Question

A first order reaction takes 23.1 minutes for 50% completion.calculate the time required for 75% completion of this reaction.

Answer 1

50℅ completion means half complete the reaction .
hence,
half life of reaction = 23.1 minutes
we know,
half life for 1st order reaction = ln2/K
23.1 = ln2/K
K = ln2/23.1

now, use 1st order reaction equation,
d[A]/dt = -K[A]
d[A]/[A] = -K.dt
ln[A] -ln[A°] = -Kt
ln[A]/[A°] = -Kt

t = 1/K ln[A°]/[A]

[A] = 0.25[A°]

so,

t = 1/K ln4 = 2/K ln2
put K = ln2/23.1
so,
t= {2/(ln2/23.1)}ln2
=2×23.1 = 46.2 minutes