A student has studied the decomposition of a gas at 25°C. He obtained the following data. The order of the reaction is: [2023]

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Solution

Q.
A student has studied the decomposition of a gas ${AB}_{3}$ at 25°C. He obtained the following data.

$p$ (mm Hg) 50 100 200 400

relative $t_{1 / 2}$ (s) 4 2 1 0.5

The order of the reaction is: [2023]

1 1

2 0.5

3 0 (zero)

4 2

Ans.
(4)

$T_{\frac{1}{2}} \propto {(C_{0})}^{1 - n}$

$\frac{{(T_{\frac{1}{2}})}_{1st}}{{(T_{\frac{1}{2}})}_{2nd}} = {(\frac{P_{1}}{P_{2}})}^{1 - n}$

$\Rightarrow \frac{4}{2} = {(\frac{50}{100})}^{1 - n} \Rightarrow 2 = {(\frac{1}{2})}^{1 - n}$

$2 = {(2)}^{n - 1}$

$n - 1 = 1 \Rightarrow n = 2$

$Order = 2$

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