=131.3kJ/mol and ΔS∘=127.6J/K⋅mol at 298K. At temperatures greater than ________ ∘C this reaction is spontaneous under standard conditions.

Answer 1

At temperatures greater than 756 °C this reaction is spontaneous under standard conditions.

Step-by-step explanation:

Let's consider the following reaction.

C(s) + H₂O(g) ⇄ CO(g) + H₂(g)

The reaction is spontaneous when the standard Gibbs free energy ΔG° < 0. ΔG° is related to the standard enthalpy of the reaction (ΔH°) and the standard entropy of the reaction (ΔS°) through the following expression.

ΔG° = ΔH° - T.ΔS°

If ΔG° < 0

ΔH° - T.ΔS° < 0

ΔH° < T.ΔS°

T > ΔH°/ΔS° = (131.3 × 10³ J/mol)/(127.6 J/K.mol) = 1029 K

The temperature in Celsius is:

°C = K - 273.15 = 1029 - 273.15 = 756 °C