The rate constant of a first order reaction is `10^(-3) m i n^(-1)` at `300K`. The temperature coefficient of the reaction is 2. What is the rate constant of the reaction at `350K` approximately ?

Options

A. `16xx10^(-3)`
B. `64xx10^(-3)`
C. `32xx10^(-3)`
D. 250

Explanation

To find the rate constant of a first-order reaction at a new temperature using the temperature coefficient, we can follow these steps:

### Step 1: Understand the given data
- The rate constant at 300 K, \( k_{300} = 10^{-3} \, \text{min}^{-1} \)
- The temperature coefficient, \( Q = 2 \)
- The new temperature, \( T = 350 \, \text{K} \)

### Step 2: Calculate the change in temperature
The change in temperature from 300 K to 350 K is:
\[ \Delta T = 350 \, \text{K} - 300 \, \text{K} = 50 \, \text{K} \]

### Step 3: Determine how many 10 K intervals are in the temperature change
Since the temperature coefficient is defined for a 10 K increase, we need to find how many 10 K intervals fit into a 50 K change:
\[ \text{Number of intervals} = \frac{50 \, \text{K}}{10 \, \text{K}} = 5 \]

### Step 4: Apply the temperature coefficient
The rate constant increases by a factor of 2 for each 10 K increase. Therefore, after 5 intervals, the rate constant will increase by a factor of:
\[ Q^n = 2^5 = 32 \]

### Step 5: Calculate the new rate constant
Now, we can calculate the new rate constant at 350 K:
\[ k_{350} = k_{300} \times Q^n = 10^{-3} \, \text{min}^{-1} \times 32 = 32 \times 10^{-3} \, \text{min}^{-1} \]

### Step 6: Final answer
Thus, the rate constant of the reaction at 350 K is approximately:
\[ k_{350} \approx 0.032 \, \text{min}^{-1} \]