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Half life

The following...

Question

The following graph shows how $t_{1 / 2}$ (half-life) of a reactant, $R$ changes with the initial reactant concentration $a_{0}$ . The order of the reaction will be?

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Solution

The correct option is C $2$
Half-life period $t_{1 / 2} \propto \frac{1}{a_{0}^{n - 1}}$ ...(i)
where, $a_{0} =$ initial concentration and $n =$ order of reaction since graph between $t_{1 / 2}$ and $\frac{1}{a_{0}}$ is a straight line,
$t_{1 / 2} \propto \frac{1}{a_{0}}$ ...(ii)
From equation (i) and (ii),
$\Rightarrow \frac{1}{a_{0}^{n - 1}} = \frac{1}{a_{0}}$
or $n - 1 = 1$
$∴ n = 2$
Hence, the reaction is of second order.

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