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

To solve the problem regarding the spontaneity of the reaction where quick lime (CaO) is produced from limestone (CaCO₃), we need to analyze the given thermodynamic data and apply the Gibbs free energy equation.

### Step-by-Step Solution:

1. **Identify the Reaction and Given Data:**
The reaction is:
\[
\text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g)
...