Consider two reactions having same Arrhenius factor A, but different energy of activation.
(i) `A rarr B , Ea_(1)=20kJ`
(ii) `Crarr D, Ea_(2)=30kJ`
Both are at temperature `25^(@)C` It temperature in both reaction is increased slightly in such a way that change in temperature in both case is same than choose the correct options.

Options

A. The second reaction is faster
B. The second reaction is more sensitive towards temperature variation
C. If temperature increases, rate of first reaction increase more sharply
D. All the above are correct

Answer

To solve the problem, we need to analyze the two reactions given their activation energies and how they respond to temperature changes.

### Step-by-Step Solution:

1. **Identify the Reactions and Activation Energies:**
- Reaction 1: \( A \rightarrow B \) with \( E_{a1} = 20 \, \text{kJ} \)
- Reaction 2: \( C \rightarrow D \) with \( E_{a2} = 30 \, \text{kJ} \)

2. **Understand the Arrhenius Equation:**
The rate constant \( k \) for a reaction can be expressed using the Arrhenius equation:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]
where:
- \( A \) is the Arrhenius factor (pre-exponential factor),
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

3. **Compare the Activation Energies:**
Since both reactions have the same Arrhenius factor \( A \), the reaction with the lower activation energy will have a higher rate constant at a given temperature. Therefore:
- Reaction 1 (20 kJ) will have a higher rate constant than Reaction 2 (30 kJ) at the same temperature.

4. **Effect of Temperature Increase:**
When the temperature is increased slightly for both reactions:
- The rate constant \( k \) for both reactions will increase, but the increase will be more significant for the reaction with the lower activation energy (Reaction 1).
- This is because the exponential term \( e^{-\frac{E_a}{RT}} \) is more sensitive to temperature changes when \( E_a \) is lower.

5. **Conclusion on Sensitivity to Temperature:**
- Reaction 2, with a higher activation energy, is less sensitive to temperature changes compared to Reaction 1.
- Therefore, the statement that "the second reaction is more sensitive towards temperature variation" is incorrect.

6. **Rate of Reactions with Temperature Increase:**
- The rate of Reaction 1 will increase more sharply with a temperature increase compared to Reaction 2 due to its lower activation energy.

7. **Final Evaluation of Options:**
- Option A: Incorrect - Reaction 2 is not faster.
- Option B: Incorrect - Reaction 2 is not more sensitive to temperature.
- Option C: Correct - Rate of Reaction 1 increases more sharply.
- Option D: Incorrect - Not all options are correct.

### Correct Answer:
Only option C is correct: "If temperature increases, the rate of the first reaction increases more sharply."