The rate of a certain reaction increases by `2.3` times when the temperature is raised form `300K` to `310 K`. If `k` is the rate constant at `300K,` then the rate constant at `310 K` will be equal to

Options

A. `2k`
B. `k`
C. `2.3 k`
D. `3 k^(2)`

Explanation

To solve the problem, we need to determine the rate constant at 310 K given that the rate of the reaction increases by 2.3 times when the temperature is raised from 300 K to 310 K.

### Step-by-Step Solution:

1. **Understand the relationship between rate and rate constant**:
The rate of a reaction is directly proportional to the rate constant (k) at a given temperature. Therefore, if the rate increases by a factor, the rate constant also increases by the same factor.

2. **Identify the initial rate constant**:
Let the rate constant at 300 K be denoted as \( k \).

3. **Apply the information given**:
Since the rate increases by 2.3 times when the temperature is raised from 300 K to 310 K, we can express this as:
\[ \text{Rate at 310 K} = 2.3 \times \text{Rate at 300 K} \]
This implies:
\[ k_{310} = 2.3 \times k \]
where \( k_{310} \) is the rate constant at 310 K.

4. **Conclude the calculation**:
Therefore, the rate constant at 310 K is:
\[ k_{310} = 2.3k \]

### Final Answer:
The rate constant at 310 K is \( 2.3k \).

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