Problem 50 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The thermal dissociation equilibrium of \(\mathrm{CaCO}_{3}\) (s) is studied under different conditions \(\mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) .\) For this equilibrium, the correct statement(s) is (are) (a) \(\Delta H\) is dependent on \(T\) (b) \(K\) is independent of the initial amount of \(\mathrm{CaCO}_{3}\) (c) \(K\) is dependent on the pressure of \(\mathrm{CO}_{2}\) at a given \(T\) (d) \(\Delta H\) is independent of catalyst, if any

Step-by-Step Solution

Answer

Statements (b) and (d) are correct.

Step 1: Understanding the Equilibrium

The reaction given is a typical example of a thermal dissociation reaction where calcium carbonate (\(\mathrm{CaCO_3(s)}\)) dissociates into calcium oxide (\(\mathrm{CaO(s)}\)) and carbon dioxide gas (\(\mathrm{CO_2(g)}\)). The equilibrium involved is based on the decomposition of a solid into another solid and a gas.

Step 2: Analyzing Statement (a)

Statement (a) is about the enthalpy change (\(\Delta H\)) being dependent on temperature (\(T\)). Generally, the enthalpy change of a reaction is considered to be independent of temperature in an ideal situation unless provided with explicit information indicating otherwise. Therefore, for most reactions at moderate temperatures, \(\Delta H\) remains constant.

Step 3: Analyzing Statement (b)

Statement (b) suggests that the equilibrium constant \(K\) is independent of the initial amount of \(\mathrm{CaCO_3}\). Since equilibrium constants for reactions involving solids and gases are defined based on partial pressures or concentrations that do not include solids, \(K\) indeed remains independent of the initial amounts of solids such as \(\mathrm{CaCO_3(s)}\).

Step 4: Analyzing Statement (c)

Statement (c) proposes that \(K\) is dependent on the pressure of \(\mathrm{CO_2}\) at a given temperature. The equilibrium constant is defined in terms of the partial pressures of gases involved, but at a given temperature, \(K\) itself is constant. Changes in pressure affect the position of the equilibrium, not the value of \(K\).

Step 5: Analyzing Statement (d)

Statement (d) indicates that \(\Delta H\) is independent of a catalyst, if any. Catalysts only affect the rate of a reaction by providing an alternative pathway with a lower activation energy. They do not affect the position of equilibrium or the enthalpy change of the reaction.

Step 6: Conclusion

The correct statements based on the analysis above are that \(K\) is independent of the initial amount of \(\mathrm{CaCO_3}\) (statement b) and that \(\Delta H\) is independent of the catalyst (statement d). Statement (a) is incorrect as \(\Delta H\) is typically constant, and statement (c) is incorrect as \(K\) is independent of the partial pressure of \(\mathrm{CO_2}\) at a given temperature.

Key Concepts

Thermal Dissociation

Thermal dissociation occurs when a compound breaks down into simpler substances upon heating. In the given problem, calcium carbonate (\(\mathrm{CaCO_3(s)}\)) undergoes thermal dissociation to form calcium oxide (\(\mathrm{CaO(s)}\)) and carbon dioxide gas (\(\mathrm{CO_2(g)}\)). This process is a reversible reaction, meaning that it can reach a point where the rate of decomposition equals the rate of the reverse reaction, forming an equilibrium.
• These reactions are common in thermal decomposition processes.
• The presence of gases, such as carbon dioxide, shifts the reaction dynamics.
When studying thermal dissociation, it's important to note the role of temperature. Increasing temperature usually favors the endothermic direction, in this case, the decomposition of \(\mathrm{CaCO_3}\). Consequently, understanding how this equilibrium is established provides insight into factors impacting the yield of the products.

Equilibrium Constant

The equilibrium constant, denoted as \(K\), is a crucial concept when analyzing chemical equilibria. This constant characterizes the ratio of the concentrations of the products to that of the reactants, each raised to the power of their stoichiometric coefficients at equilibrium. For reactions involving gases, such as the decomposition of \(\mathrm{CaCO_3}\), \(K\) is expressed in terms of partial pressures.
• In solid-gas equilibria, solids are not included in the expression for \(K\).
• The equilibrium constant is solely dependent on temperature, and not on the initial amounts of reactants.
It's essential to understand that \(K\) remains constant given a specific temperature. Changes in conditions such as pressure or volume will influence the equilibrium position itself but not the value of \(K\). This explains why \(K\) is independent of the initial amount of \(\mathrm{CaCO_3}\) used, as this does not alter the established equilibrium ratio.

Enthalpy Change

Enthalpy change (\(\Delta H\)) refers to the heat change at constant pressure during a chemical reaction. It is a fundamental property that determines whether a reaction is endothermic or exothermic. For the task at hand, the reaction of \(\mathrm{CaCO_3}\) breaking down is typically endothermic, meaning it absorbs heat.
• \(\Delta H\) remains constant for a reaction at a given condition unless specific external factors (extreme temperature changes) are applied.
• Catalysts influence the reaction rate but not its enthalpy change.
Understanding \(\Delta H\) provides insight into the thermal requirements of a process. While temperature can alter the equilibrium position, \(\Delta H\) itself does not change with the addition of a catalyst or adjustments in initial reactants. This highlights the unique characteristics of \(\Delta H\) as a measure of reaction energy changes, separate from dynamic processes.