At 300 K rate constant for `A to` product at t= 50 min in `0.02 ^(-1)`, then rate constant at t= 75 min and 310 K will be in `s^(-1)`

Options

A. `0.04/25`
B. `0.04 xx 25`
C. 0.04
D. `0.02/25`

Explanation

To solve the problem, we need to determine the rate constant at 310 K given that the rate constant at 300 K is 0.02 s⁻¹. We will also consider the effect of temperature change on the rate constant.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Rate constant at 300 K (K₁) = 0.02 s⁻¹
- Time at which K₁ is measured = 50 min (not directly needed for K calculation)
- Temperature increase = 310 K - 300 K = 10 K

2. **Use the Temperature Coefficient:**
- The temperature coefficient (η) indicates how the rate constant changes with temperature. For a typical reaction, a 10 K increase can approximately double the rate constant.
- Therefore, we can express this relationship as:
\[ \frac{K_{2}}{K_{1}} = η \]
- For a 10 K increase, η is approximately 2.

3. **Calculate the New Rate Constant (K₂):**
- Using the relationship from step 2:
\[ K_{2} = K_{1} \times η \]
- Substituting the values:
\[ K_{2} = 0.02 \, \text{s}^{-1} \times 2 = 0.04 \, \text{s}^{-1} \]

4. **Final Answer:**
- The rate constant at 310 K is **0.04 s⁻¹**.