For the reaction: (s) ⇌ (s) + (g), Kp is — Chemical Equilibrium Chemistry Question

💡 Solution & Explanation

Step 1 - Analyze the given chemical equation and physical phases The given chemical equation represents a heterogeneous equilibrium involving the thermal decomposition of solid calcium carbonate (\ce{CaCO3}) into solid calcium oxide (\ce{CaO}) and gaseous carbon dioxide (\ce{CO2}): \[\ce{CaCO3(s) <=> CaO(s) + CO2(g)}\] Here, we have two distinct physical phases: 1. **Solid phase:** \ce{CaCO3(s)} and \ce{CaO(s)} 2. **Gaseous phase:** \ce{CO2(g)} Step 2 - Define the thermodynamic basis for the equilibrium constant (\(K_p\)) For any chemical equilibrium, the thermodynamic equilibrium constant (\(K\)) is expressed in terms of the activities (\(a\)) of the participating reactants and products: \[K = \frac{a_{\ce{CaO(s)}} \cdot a_{\ce{CO2(g)}}}{a_{\ce{CaCO3(s)}}}\] According to chemical thermodynamics: * The active mass (or thermodynamic activity) of any pure solid or pure liquid phase is constant at a constant temperature and is taken as unity (exactly equal to \(1\)): \[a_{\ce{CaCO3(s)}} = 1\] \[a_{\ce{CaO(s)}} = 1\] This is because the concentration of a pure solid or liquid is independent of its total quantity (since its density and molar mass remain constant). * For gaseous components, the activity is represented by their respective equilibrium partial pressures (\(P\)): \[a_{\ce{CO2(g)}} = P_{\ce{CO2}}\] Step 3 - Write the simplified expression for \(K_p\) Substituting the activities of the solid and gaseous components into the general equilibrium equation: \[K_p = \frac{(1) \cdot P_{\ce{CO2}}}{1}\] \[K_p = \boxed{P_{\ce{CO2}}}\] Therefore, the equilibrium constant in terms of partial pressure (\(K_p\)) depends solely on the partial pressure of gaseous carbon dioxide. Step 4 - Evaluate the options * **Option (A) \(P_{\ce{CO2}}\)**: Correct. As derived above, since the solid phases have an activity of 1, \(K_p\) is equal to the partial pressure of carbon dioxide. * **Option (B) \(P_{\ce{CO2}} / P_{\ce{CaCO3}}\)**: Incorrect. This expression incorrectly includes a partial pressure term for the solid reactant calcium carbonate. Pure solids do not exert a partial pressure in the gaseous phase. * **Option (C) \([\ce{CaO}][\ce{CO2}] / [\ce{CaCO3}]\)**: Incorrect. This represents the concentration-based reaction quotient or \(K_c\) before omitting the constant solid concentration terms. It does not represent \(K_p\). * **Option (D) \(P_{\ce{CaCO3}} / (P_{\ce{CaO}} \cdot P_{\ce{CO2}})\)**: Incorrect. This is the inverted form of the equilibrium constant and incorrectly treats pure solids as gases by including their partial pressures.