The thermal dissociation equilibrium of CaCO₃(s) is given by:

$\mathrm{CaCO}{3}_{\left(s\right)}\underset{}{\overset{}{\rightleftharpoons }}\mathrm{CaO}{\left(s\right)}_{}+\mathrm{CO}{2}_{\left(g\right)}$

This is a heterogeneous equilibrium involving two solids and one gas. Let's analyze each statement:

Step 1: Understanding the Equilibrium Constant (K)

For the reaction: $\mathrm{aA}+\mathrm{bB}\rightleftharpoons \mathrm{cC}+\mathrm{dD}$, the equilibrium constant K is given by:

$K=\frac{\left[C{]}^c\right[D{]}^d}{\left[A{]}^a\right[B{]}^b}$

However, for pure solids, the concentration is constant and taken as 1. So, for this reaction:

$K=\frac{\left[\mathrm{CaO}{]}_{\left(s\right)}\right[\mathrm{CO}{2]}_{\left(g\right)}}{[\mathrm{CaCO}{3]}_{\left(s\right)}}=\frac{1\times P_{\mathrm{CO}2}}{1}=P_{\mathrm{CO}2}$

Thus, K = P_CO2, which is the partial pressure of CO₂ at equilibrium. K is constant at a given temperature and does not depend on the initial amount of CaCO₃ or the pressure of CO₂ (it defines the pressure at equilibrium). Therefore:

• "K is dependent on the pressure of CO₂ at a given T" is incorrect because K defines P_CO2 at equilibrium; it is not dependent on it.
• "K is independent of the initial amount of CaCO₃" is correct because K only depends on temperature for a given reaction.

Step 2: Understanding Enthalpy Change (ΔH)

ΔH is the standard enthalpy change for the reaction. It is a thermodynamic property that depends on the temperature (T) according to Kirchhoff's law:

$\frac{d\left(\mathrm{\Delta H}\right)}{\mathrm{dT}}=\mathrm{\Delta C}p$

where ΔCp is the change in heat capacity. So, ΔH generally varies with temperature. Therefore:

• "ΔH is dependent on T" is correct.

Catalysts lower the activation energy but do not alter the thermodynamics (ΔH, ΔG, K) of a reaction. ΔH is a state function and depends only on the initial and final states, not on the path (catalyst). Therefore:

• "ΔH is independent of the catalyst, if any" is correct.

Final Answer:

The correct statements are:

• ΔH is dependent on T
• K is independent of the initial amount of CaCO₃
• ΔH is independent of the catalyst, if any

Related Topics and Formulae:

Heterogeneous Equilibrium: Involves reactants and products in different phases. The concentrations of pure solids and liquids are constant and not included in the equilibrium constant expression.

Equilibrium Constant (K): For a general reaction, K = [products] / [reactants] (raised to their stoichiometric coefficients), with solids/liquids taken as 1. K depends only on temperature.

Enthalpy Change (ΔH): ΔH = H_products - H_reactants. It is temperature-dependent and unaffected by catalysts.

Catalyst: Speeds up the reaction by providing an alternative path but does not change ΔH, ΔG, or K.