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Ratio of initial concentrations of zero order (A), first order (B) and second order (C) reactions is 1: 2: 4. If the ratio of rate constants of A, B, C is 4: 0.693: 1 then the ratio of half lives of A, B, C respectively

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1:8:2

1:1:1

4:1:1

1:4:2

answer is C.

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Detailed Solution

order	$t_{\frac{1}{2}}$
zero(A)	$t_{\frac{1}{2}} = \frac{a}{2 K_{0}}$
first (B)	$t_{\frac{1}{2}} = \frac{0.693}{K_{1}}$
second(C)	$t_{\frac{1}{2}} = \frac{1}{{aK}_{2}}$

ratio

${(t_{\frac{1}{2}})}_{(A)} : {(t_{\frac{1}{2}})}_{(B)} : {(t_{\frac{1}{2}})}_{(C)} = \frac{1}{8} : 1 : \frac{1}{4} = 1 : 8 : 2$

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