The thermal dissociation equilibrium of CaCO _ 3 (s ) is studied...

Kirchoff's Equation-
$\Delta {H}_{T} = \Delta {H}^{∘} + \mathop{∫}_{298}^{T}{\left(\Delta Cp\right)}_{reac}dT$
$\Delta {\text{H}}_{\text{reac}}$ is dependent on temperature.
$\text{K} = \dfrac{\left[{\text{CO}}_{2}\right] \times 1}{1}$ as solids are treated at unit activity. $K$ is independent of initial amount of ${CaCO}_{3}$.
${K}_{p} = {pCO}_{2} ( g )$ at a given temperature ${K}_{p}$ depends only on temperature.
$\Delta \text{H} = {\text{E}}_{\text{a} \left(\text{\text{ for }}\right)}$ - {\text{E}}_{\text{b} \left(\text{back}\right)}

A catalyst lowers only the activation energies & $\Delta {\text{H}}_{\text{react}}$ is independent of catalyst.