It is planned to carry the reaction
`CaCO_(3)(s) hArr CaO (s) +CO_(2)(g)`
at 1273K and 1 bar
(a) Is this reaction spontaneous at this temperature and pressure ?
(b) Calculate the value of
(i) `K_(p)` at 1273 K for the reaction and
(ii) partial pressure of `CO_(2)` at equilibrium
Given `Delta_(f) H^(@)` values (`kJ mol^(-1)) :`
`CaCO_(3)(s) =-1206.9, CaO(s)= - 635.1, CO_(2)(g) = - 393.5`
`S^(@) ` value `(JK^(-1) mol^(-1))`
`CaCO_(3)(s) =92.9, CaO(s) = 39.8, CO_(2)(g) = 213.7`.

Explanation

To solve the problem step by step, we will address each part of the question systematically.

### Given Data:
- Reaction: \( \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \)
- Temperature (T) = 1273 K
- Pressure (P) = 1 bar
- Enthalpy of formation (\( \Delta_f H^\circ \)):
- \( \text{CaCO}_3(s) = -1206.9 \, \text{kJ/mol} \)
...