What is half life period of a reaction? Calculate the half life period of a first order reaction?

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Solution

Half life period :
Half life period of a reaction is time in which concentration of reactants becomes half of the initial.
$tfrac12=frac0.693k$
For first order reaction
Rate equation
$k = \frac{2.303}{t} l o g_{10} \frac{a}{a - x}$ ------(i)
$t = \frac{2.303}{k} l o g_{10} \frac{a}{a - x}$
a = initial concentration
a.x = conc. after 't' time half life
$t = t_{\frac{1}{2}} k (a - x) = \frac{a}{2}$
$t_{\frac{1}{2}} = \frac{2.303}{k} l o g_{10} \frac{a}{\frac{a}{2}}$
$t_{\frac{1}{2}} = \frac{2.303}{k} l o g_{10} 2 l o g_{10} 2 = 0.3010$
$t_{\frac{1}{2}} = \frac{2.303}{k} \times 0.3010$
$t_{\frac{1}{2}} = \frac{0.693}{k}$

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