Problem 49 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant \(K\) in terms of change in entropy is described by [Adv. 2017] (a) With increase in temperature, the value of \(K\) for exothermic reaction decreases because the entropy change of the system is positive (b) With increase in temperature, the value of \(K\) for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases (c) With increase in temperature, the value of \(K\) for endothermic reaction increases because the entropy change of the system is negative (d) With increase in temperature, the value of \(K\) for exothermic reaction decreases because favourable change in entropy of the surroundings decreases

Step-by-Step Solution

Answer

Correct statements: (b) and (d).

Step 1: Understand the Van't Hoff Equation

The Van't Hoff equation provides the relationship between the equilibrium constant \(K\) and temperature \(T\): \( \ln K = -\frac{\Delta H^\circ}{R} \left(\frac{1}{T}\right) + \frac{\Delta S^\circ}{R} \), where \( \Delta H^\circ \) is the standard enthalpy change, and \( \Delta S^\circ \) is the standard entropy change. This tells us how \(K\) changes with \(T\).

Step 2: Exothermic Reactions and Temperature

For exothermic reactions, the enthalpy change \( \Delta H^\circ \) is negative. According to the Van't Hoff equation, as temperature increases, \(K\) decreases because the term \( -\frac{\Delta H^\circ}{R} \left(\frac{1}{T}\right) \) becomes less negative. Hence, option (a) and (d) are partially correct because \(K\) decreases, but we have to check the entropy explanation.

Step 3: Entropy Change in the System and Surroundings

For exothermic reactions, the entropy of the surroundings increases since the system releases heat. Increasing temperature decreases the effect of heat release on the surroundings. Thus, the favorable change in entropy of the surroundings decreases, supporting option (d).

Step 4: Endothermic Reactions and Temperature

For endothermic reactions, \( \Delta H^\circ \) is positive, so as temperature increases, \(K\) increases. This corresponds to option (b) as it emphasizes the effect of entropy change on the surroundings.

Key Concepts

Equilibrium Constant

In chemical reactions, the equilibrium constant, represented by the symbol \(K\), is a fundamental concept that describes the balance between reactants and products in a reaction at a given temperature. The value of \(K\) indicates the extent to which a reaction will proceed before reaching equilibrium.

• If \(K\) is large, products are favored at equilibrium.
• If \(K\) is small, reactants are favored at equilibrium.

The Van't Hoff equation allows us to understand how this equilibrium constant changes with temperature, providing insight into the behavior of reactions under different conditions.

Endothermic Reactions

Endothermic reactions absorb heat from their surroundings. This means they require energy input to proceed. The standard enthalpy change, \(\Delta H^\circ\), for these reactions is positive. As a result, increasing the temperature tends to favor product formation.
In the context of the Van't Hoff equation, as temperature rises, the equilibrium constant \(K\) increases for endothermic reactions. This happens because the system absorbs more heat, making the forward reaction more favorable. Thus, more products are formed.

Exothermic Reactions

Exothermic reactions release heat into their surroundings. The standard enthalpy change, \(\Delta H^\circ\), for these reactions is negative. As a result, increasing the temperature discourages the formation of products.
According to the Van't Hoff equation, as temperature increases, the equilibrium constant \(K\) decreases for exothermic reactions. The negative enthalpy term becomes less pronounced, shifting the balance towards the formation of reactants rather than products.

Entropy Change

Entropy is a measure of disorder or randomness in a system. In chemical reactions, the standard entropy change, \(\Delta S^\circ\), indicates whether the reaction leads to an increase or decrease in disorder.

• For endothermic reactions, an increase in system entropy is often observed, which complements the absorption of heat.
• For exothermic reactions, entropy in the surroundings increases due to the release of heat.

Both system and surroundings' entropy changes are crucial in determining the reaction's spontaneity and temperature dependence.

Temperature Effect on Equilibrium

The impact of temperature on chemical equilibrium is crucial. According to Le Chatelier's principle, a change in temperature will shift the equilibrium to counteract the effect of the change. This is mathematically described using the Van't Hoff equation.

• For endothermic reactions, increasing temperature shifts the equilibrium position towards products, increasing \(K\).
• For exothermic reactions, increasing temperature shifts the equilibrium position towards reactants, decreasing \(K\).

Understanding this helps predict how reactions will behave under different thermal conditions, which is essential for controlling chemical processes.