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In a first-order reaction A $\to$ B, if k is rate constant and inital concentration of the reactant A is 0.5 M, then the half-life is

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$\frac{\log 2}{k}$

$\frac{\log 2}{k \sqrt{0 .5}}$

$\frac{\ln 2}{k}$

$\frac{0 .693}{0 .5 k}$

answer is C.

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Detailed Solution

for a first order reaction
$k = \frac{2 .303}{t} \log_{10} \frac{a}{a - x} when t = t_{1 / 2} k = \frac{2 .303}{t_{1 / 2}} \log_{10} \frac{a}{a - a / 2} or t_{1 / 2} = \frac{2 .303}{k} \log_{10} 2 = \frac{\ln 2}{k}$

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