t_{87.5} is the time required for the reactio | vedclass

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(C) For a first order reaction,the time taken for $50 \%$ completion is the half-life,$t_{50} = t_{1/2}$.At $87.5 \%$ completion,the remaining amount

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) For a first order reaction,the time taken for $50 \%$ completion is the half-life,$t_{50} = t_{1/2}$.At $87.5 \%$ completion,the remaining amount of reactant is $A_t = A_0 - 0.875 A_0 = 0.125 A_0 = \frac{A_0}{8}$.Using the half-life concept:$A_0$ $\xrightarrow{t_{1/2}} \frac{A_0}{2}$ $\xrightarrow{t_{1/2}} \frac{A_0}{4}$ $\xrightarrow{t_{1/2}} \frac{A_0}{8}$.This shows that $t_{87.5} = 3 	imes t_{1/2}$.Since $t_{50} = t_{1/2}$,we have $t_{87.5} = 3 	imes t_{50}$.Therefore,$x = 3$.

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