The reaction A xrightarrow{k} Product is zero | vedclass

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Question

(A) For a zero order reaction,the half-life is given by $t_{1/2} = \frac{[A]_0}{2k}$.For a first order reaction,the half-life is given by $t_{1/2} = \

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$(\log _e 4) \ M$

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(A) For a zero order reaction,the half-life is given by $t_{1/2} = \frac{[A]_0}{2k}$.For a first order reaction,the half-life is given by $t_{1/2} = \frac{\ln 2}{k}$.Given that the half-lives are equal,we equate the two expressions:$\frac{[A]_0}{2k} = \frac{\ln 2}{k}$.Solving for the initial concentration $[A]_0$:$[A]_0 = 2 \ln 2$.Using the logarithmic property $n \ln x = \ln x^n$,we get:$[A]_0 = \ln 2^2 = \ln 4 = \log _e 4 \ M$.

The reaction $A \xrightarrow{k}$ Product is zero order,while the reaction $B \xrightarrow{k}$ Product is a first order reaction. For what initial concentration of $A$ are the half-lives of the two reactions equal?

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