N2O4(aq) $\rightleftharpoons$ 2NO2(g) $\bigtriangleup$H = +ve In the reaction above, an increase in temperature will

Analysis of the Question

This question tests your understanding of Le Chatelier’s Principle and how temperature changes affect the equilibrium constant ($K$) of a chemical reaction.

Concept Explanation

Le Chatelier’s Principle states that if a dynamic equilibrium is disturbed by changing the conditions (like temperature, pressure, or concentration), the position of equilibrium shifts to counteract the change.

1. Temperature and Equilibrium Shift: • The reaction is given as $\Delta H = +ve$, which means it is an endothermic reaction (it absorbs heat). • In an endothermic reaction, heat acts like a reactant: $\text{Heat} + \text{N}_2\text{O}_4 \rightleftharpoons 2\text{NO}_2$. • If you increase the temperature, the system tries to absorb the excess heat by shifting the equilibrium to the right (the product side).

2. Temperature and the Equilibrium Constant ($K$): • The equilibrium constant ($K$) is temperature-dependent. • For an endothermic reaction, an increase in temperature increases the concentration of products relative to reactants. Since $K = \frac{[\text{Products}]}{[\text{Reactants}]}$, an increase in products leads to a larger value for $K$.

Step-by-Step Solution

• Step 1: Identify the nature of the reaction. Since $\Delta H$ is positive, the forward reaction is endothermic.
• Step 2: Apply the temperature change. Increasing the temperature provides more energy to the endothermic forward reaction.
• Step 3: Determine the shift. The equilibrium shifts to the right (towards the products, $\text{NO}_2$).
• Step 4: Determine the effect on $K$. Because the concentration of the products ($\text{NO}_2$) increases and the concentration of the reactant ($\text{N}_2\text{O}_4$) decreases, the ratio $\frac{[\text{NO}_2]^2}{[\text{N}_2\text{O}_4]}$ increases. Thus, the value of the equilibrium constant increases.

Evaluation of Options

• A is incorrect because the equilibrium shifts to the right, increasing product production, not reactant production.
• B is correct because, for endothermic reactions, $K$ increases as temperature increases.
• C is incorrect because the equilibrium shifts to the right (forward), not the left.
• D is incorrect because $K$ only decreases with temperature in exothermic reactions ($\Delta H = -ve$).

Exam Tip

Remember the "Endo-Up" rule: For Endothermic reactions, increasing temperature makes the equilibrium constant go Up. For Exothermic reactions, increasing temperature makes the equilibrium constant go Down.