The half-life period for a first-order reacti | vedclass

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(B) For a first-order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.At half-life $(t = t_{1/2})$,the concent

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Independent of concentration

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(B) For a first-order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.At half-life $(t = t_{1/2})$,the concentration $[A] = \frac{[A]_0}{2}$.Substituting these values: $k = \frac{2.303}{t_{1/2}} \log \frac{[A]_0}{[A]_0/2} = \frac{2.303}{t_{1/2}} \log 2$.Thus,$t_{1/2} = \frac{2.303 	imes 0.3010}{k} = \frac{0.693}{k}$.Since $t_{1/2}$ depends only on the rate constant $k$ and not on the initial concentration $[A]_0$,it is independent of the concentration.

The half-life period for a first-order reaction is . . . . . . .

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