Question

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.

Answer 1

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`