At `380^(@)` the half-life period for thefirst order decomposition of`H_(2)O_(2)` is 360 min. The energy of activation of the reaction is 200 kJ `mol^(-)`. Calculation the time required for 75% decomposition at`450^(@)` C
(1) 20.35 min,
(2) 40.7 min
( c) 120 min
(d) 60 min

Explanation

To solve the problem, we need to find the time required for 75% decomposition of \( H_2O_2 \) at \( 450^\circ C \). We will use the first-order kinetics and the Arrhenius equation to find the rate constant at the new temperature.

### Step-by-Step Solution:

1. **Determine the Rate Constant at \( 380^\circ C \)**:
The half-life (\( t_{1/2} \)) for a first-order reaction is related to the rate constant (\( k \)) by the formula:
\[
t_{1/2} = \frac{0.693}{k}
...