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(C) For a first order reaction,the rate constant $K$ is given by $K = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given that the concentration reduces t

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$1/2 \ hr$

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(C) For a first order reaction,the rate constant $K$ is given by $K = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given that the concentration reduces to $25\%$ in $1 \ hr$,we have $[A]_0 = 100$ and $[A]_t = 25$ at $t = 1 \ hr$.$K = \frac{2.303}{1} \log \frac{100}{25} = 2.303 \log 4 = 2.303 	imes 2 \log 2$.The half-life period $t_{1/2}$ is given by $t_{1/2} = \frac{0.693}{K} = \frac{2.303 \log 2}{K}$.Substituting $K = 2.303 	imes 2 \log 2$ into the equation:$t_{1/2} = \frac{2.303 \log 2}{2.303 	imes 2 \log 2} = \frac{1}{2} \ hr = 0.5 \ hr$.

In a first order reaction,the concentration of the reactant is reduced to $25\%$ in one hour. The half-life period of the reaction is:

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