The equilibrium constant of a reversible reaction at a given temperature

Options

A. depends on initial concentration of reactants
B. depends on the concentration of products at equilibrium
C. does not depend on the initial concentration
D. is not a characteristic of the reaction.

Answer

To determine the equilibrium constant of a reversible reaction at a given temperature, we can follow these steps:

### Step 1: Understand the Reaction
Consider a hypothetical reversible reaction:
\[ A_{(l)} + B_{(l)} \rightleftharpoons C_{(l)} + D_{(l)} \]
Here, A and B are reactants, while C and D are products.

### Step 2: Define Initial Concentrations
Let’s denote the initial concentrations of the reactants and products as:
- Initial concentration of A = \( [A]_0 \)
- Initial concentration of B = \( [B]_0 \)
- Initial concentration of C = \( [C]_0 \)
- Initial concentration of D = \( [D]_0 \)

### Step 3: Define Equilibrium Concentrations
At equilibrium, the concentrations can be represented as:
- Equilibrium concentration of A = \( [A]_{eq} \)
- Equilibrium concentration of B = \( [B]_{eq} \)
- Equilibrium concentration of C = \( [C]_{eq} \)
- Equilibrium concentration of D = \( [D]_{eq} \)

### Step 4: Write the Expression for the Equilibrium Constant
The equilibrium constant \( K_{eq} \) for the reaction can be expressed as:
\[ K_{eq} = \frac{[C]_{eq}^c \cdot [D]_{eq}^d}{[A]_{eq}^a \cdot [B]_{eq}^b} \]
where \( a, b, c, \) and \( d \) are the stoichiometric coefficients of the respective species in the balanced equation.

### Step 5: Analyze Dependence on Concentration
From the expression of \( K_{eq} \), we can see that:
- The equilibrium constant depends on the concentrations of the products and reactants at equilibrium, not their initial concentrations.
- Therefore, it does not depend on the initial concentrations of the reactants or products.

### Step 6: Consider Temperature
The equilibrium constant is dependent on temperature. According to Van't Hoff's equation:
\[ K_{eq} = A e^{-\frac{\Delta H^0}{RT}} \]
where:
- \( A \) is the pre-exponential factor,
- \( \Delta H^0 \) is the standard enthalpy change of the reaction,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

### Conclusion
Based on the analysis:
- The equilibrium constant does not depend on the initial concentrations of reactants or products.
- It is a characteristic of the reaction at a given temperature.

Thus, the correct answer is: **does not depend on the initial concentration.**