The rate of a reaction

Options

A. increase with increase in temperature
B. decrease with increase in temperature
C. does not depend on temperature
D. does not depend on concentration

Explanation

### Step-by-Step Solution

1. **Understanding Rate of Reaction**: The rate of a reaction is defined as the change in concentration of reactants or products per unit time. It is influenced by various factors including concentration, temperature, and the presence of catalysts.

2. **Rate Equation**: The rate of a reaction can be expressed mathematically as:
\[ \text{Rate} = k \cdot [A]^n \]
where \( k \) is the rate constant, \([A]\) is the concentration of the reactant, and \( n \) is the order of the reaction.

3. **Effect of Temperature on Rate Constant**: According to the Arrhenius equation, the rate constant \( k \) is related to temperature \( T \) as follows:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]
where \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

4. **Analyzing the Arrhenius Equation**: From the Arrhenius equation, we can see that as the temperature \( T \) increases, the term \(-\frac{E_a}{RT}\) becomes less negative, which results in an increase in the value of \( k \).

5. **Conclusion on Rate of Reaction**: Since the rate of reaction is directly proportional to the rate constant \( k \), an increase in temperature leads to an increase in the rate constant \( k \), which in turn increases the rate of the reaction. Therefore, the rate of the reaction increases with an increase in temperature.

6. **Final Answer**: The correct answer to the question is that the rate of the reaction **increases with an increase in temperature**.