Derive the relation between half life and rate constant for a first order reaction
The integrated rate law for the first order reaction is given by the equation
`k= 2.303/t log_10"[A]_o/[A]_t`
Where [A]0 = initial concentration of the reactant at t = 0
The concentration falls to [A]t at time t from the start of the reaction.
The concentration of the reactant falls to [A]0/2 at time t1/2.
Therefore, t = t1/2
[A]t = [A]0/2
So, the equation can be written as
`k= 2.303/t_(1/2) log_10"[A]_o /([A]_o/2)`
- Integrated Rate Equations - Half-life of a Reaction