The specific rate constant of a first-order reaction depends on the :

Options

A. concentration of the reactant
B. concentration of the product
C. time
D. temperature

Explanation

To determine what the specific rate constant of a first-order reaction depends on, we can analyze the factors influencing the rate constant (k) in chemical kinetics.

### Step-by-Step Solution:

1. **Understanding Rate Constants**: The specific rate constant (k) for any reaction is a proportionality factor that relates the rate of a reaction to the concentrations of the reactants. For a first-order reaction, the rate law can be expressed as:
\[ \text{Rate} = k[A] \]
where [A] is the concentration of the reactant.

2. **Factors Affecting Rate Constant**: The rate constant (k) is influenced by several factors, but primarily it is dependent on temperature. According to the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( A \) is the pre-exponential factor (frequency factor),
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

3. **Temperature Dependence**: From the Arrhenius equation, we see that as the temperature (T) increases, the exponential term \( e^{-\frac{E_a}{RT}} \) increases, leading to an increase in the rate constant (k). This means that the rate constant is directly related to temperature.

4. **Independence from Other Factors**: The rate constant does not depend on the concentration of the reactants or products, nor does it depend on time. It is a characteristic of the reaction at a given temperature.

5. **Conclusion**: Therefore, we conclude that the specific rate constant of a first-order reaction depends solely on the temperature of the reaction.

### Final Answer:
The specific rate constant of a first-order reaction depends on the **temperature**.

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