The effect of temperature on the rate constant of a reaction is given by

Options

A. Arrhenius Equation
B. Nernst Equation
C. Vant Hoff Equation
D. Gibb's Helmholtz Equation

Answer

To solve the question regarding the effect of temperature on the rate constant of a reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Options**: The question presents four equations:
- Arrhenius equation
- Nernst equation
- Van't Hoff equation
- Gibbs-Helmholtz equation

2. **Understanding the Arrhenius Equation**:
- The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
- This equation shows that the rate constant \( k \) is directly affected by temperature \( T \).

3. **Analyzing the Nernst Equation**:
- The Nernst equation is:
\[ E = E^0 - \frac{RT}{nF} \ln Q \]
where \( E \) is the cell potential, \( E^0 \) is the standard cell potential, \( n \) is the number of moles of electrons, \( F \) is Faraday's constant, and \( Q \) is the reaction quotient.
- This equation relates to electrochemistry and does not provide a direct relationship between temperature and the rate constant of a reaction.

4. **Examining the Van't Hoff Equation**:
- The Van't Hoff equation relates to equilibrium constants:
\[ \ln K = -\frac{\Delta H}{R} \cdot \frac{1}{T} + C \]
where \( K \) is the equilibrium constant and \( \Delta H \) is the change in enthalpy.
- This equation describes how temperature affects the equilibrium constant, not the rate constant.

5. **Reviewing the Gibbs-Helmholtz Equation**:
- The Gibbs-Helmholtz equation is:
\[ \left( \frac{\partial G}{\partial T} \right)_P = -\frac{H}{T^2} \]
where \( G \) is Gibbs free energy and \( H \) is enthalpy.
- This equation shows the relationship between Gibbs free energy and temperature, but it does not relate to the rate constant.

6. **Conclusion**:
- After analyzing all the options, it is clear that the only equation that directly relates the effect of temperature on the rate constant of a reaction is the **Arrhenius equation**.

### Final Answer:
The effect of temperature on the rate constant of a reaction is given by **Arrhenius equation** (Option 1).

---