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(A) For a first order reaction,the time taken to complete a fraction $f$ is given by $t = \frac{2.303}{k} \log(\frac{1}{1-f})$.For half-life $(t_{1/2}

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$2$

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(A) For a first order reaction,the time taken to complete a fraction $f$ is given by $t = \frac{2.303}{k} \log(\frac{1}{1-f})$.For half-life $(t_{1/2})$,$f = 0.5$,so $t_{1/2} = \frac{2.303}{k} \log(2)$.For $\frac{3}{4}$ th completion,$f = 0.75$,so $t_{3/4} = \frac{2.303}{k} \log(\frac{1}{1-0.75}) = \frac{2.303}{k} \log(4) = \frac{2.303}{k} \log(2^2) = 2 	imes \frac{2.303}{k} \log(2)$.Therefore,the ratio $\frac{t_{3/4}}{t_{1/2}} = \frac{2 	imes \frac{2.303}{k} \log(2)}{\frac{2.303}{k} \log(2)} = 2$.

For a first order reaction,the ratio between the time taken to complete $\frac{3}{4}$ th of the reaction and time taken to complete half of the reaction is

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