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Question

Show that the half-life period of a first order reaction is independent of the initial concentration of the reactant.

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Solution

Half life period t1/2 of a reaction is defined as the time required to reduced the concentration of a reactant to one half of its initial value.

k1=2.303tlog(aax)

if amount reacted x=a2then t=t1/1

t1/2=2.303tlog(aaa/2)

t1/2=2.303log(2.0)k1t1/2=0.693k1secs

Thus half life period of a first order reaction is independent of the initial concentration of the reactant.

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