Question

The thermal dissociation equilibrium of $CaC{{O}_{3}}(s)$ is studied under different conditions.
\[CaC{{O}_{3}}(s)\rightleftharpoons CaO(s)+C{{O}_{2}}(g)\]
For this equilibrium, the correct statement(s) is (are):
(A) $\Delta H$ is dependent on T.
(B) K is dependent on the initial amount of $CaC{{O}_{3}}(s)$.
(C) K is dependent on the pressure of $C{{O}_{2}}$ at a given T.
(D) $\Delta H$ is independent of the catalyst if any.

Answer 1

Hint: This question has multiple correct answers. To answer this, write the equilibrium constant equations for the given reaction in terms of partial pressure and in terms of concentration. Remember that we exclude the pure solids and liquids while writing the equilibrium equation as their amount remains unchanged throughout the reaction.

Complete step by step solution:
The given equation is the dissociation of calcium carbonate into calcium oxide and carbon dioxide. Let us go through the options and check if they are correct or not.
In the first option, we have that $\Delta H$ is dependent on T.
We know that $\Delta H$ is the enthalpy of the system. Enthalpy is a state function and is dependent upon the change in internal energy, volume and pressure of the system. The enthalpy change of a reaction is also dependent upon the temperature change. Therefore, this statement is correct.
In the next option, we have K is dependent on the initial amount of $CaC{{O}_{3}}(s)$. We can see that the reaction is in equilibrium. The starting compound is a pure solid and so is the calcium oxide that is produced. We know that amount of pure solid or liquid is excluded from the equilibrium constant as their concentration says the same throughout the reaction. Therefore, this statement is also correct.
Then we have K is dependent on the pressure of $C{{O}_{2}}$ at a given T. If we write the equilibrium constant in terms of partial pressure since calcium carbonate and calcium oxide are pure solids so they are excluded from the equation. So K is dependent only on the partial pressure of carbon dioxide. Therefore, this statement is also correct.
\[K={{P}_{C{{O}_{2}}}}\]
And lastly, we have $\Delta H$ is independent of the catalyst if any. We know that catalysts do not affect the reactants or the products. A catalyst lowers the activation energy thus providing us with a lower energy pathway and helps to reach equilibrium at a faster rate. Therefore, the enthalpy is independent of catalyst. So this statement is also correct.
We can see from the above discussion that all the statements given above are correct.
Therefore, the correct answers are options- [A] $\Delta H$ is dependent on T, [B] K is dependent on the initial amount of $CaC{{O}_{3}}(s)$, [C] K is dependent on the pressure of $C{{O}_{2}}$ at a given T and [D] $\Delta H$ is independent of the catalyst if any.

Note: We should not confuse enthalpy with entropy. Enthalpy is a measure of the change in work done or heat released or required during the reaction whereas entropy is the general randomness or the degree of disorder of the system. The given reaction is a dissociation reaction as a single compound dissociates to give us two different products.