is the time required for the reaction to undergo 87.5% completion and is the time required for the reaction to undergo 50% completion. The relation between and for a first-order reaction is The value of is _______. (Nearest Integer)

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Solution

Q.
$t_{87.5}$ is the time required for the reaction to undergo 87.5% completion and $t_{50}$ is the time required for the reaction to undergo 50% completion. The relation between $t_{87.5}$ and $t_{50}$ for a first-order reaction is $t_{87.5} = x \times t_{50} .$

The value of $x$ is _______. (Nearest Integer) [2023]

Ans.
(3)

$a_{t} = a_{0} \times \frac{12.5}{100} = \frac{a_{0}}{8} (87.5 % completion)$

$a_{0} \overset{t_{1 / 2}}{\to} a_{0 / 2} \overset{t_{1 / 2}}{\to} a_{0 / 4} \overset{t_{1 / 2}}{\to} \frac{a_{0}}{8}$

$t_{87.5} = 3 t_{1 / 2}$ $∴$ $x = 3$

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