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 the rate constant (K) at different times
We will use the first-order reaction formula:
\[ K = \frac{2.303}{t} \log \left( \frac{[A_0]}{[A]} \right) \]
where:
...