The equilibrium constant of a reversible chemical reaction at a given temperature

does not depend on the initial concentration of reactants

The correct answer is option 3. does not depend on the initial concentration of reactants.

The equilibrium constant (\(K\)) of a reversible chemical reaction is a fundamental concept in chemical equilibrium. It provides a quantitative measure of the position of equilibrium and is unique to each reaction at a given temperature. Here’s a detailed explanation addressing the given options:

For a general reversible reaction:

\(aA + bB \rightleftharpoons cC + dD\)

the equilibrium constant expression is given by:

\(K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \)

where:

\([A]\), \([B]\), \([C]\), and \([D]\) are the equilibrium concentrations of the reactants and products.

\(a\), \(b\), \(c\), and \(d\) are the stoichiometric coefficients of the respective species in the balanced equation.

Analysis of the Given Options

(1) Depends on the initial concentration of the reactants: The statement is incorrect. The equilibrium constant is independent of the initial concentrations of the reactants or products. It is solely determined by the equilibrium concentrations, which adjust according to the initial conditions to maintain the constant value of \(K\).

(2) Depends on the concentration of one of the products at equilibrium: The statement is incorrect. The equilibrium constant is determined by the concentrations of all reactants and products at equilibrium, as shown in the equilibrium expression. It is not dependent on any single concentration but rather the ratio of the products to reactants raised to their stoichiometric powers.

(3) Does not depend on the initial concentration of reactants: The statement is correct. The equilibrium constant \(K\) is a characteristic of the reaction at a given temperature and does not depend on the initial concentrations of the reactants or products. The system will adjust the concentrations of reactants and products until the equilibrium condition, as dictated by \(K\), is met.

(4) Is not characteristic of the reaction: The statement is incorrect. The equilibrium constant is indeed characteristic of a specific reaction at a particular temperature. It is a unique value for each reaction and is used to predict the direction of the reaction and the extent to which reactants are converted to products.

Detailed Explanation

The equilibrium constant \(K\) is a reflection of the ratio of the concentrations of the products to the reactants at equilibrium. Here’s why the correct understanding aligns with Option (3):

Reaction Independence: The equilibrium constant is intrinsic to the reaction and is calculated from the equilibrium concentrations, which are a result of the reaction proceeding until equilibrium is achieved.

Temperature Dependence: The value of \(K\) changes with temperature but remains constant at a given temperature for a particular reaction.

Initial Concentrations: While the initial concentrations of reactants and products can affect how the system reaches equilibrium (i.e., the path taken to reach equilibrium), they do not affect the equilibrium constant itself. The system adjusts its concentrations dynamically to satisfy the equilibrium expression once equilibrium is achieved.

Consider the reaction:

\( N_2 (g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g) \)

If the equilibrium constant \(K\) for this reaction at a certain temperature is given by:

\(K = \frac{[NH_3]^2}{[N_2][H_2]^3} \)

Regardless of the initial amounts of \(N_2\) and \(H_2\) (whether you start with high or low initial concentrations), the reaction will adjust the concentrations of \(N_2\), \(H_2\), and \(NH_3\) to satisfy the equilibrium constant \(K\).

The equilibrium constant \(K\) does not depend on the initial concentrations of the reactants or products but is a fixed value for a given reaction at a specific temperature, reflecting the ratio of the equilibrium concentrations of the products to the reactants. Therefore, the correct statement is: (3) does not depend on the initial concentration of reactants.