Thermal Dissociation Equilibrium of Calcium Carbonate

To determine the correct statements for the thermal dissociation equilibrium of calcium carbonate:

$\text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g)$

we analyze each option individually:

1. Statement (A): $\Delta H$ is dependent on $T$ According to Kirchhoff's law of thermochemistry, the change in enthalpy of a reaction varies with temperature as: $\frac{d(\Delta H)}{dT} = \Delta C_p$ where $\Delta C_p = \sum C_{p,\text{products}} - \sum C_{p,\text{reactants}}$. Since $\Delta C_p \neq 0$ for this reaction, the enthalpy change ($\Delta H$) depends on the absolute temperature $T$. Hence, statement (A) is correct.

2. Statement (B): $K$ is independent of the initial amount of $\text{CaCO}_3$ For the given heterogeneous reaction, the equilibrium constant in terms of partial pressures is given by: $K_p = P_{\text{CO}_2}$ The activities of pure solids ($\text{CaCO}_3$ and $\text{CaO}$) are taken as unity. Therefore, the equilibrium constant $K$ depends solely on temperature and is completely independent of the initial mass or amount of solid $\text{CaCO}_3$ present (provided sufficient material exists to establish equilibrium). Hence, statement (B) is correct.

3. Statement (C): $K$ is dependent on the pressure of $\text{CO}_2$ at a given $T$ The equilibrium constant $K$ is a thermodynamic function that depends only on temperature $T$. Changing the pressure of $\text{CO}_2$ will shift the equilibrium position according to Le Chatelier's principle, but the value of $K$ itself remains constant at a fixed temperature $T$. Hence, statement (C) is incorrect.

4. Statement (D): $\Delta H$ is independent of the catalyst, if present Enthalpy ($H$) is a state function, meaning $\Delta H = H_{\text{products}} - H_{\text{reactants}}$ depends only on the initial and final thermodynamic states of the system. A catalyst provides an alternative pathway with lower activation energy for both forward and reverse reactions, but it does not alter the thermodynamic state properties or the value of $\Delta H$. Hence, statement (D) is correct.

Thus, the correct statements are A, B, and D.