Problem 9 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Eor a reversible reaction: \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}\), if the concentrations of the reactants are doubled at a definite temperature, then equilibrium constant will (a) be doubled (b) be halved (c) be one fourth (d) remain same

Step-by-Step Solution

Answer

The equilibrium constant (d) will remain same.

Step 1: Understanding the concept of equilibrium constant (K)

For any reversible reaction, the equilibrium constant (K) is the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their coefficients in the balanced equation. For the reaction given, \( \mathrm{A} + \mathrm{B} \rightleftharpoons \mathrm{C} \), the equilibrium constant (K) is given by \( K = \frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]} \) where [C], [A], and [B] are the concentrations of C, A, and B, respectively. K is only dependent on the temperature and not on the concentrations of the reactants or products.

Step 2: Analyzing the effect of changing concentrations on K

Doubling the concentration of the reactants A and B does not affect the equilibrium constant. Instead, the system will adjust until a new equilibrium is reached, where the concentration of products and reactants will satisfy the original K value at the given temperature.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. Consequently, the concentrations of reactants and products remain constant over time, but not necessarily equal.

For the reaction \( \text{A} + \text{B} \rightleftharpoons \text{C} \), at equilibrium, the rate at which \text{A} and \text{B} combine to form \text{C} is equal to the rate at which \text{C} decomposes back into \text{A} and \text{B}. It is essential to understand that reaching equilibrium doesn't mean that the reactants and products are no longer reacting. Rather, there is a dynamic balance between the forward and reverse reactions, with no net change in concentration.

Equilibrium can be disturbed by changes in concentration, temperature, or pressure. However, the value of the equilibrium constant (\text{K}) only changes with temperature. The equilibrium constant is a quantitative measure of the reaction's position at equilibrium and helps predict the direction of the reaction.

Reaction Quotient

The reaction quotient (\text{Q}) is a measure of the relative amounts of products and reactants present during a reaction at a given instant, used to predict the direction in which the reaction will proceed to reach equilibrium. It is calculated in the same way as the equilibrium constant but is used before the system reaches equilibrium.

For the reaction \( \text{A} + \text{B} \rightleftharpoons \text{C} \), the reaction quotient (\text{Q}) is given by \( Q = \frac{[\text{C}]}{[\text{A}][\text{B}]} \). If \text{Q} is less than \text{K}, the forward reaction will be favored until equilibrium is achieved. Conversely, if \text{Q} is greater than \text{K}, the reverse reaction will be favored. When \text{Q} equals \text{K}, the system is at equilibrium, and there are no further net changes in concentrations of reactants and products.

This concept allows us to predict the effect of changing concentrations on the system's equilibrium. For instance, doubling the concentrations of \text{A} and \text{B} will temporarily shift \text{Q}, but the system will adjust, and eventually, \text{K} will remain constant if the temperature is unchanged.

Le Chatelier's Principle

Le Chatelier's Principle is a qualitative tool for predicting how a change in conditions can affect the chemical equilibrium of a reaction. It states that if an external change is applied to a system at equilibrium, the system adjusts in such a way as to partially counteract the imposed change and a new equilibrium is established.

For example, in the reaction \( \text{A} + \text{B} \rightleftharpoons \text{C} \), if the concentration of \text{A} or \text{B} is increased, the system reacts by favoring the forward reaction to use up the extra reactants and form more \text{C}, thus partially offsetting the change.

This principle applies to changes in concentration, temperature, and pressure. It is important to note that while Le Chatelier's Principle predicts the direction in which the system will move to re-establish equilibrium, it does not define the equilibrium constant. This principle helps us understand the dynamic nature of equilibrium and the system's response to maintain equilibrium in the event of a disturbance.