A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be `k_(1) and k_(2)` respectively. Then

Options

A. `k_(2)=4 k_(1)`
B. `k_(2)=2 k_(1)`
C. `k_(2) = 0.25 k_(1)`
D. `k_(2)=0.5 k_(1)`

Explanation

To analyze the relationship between the rate constants \( k_1 \) and \( k_2 \) at temperatures 300 K and 280 K respectively, we can use the concept of the temperature coefficient, which states that for many reactions, the rate constant approximately doubles for every 10 °C (or 10 K) increase in temperature.

### Step-by-Step Solution:

1. **Identify the Temperatures and Rate Constants**:
- Let \( T_1 = 300 \, \text{K} \) with rate constant \( k_1 \).
- Let \( T_2 = 280 \, \text{K} \) with rate constant \( k_2 \).

2. **Calculate the Temperature Difference**:
- The difference in temperature \( \Delta T = T_1 - T_2 = 300 \, \text{K} - 280 \, \text{K} = 20 \, \text{K} \).

3. **Determine the Number of 10 °C Increments**:
- Since the temperature difference is 20 K, we can divide this by 10 K to find the number of increments:
\[ \text{Number of increments} = \frac{20 \, \text{K}}{10 \, \text{K}} = 2 \]

4. **Apply the Doubling Rule**:
- According to the temperature coefficient, for each 10 K increase, the rate constant doubles. Thus, for a 20 K increase, the rate constant will double twice:
\[ k_1 = 2^2 \times k_2 = 4 \times k_2 \]

5. **Establish the Relationship**:
- Therefore, we can express the relationship between \( k_1 \) and \( k_2 \) as:
\[ k_1 = 4 k_2 \]

### Final Answer:
The relationship between the rate constants is:
\[ k_1 = 4 k_2 \]