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Two first order reaction have halflives in 1:2 ratio. After two halflives of first reaction. What is the ratio of their rates of reactions ? (Initial concentrations same)

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1:2

1:3

1:4

1:1

answer is D.

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Detailed Solution

Reaction 1: 100% $\overset{xmin}{\to} 50 % {(\frac{t_{1}}{2})}_{1} = x m i n$

$Reaction 2 : 100 % \overset{2 x \min}{\to} 50 % (\frac{t_{1}}{2}) . 2 xmin$

$∴ \frac{{(t_{\frac{1}{2}})}_{1}}{{(t_{\frac{1}{2}})}_{2}} = 1 : 2$

$Reaction 3 : 100 % \to_{t_{\frac{1}{2}}}^{xmin} 50 \to_{t_{\frac{1}{2} 25}}^{x \min}$

$(from 1) 2 t_{\frac{1}{2}} \to x + x = 2 x \to {(t_{\frac{1}{2}})}_{3}$

$∴ \frac{{(t_{\frac{1}{2}})}_{3}}{{(t_{\frac{1}{2}})}_{2}} = \frac{2 x}{2 x} = \frac{1}{1} \Rightarrow 1 : 1$

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