The rate constant of a reaction is `3.2 times 10^–4` at 280 K, what will be its value at 300 K approximately?

Options

A. `9.6 times 10^-4`
B. `3.2 times 10^-5`
C. `6.4 times 10^-4`
D. `1.28 times 10^-3`

Answer

To find the rate constant (K2) at 300 K given the rate constant (K1) at 280 K, we can use the fact that the rate constant approximately doubles for every 10-degree rise in temperature.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Rate constant at T1 (K1) = \(3.2 \times 10^{-4}\)
- Temperature T1 = 280 K
- Temperature T2 = 300 K

2. **Calculate the Temperature Change (ΔT):**
\[ \Delta T = T2 - T1 = 300 \, \text{K} - 280 \, \text{K} = 20 \, \text{K} \]

3. **Determine the Number of 10-degree Increments:**
\[ \text{Number of increments} = \frac{\Delta T}{10} = \frac{20}{10} = 2 \]

4. **Use the Doubling Rule for Rate Constants:**
- Since the rate constant doubles for every 10-degree increase, we can express the change in rate constant as:
\[ K2 = K1 \times 2^{\text{Number of increments}} = K1 \times 2^2 \]
- Here, \(2^2 = 4\).

5. **Calculate K2:**
\[ K2 = 3.2 \times 10^{-4} \times 4 = 1.28 \times 10^{-3} \]

6. **Final Result:**
- The value of the rate constant at 300 K is approximately \(1.28 \times 10^{-3}\).