Question

For the reaction C(s)+H2O(g)→CO2(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

Answer : At temperatures greater than $755.9^oC$ this reaction is spontaneous under standard conditions.

Explanation : Given,

$\Delta H$ = 131.3 KJ/mole = 131300 J/mole

$\Delta S$ = 127.6 J/mole.K

Gibbs–Helmholtz equation is :

$\Delta G=\Delta H-T\Delta S$

As per question the reaction is spontaneous that means the value of $\Delta G$ is negative or we can say that the value of $\Delta G$ is less than zero.

$\Delta G$

The above expression will be:

$0>\Delta H-T\Delta S$

$T\Delta S>\Delta H$

$T>\frac{\Delta H}{\Delta S}$

Now put all the given values in this expression, we get :

$T>\frac{131300J/mole}{127.6J/mole.K}$

$T>1028.99K$

$T>755.9^oC$

Therefore, at temperatures greater than $755.9^oC$ this reaction is spontaneous under standard conditions.