Two reaction : `X rarr` Products and `Y rarr` Products have rate constants `k_(1)` and `k_(2)` at temperature `T` and activation energies `E_(1)` and `E_(2)`, respectively. If `k_(1) gt k_(2)` and `E_(1) lt E_(2)` (assuming that the Arrhenius factor is same for both the Products), then
(I) On increaisng the temperature, increase in `k_(2)` will be greater than increaisng in `k_(1)`.
(II) On increaisng the temperature, increase in `k_(1)` will be greater than increase in `k_(2)`.
(III) At higher temperature, `k_(1)` will be closer to `k_(2)`.
(IV) At lower temperature, `k_(1) lt k_(2)`

Options

A. I
B. II
C. I, III
D. I, III, IV

Explanation

To solve the problem, we will analyze the information given about the two reactions and apply the Arrhenius equation to understand the behavior of the rate constants \( k_1 \) and \( k_2 \) with respect to temperature changes.

### Step-by-Step Solution:

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

2. **Given Information**:
- For reaction \( X \):
- Rate constant: \( k_1 \)
- Activation energy: \( E_1 \)
- For reaction \( Y \):
- Rate constant: \( k_2 \)
- Activation energy: \( E_2 \)
- Conditions: \( k_1 > k_2 \) and \( E_1 < E_2 \)

3. **Effect of Temperature on Rate Constants**:
Since \( E_1 < E_2 \), we know that:
- The reaction with lower activation energy (\( E_1 \)) will have a higher rate constant (\( k_1 \)) at a given temperature compared to the one with higher activation energy (\( E_2 \)).
- When the temperature increases, both \( k_1 \) and \( k_2 \) will increase, but the increase in \( k_1 \) will be greater than that in \( k_2 \) because the exponential factor is more sensitive to changes in temperature for lower activation energies.

4. **Analyzing the Statements**:
- **Statement I**: "On increasing the temperature, increase in \( k_2 \) will be greater than increase in \( k_1 \)."
- This is **incorrect** because \( k_1 \) will increase more than \( k_2 \) due to its lower activation energy.

- **Statement II**: "On increasing the temperature, increase in \( k_1 \) will be greater than increase in \( k_2 \)."
- This is **correct** as explained above.

- **Statement III**: "At higher temperature, \( k_1 \) will be closer to \( k_2 \)."
- This is **incorrect** because \( k_1 \) will still be greater than \( k_2 \) due to the difference in activation energies.

- **Statement IV**: "At lower temperature, \( k_1 < k_2 \)."
- This is **incorrect** because at the initial temperature \( T \), we know \( k_1 > k_2 \).

5. **Conclusion**:
The only correct statement is **Statement II**. Therefore, the answer is that the increase in \( k_1 \) will be greater than the increase in \( k_2 \) upon increasing the temperature.

### Final Answer:
**The correct statement is (II): On increasing the temperature, increase in \( k_1 \) will be greater than increase in \( k_2 \).**