The ratio of t_{0.75} and t_{0.5} for a first | vedclass

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Question

(C) For a first-order reaction,the time $t$ required for a fraction of reaction to complete is given by $t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$

Vedclass · Accepted Answer

$2 : 1$

Vedclass · Answer

(C) For a first-order reaction,the time $t$ required for a fraction of reaction to complete is given by $t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$.For $t_{0.5}$ (half-life),$[A]_t = 0.5[A]_0$,so $t_{0.5} = \frac{2.303}{k} \log 2$.For $t_{0.75}$,$[A]_t = 0.25[A]_0$,so $t_{0.75} = \frac{2.303}{k} \log \frac{[A]_0}{0.25[A]_0} = \frac{2.303}{k} \log 4 = \frac{2.303}{k} \log 2^2 = 2 	imes \frac{2.303}{k} \log 2$.Therefore,$t_{0.75} = 2 	imes t_{0.5}$.The ratio $\frac{t_{0.75}}{t_{0.5}} = \frac{2}{1}$ or $2 : 1$.

The ratio of $t_{0.75}$ and $t_{0.5}$ for a first-order reaction is:

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