For the catalytic decomposition of AB_3, the | vedclass

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(C) The relationship between half-life $(t_{1/2})$ and initial concentration $(a)$ for a reaction of order $n$ is given by: $t_{1/2} \propto a^{1-n}$.

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$2$

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(C) The relationship between half-life $(t_{1/2})$ and initial concentration $(a)$ for a reaction of order $n$ is given by: $t_{1/2} \propto a^{1-n}$.
Given:
For $a_1 = 50 \, 	ext{mm}$, $t_{1/2,1} = 4 \, 	ext{hours}$.
For $a_2 = 100 \, 	ext{mm}$, $t_{1/2,2} = 2 \, 	ext{hours}$.
Using the ratio: $\frac{t_{1/2,1}}{t_{1/2,2}} = \left( \frac{a_1}{a_2} ight)^{1-n}$.
Substituting the values: $\frac{4}{2} = \left( \frac{50}{100} ight)^{1-n}$.
$2 = \left( \frac{1}{2} ight)^{1-n} = (2^{-1})^{1-n} = 2^{n-1}$.
Comparing the exponents: $1 = n - 1$, which gives $n = 2$.

For the catalytic decomposition of $AB_3$, the half-life period is $4 \, \text{hours}$ at $50 \, \text{mm}$ and $2 \, \text{hours}$ at $100 \, \text{mm}$. What is the order of the reaction?

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