The rate of a reaction increases by 2.5 times when the temperature is raised from 300K to 310K. If K is the rate constant at 310 K will be equal to

Options

A. (a) K
B. (b) 2K
C. (c) 2.5K
D. (d) 3K

Answer

To solve the problem, we will use the concept of the temperature coefficient and the relationship between the rate of reaction and the rate constant.

### Step-by-Step Solution:

1. **Understanding the Problem**: We know that the rate of a reaction increases by 2.5 times when the temperature is raised from 300 K to 310 K. We need to find the rate constant \( K \) at 310 K.

2. **Using Temperature Coefficient**: The temperature coefficient \( \theta \) is defined as the ratio of the rate of reaction at \( T + 10 \) K to the rate at \( T \) K. In this case, we can express it as:
\[ \theta = \frac{K_{310}}{K_{300}} = 2.5 \]

3. **Expressing the Rate Constants**: From the equation above, we can rearrange it to express the rate constant at 310 K in terms of the rate constant at 300 K:
\[ K_{310} = 2.5 \times K_{300} \]

4. **Assuming a Value for \( K_{300} \)**: Let’s denote the rate constant at 300 K as \( K \). Therefore, we can write:
\[ K_{300} = K \]

5. **Substituting the Value**: Now substituting \( K_{300} \) in our previous equation, we get:
\[ K_{310} = 2.5 \times K \]

6. **Conclusion**: Therefore, the rate constant at 310 K is \( 2.5K \).

### Final Answer:
The rate constant \( K \) at 310 K will be equal to \( 2.5K \).

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