For the reaction: `2 A _(2) O (s) to 4 Ag (s) + O _(2) (g), ` `Delta H = 61.17kJ and Delta S = 132 JK ^(-1) at 298 K` and 1 atm. Show that the reaction is not spontaneous at the given temperature. Above what temperature will the reaction become spontancous?

Explanation

Given: `Delta H = 61. 17 kJ, Delta S = 132 J K ^(-1) , T = 298 K`
According to Gibbs-Helmhoktz equation, `Delta G = Delta H - T Delta S`
`Delta G = 61. 16 xx 10 ^(3) J - ( 298 K xx 132 JK ^(-1)) = 21. 834 xx 10 ^(3) J = 21. 834 kJ`
Since `Delta S` at 298 K is `+ 21.834 kJ` the reaction is non-spontaneous. Reaction becomes spontaneous when
`Delta G lt 0 i.e., Delta H - T Delta S lt 0 or T Delta S gt Delta H`
Temperature above which the reaction becomes spontaneous is given by
`T gt ( Delta H )/(Delta S) or T gt ( 61. 17 xx 10 ^(3) J)/(132 JK ^(-1)) or T gt 463.4 K`