A first order gas reaction
` A_2 B_(2 (g)) to 2 A_((g) ) + 2 B_((g))`
at the temperature `400^@ C` has the rate constant `k = 2.0 xx 10^(-4)s^(-1)`. What percentage of `A_2 B_2` is decomposed on heating for 900 seconds?

Explanation

To solve the problem, we need to determine the percentage of the reactant \( A_2B_2 \) that decomposes after 900 seconds, given that the reaction is first-order with a rate constant \( k = 2.0 \times 10^{-4} \, s^{-1} \).

### Step-by-Step Solution:

1. **Identify the Reaction and Rate Constant**:
The reaction is:
\[
A_2B_2(g) \rightarrow 2A(g) + 2B(g)
...