Problem 121 - A Complete Resource Book in Chemistry for JEE Main

Question

For the system at equilibrium which of the following are correct? (a) On increasing the temperature of an endothermic reaction, the equilibrium shifts in forward direction because Q decreases. (b) On increasing the temperature of an endothermic reaction, the concentration in moles per litre of the reactants increases. (c) \(\log \mathrm{K}=\frac{1}{2.303 \mathrm{R}}\left(\Delta \mathrm{S}^{\circ}-\frac{\Delta \mathrm{H}^{\circ}}{\mathrm{T}}\right)\) (d) On increasing the temperature of an endothermic reaction, the equilibrium shifts in forward direction because \(\mathrm{K}\) increases.

Step-by-Step Solution

Answer

Statements (c) and (d) are correct.

Step 1: Analyze statement (a)

Statement (a) claims that increasing the temperature of an endothermic reaction decreases the reaction quotient, \( Q \), causing the equilibrium to shift forward. However, this isn't accurate because increasing the temperature affects the equilibrium constant \( K \), not the current reaction quotient \( Q \). In fact, \( K \) would increase due to Le Chatelier's principle. Thus, statement (a) is incorrect.

Step 2: Evaluate statement (b)

Statement (b) suggests that increasing the temperature of an endothermic reaction increases the concentration of the reactants. This goes against Le Chatelier's principle, as increasing the temperature should favor the products in an endothermic reaction, thus decreasing the concentration of reactants. Therefore, statement (b) is incorrect.

Step 3: Verify statement (c)

Statement (c) provides a formula for the log of the equilibrium constant \( K \). The equation \( \log \mathrm{K}=\frac{1}{2.303 \mathrm{R}}\left(\Delta \mathrm{S}^{\circ}-\frac{\Delta \mathrm{H}^{\circ}}{\mathrm{T}}\right) \) follows from the thermodynamic derivation based on the Gibbs free energy equation. Therefore, statement (c) is correct.

Step 4: Assess statement (d)

Statement (d) claims that increasing the temperature of an endothermic reaction causes the equilibrium to shift forward because \( \mathrm{K} \) increases. This is consistent with Le Chatelier's principle; for an endothermic reaction, an increase in temperature will increase \( K \), favoring the formation of products. Thus, statement (d) is correct.

Key Concepts

Endothermic Reactions

In chemistry, reactions can be categorized as either endothermic or exothermic based on whether they absorb or release heat. Endothermic reactions are those that absorb heat from their surroundings.
They essentially "take in" energy in the form of heat, which leads to a cooling effect on their surroundings. Understanding this concept is crucial when thinking about how temperature affects chemical equilibrium. When the temperature is increased for an endothermic reaction, additional heat acts as a reactant.
As a result, the reaction tends to proceed forward, producing more products. This understanding helps to explain shifts in equilibrium caused by temperature changes.

Le Chatelier's Principle

Le Chatelier's principle is a crucial tool for predicting how a change in conditions can affect the position of equilibrium of a chemical reaction. It states that if an external change is applied to a system at equilibrium, the system will adjust itself to minimize that change and reach a new equilibrium. When you apply heat to an endothermic reaction (as heat is effectively a reactant here), the equilibrium shifts towards the products to "take in" the added heat.
This is why increasing the temperature of an endothermic reaction typically results in more products being formed. This principle can be applied to various conditions, including changes in concentration, pressure, or temperature, giving a valuable insight into how equilibrium adjusts to maintain balance.

Equilibrium Constant (K)

The equilibrium constant, denoted as \( K \), is a measure of the ratio of the concentrations of products to reactants at equilibrium.
It gives us an idea of the position of equilibrium – whether it lies toward the products or the reactants.For an endothermic reaction, increasing the temperature increases \( K \), indicating a shift towards the formation of more products. The mathematical expression for \( K \) comes from the concentrations of the products and reactants raised to the power of their coefficients in the balanced chemical equation.Moreover, the value of \( K \) is temperature dependent. As temperature changes, \( K \) can either increase or decrease, depending on whether the reaction is endothermic or exothermic.
In endothermic reactions, since the reaction absorbs heat, \( K \) will increase with a temperature rise.

Reaction Quotient (Q)

The reaction quotient, \( Q \), is very similar to the equilibrium constant \( K \) in that it is calculated using the concentrations of reactants and products. However, \( Q \) is evaluated at any point in time, not just at equilibrium.To determine where a reaction stands concerning its equilibrium, you compare \( Q \) with \( K \):

• If \( Q < K \), the reaction will proceed in the forward direction to produce more products.
• If \( Q > K \), the reaction will go in the reverse direction to produce more reactants.
• If \( Q = K \), the system is at equilibrium.

Changes in temperature typically affect \( K \) rather than \( Q \), which is why temperature's impact is usually discussed in terms of shifts in \( K \).
Understanding \( Q \) helps in predicting in which direction a reaction will proceed when disturbed.