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

Answer

To solve the question regarding the specific rate constant of a first-order reaction, we will follow these steps:

### Step 1: Understand the Definition
The specific rate constant (k) of a reaction is a proportionality constant that relates the rate of the reaction to the concentration of the reactants. For a first-order reaction, the rate is directly proportional to the concentration of one reactant.

**Hint:** Remember that the rate constant is specific to the reaction and does not change with concentration.

### Step 2: Identify the Factors Affecting k
The specific rate constant for a first-order reaction is primarily influenced by temperature. According to the Arrhenius equation, the rate constant k is given by:

\[ k = A e^{-\frac{E_a}{RT}} \]

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.

**Hint:** Focus on how temperature and activation energy are related to the rate constant.

### Step 3: Analyze the Arrhenius Equation
From the Arrhenius equation, we can see that as the temperature (T) increases, the term \( e^{-\frac{E_a}{RT}} \) increases, which in turn increases the value of k. This means that the rate constant increases with an increase in temperature.

**Hint:** Think about how increasing temperature affects molecular collisions and energy.

### Step 4: Conclusion on the Dependence of k
Based on the Arrhenius equation, we conclude that the specific rate constant of a first-order reaction depends on temperature and activation energy. It does not depend on the concentration of reactants or products.

**Hint:** Remember that k is a constant for a given reaction at a specific temperature.

### Final Answer
The specific rate constant of a first-order reaction depends on the temperature and activation energy, as described by the Arrhenius equation.