Define half life period. Derive expression for half life period for 1st oder reaction.

Explanation

Half life period is the time during which the concentration of reactants is reduced to half . It is denoted bt `t _(1//2).`
We know that for first order reaction , ` t = ( 2. 303 )/( k ) log "" (a)/( a- x)" "...(i)`
Here, a = amount of substance initially present
x = amount of substance that has reacted in time t
`a - x =` amount of sustance left after time t
According to the difinition of half life, at half life time,` x = (a)/(2)`
`therefore t_(1//2) = ( 2. 303)/( k ) log "" (a)/( a - (a)/(2)) = ( 2 . 303 )/( k ) log "" (a)/(a //2) = (2 . 303 )/( k ) log 2`
`therefore t_(1//2) = ( 2. 303 xx 0. 3010)/(k ) = ( 0. 693)/( k )`
As in the epression for `t _(1//2)` the concentration term is not involved , so the `t _(1//2)` is independent of the initial concentration of hte reactants for first order reaction