Following data are obtained for the reaction:
`N_(2)O_(5) rarr 2NO_(2) + .^(1//2) O_(2)`
`|{:(t//s,0,300,600),([N_(2)O_(5)]//mol L^(-1),1.6 xx 10^(-2),0.8 xx 10^(-2),0.4 xx 10^(-2)):}|`
(a) Show that it follows first order reaction
(b) Calculate the half-life
(Given log 2 = 0.3010 log 4 = 0.6021]

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine if the reaction follows first-order kinetics

1. **Write the first-order rate equation:**
For a first-order reaction, the rate constant \( k \) can be calculated using the formula:
\[
k = \frac{1}{t} \ln \left( \frac{[A_0]}{[A_t]} \right)
...