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Question

For a first order reaction, $t_{99.99 %} = y \times t_{90 %}$ Find the value of y.

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Solution

For first order reaction:
$k t = l n \frac{[A_{0}]}{[A_{t}]}$
$A ⟶ P$
$a t t = 0 A_{0}$
$a t t = t_{0.9999} 0.0001 A_{0}$
$a t t = t_{0.90} 0.1 A_{0}$
$\frac{t_{0.9999}}{t_{0.90}} = \frac{l n 10^{4}}{l n 10} = 4$

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