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(D) Let the initial concentration of both $AB$ and $XY$ be $C_0$.For a first-order reaction,the concentration at time $t$ is given by $C_t = C_0 	ime

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(D) Let the initial concentration of both $AB$ and $XY$ be $C_0$.For a first-order reaction,the concentration at time $t$ is given by $C_t = C_0 	imes (1/2)^{t/t_{1/2}}$.For $AB$: $C_{AB} = C_0 	imes (1/2)^{t/30}$.For $XY$: $C_{XY} = C_0 	imes (1/2)^{t/10}$.We are given that $C_{AB} = 4 	imes C_{XY}$.Substituting the expressions: $C_0 	imes (1/2)^{t/30} = 4 	imes C_0 	imes (1/2)^{t/10}$.$(1/2)^{t/30} = 2^2 	imes (1/2)^{t/10}$.$(1/2)^{t/30} = (1/2)^{-2} 	imes (1/2)^{t/10}$.$(1/2)^{t/30} = (1/2)^{(t/10) - 2}$.Equating the exponents: $t/30 = t/10 - 2$.Multiply by $30$: $t = 3t - 60$.$2t = 60 \implies t = 30 \ min$.

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