A gas phase reaction is,
$A (g) + 2 B (g) \to C (g)$
the reaction was carried out with stoichiometric proportions's of $A$ and $B$ and the following data is obtained
Half-life (min) 10 160
Initial pressure of $A$ (atm) 40 atm 10 atm
What is overall order of reaction?

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Solution

$t_{1 / 2} α \frac{1}{(p)^{n - 1}}$ where p=pressure, $n =$ order of reaction
$\frac{(t_{1 / 2})_{1}}{(t_{1 / 2})_{2}} = (\frac{P_{2}}{P_{1}})^{n - 1}$
$\frac{10}{160} = (\frac{10}{40})^{n - 1}$
$\frac{1}{16} = (\frac{1}{4})^{n - 1}$ => n-1=2 or n=3
Overall order $= 3$

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Half-life (min)	10	160
Initial pressure of $A$ (atm)	40 atm	10 atm