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Questions
Show that for a first order reaction half life is independent of initial concentration.
Show that half-life period does not depend upon the initial concentration for the first order reaction.
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Solution
For a first order reaction, the half-life is a constant, i.e., it does not depend on the initial concentration.
The rate constant for a first order reaction is given by,
k = `2.303/t log ([A_0])/([A])`
at t = `t_(1//2)`; [A] = `([A_0])/2`
k = `2.303/t_(1//2) log ([A_0])/(([A_0])/2)`
k = `2.303/t_(1//2) log (2)`
k = `(2.303 xx 0.3010)/t_(1//2)`
k = `0.693/t_(1//2)`
`t_(1//2) = 0.693/k`
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