The decomposition of limestone
`CaCO_(3) = CaO_(s) + CO_(2) (g)`
is nonspontaneous are `176 kJ` and `160 Jk^(-1)`, respectively. At what temperature, the decomposition becomes spontaneous?

Options

A. At `10000 K`
B. Below `500^(@)C`
C. At `500^(@)C`
D. Above `827^(@)C`

Explanation

Both `Delta H^(@)` and `Delta S^(@)` are positive. Thus, `Detla G` will be negative only when the `T Delta S` term is greater in magnitude than `Delta H`. This condition is met when `T` is large relative to the equilibrium temperature `(T_(eq))`. At equilibrium, `Delta G - 0`. Thus,
`0 = Delta H^(@) = T Delta S^(@)`
or `T = (Delta H^(@))/(Delta S^(@)) = (176 xx 10^(3) J mol^(-1))/(160 J K mol^(-1))`
`= 1100 K = 827^(@)C`
Thus, above `827^(@)C, T Delta S^(@) gt Delta H^(@)` and `Delta G^(@)` is negative.