Quick lime: `(CaO)`is produced bu heating limestone `(CaCO_(3))` to derive off `CO_(2)` gas.
`CaCO_(3) (s) rarr CaO(s) +CO_(2)(g), Delta_(r)H^(Theta) = 180 k J mol^(-1), Delta_(r)S^(Theta) = 150 J K^(-1)`
Assuming that variation fo enthalpy change and entropy change with temperature to be negligible, which of the following is correct?

Options

A. Decomposition of `CaCO_(3)(s)` is always nonspontaneous.
B. Decomposition of `CaCO_(3)(s)` become spontaneous when temperature is less than `27^(@)C`.
C. Decomposition of `CaCO_(3)(s)` become spontaneous when temperature is greater than `1200^(@)C`.
D. Decomposition of `CaCO_(3)(s)` become spontaneous when temperature is greater than `927^(@)C`.

Explanation

`Delta gt 0, DeltaS gt 0 rArr` Reaction 'may' be non-sontaneous at `25^(@)C`.
`DeltaG = DeltaH - T DeltaS = 180 - 298 xx 150 xx 10^(-3) =13.5 gt 0`
`rArr` Non-spontaneous.
To make it spontaneous `(DeltaG lt 0)`, we have to increase the temperature.
`T_(switch) = (DeltaH)/(DeltaS) = (180 xx 10^(3))/(150) = 1200 K = 927^(@)C`