The initial concentration of `N_2O_5` in the first order reaction `N_2O_5 to 2NO_2 + 1//2O_2` was `1.24 xx10^(-2) "mol L"^(-1)` at 318 K. The concentration of `N_2O_5` after 60 minutes was `0.20 xx 10^(-2) "mol L"^(-1)`. Calculate the rate constant of the reaction at 318 K.

Explanation

To calculate the rate constant \( k \) for the first-order reaction \( N_2O_5 \to 2NO_2 + \frac{1}{2}O_2 \), we can use the integrated rate law for first-order reactions. Here are the steps to solve the problem:

### Step-by-Step Solution

1. **Identify the Given Data:**
- Initial concentration of \( N_2O_5 \) (\( [N_2O_5]_0 \)) = \( 1.24 \times 10^{-2} \, \text{mol L}^{-1} \)
- Concentration of \( N_2O_5 \) after 60 minutes (\( [N_2O_5]_t \)) = \( 0.20 \times 10^{-2} \, \text{mol L}^{-1} \)
- Time (\( t \)) = 60 minutes
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