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Question

What is half life period? Derive its derivation.

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Solution

It is the time in which concentration of reactant is reduced to one half of the initial concentration. It is denoted by t1/2.
Derivation of half life period:
We know that for first order reaction
K=2.303tloga(ax)
or t=2.303Kloga(ax)
If t=t1/2 and x=a2
then t1/2=2.303Kloga(aa2)
t1/2=2.303Klog2
t1/2=2.303K×0.3010 (log2=0.3010)
t1/2=0.693K
Above equation is the derivation of half life period.

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