Question

The expression which gives 1/4 life of 1st order reaction is

Answer 1

for first order reaction,

t = 2.303/k log [A]/[A]'

where k is rate constant of first order reaction, [A] is initial amount of substance and [A]' is remaining final amount of substance.

here, [A]' = 1/4 [A]

so, t = 2.303/k log { [A]/(1/4[A])}

= 2.303/k log (4)

= 2.303log4/k

= 1.386/k

hence, required expression is t = 1.386/k, which gives 1/4 life of 1st order reaction.