Half-lives of a first order and a zero order | vedclass

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(B) For a first order reaction,the rate is given by $Rate_1 = k_1 [A]_0$,where $k_1 = \frac{0.693}{t_{1/2}}$. Thus,$Rate_1 = \frac{0.693 [A]_0}{t_{1/2

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$2 	imes 0.693$

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(B) For a first order reaction,the rate is given by $Rate_1 = k_1 [A]_0$,where $k_1 = \frac{0.693}{t_{1/2}}$. Thus,$Rate_1 = \frac{0.693 [A]_0}{t_{1/2}}$.For a zero order reaction,the rate is given by $Rate_0 = k_0$,where $k_0 = \frac{[A]_0}{2 t_{1/2}}$.Given that the half-lives $(t_{1/2})$ are the same for both reactions,the ratio of the initial rates is:$\frac{Rate_1}{Rate_0} = \frac{\frac{0.693 [A]_0}{t_{1/2}}}{\frac{[A]_0}{2 t_{1/2}}} = 0.693 	imes 2 = 1.386$.

Half-lives of a first order and a zero order reaction are same. Then the ratio of the initial rates of first order reaction to that of the zero order reaction is

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