show that in a first order reaction the time required for completion of 99 9% of the reaction is 10 - Chemistry - Chemical Kinetics

Question

show that in a first order reaction the time required for
completion of 99 9% of the reaction is 10 tomes of the half life of
the first order reaction

Aditi Gupta · Accepted Answer

Solution:

1st order reaction
A→P
Equation of 1st order reaction
[A] = initial concentration of reactant
[A]t = final concentration of reactant after time t
ln[A]t = −-kt + ln[A]
t = 2 303/k(log[A]/[A]t) (ln = 2 303log)
at t = t1 /2 , [A] = [A]/2
Put these in the above equation
t1/2 = 2 303/k(log[A]/[A]/2)
t1 /2 = 2 303/k(log2)
t1 /2 = 0 693/k
when reaction is completed 99 9%
[A] = 100
[A]t = 0 1
t 99 9 = 2 303/k(log(100/0 1))
t 99 9 = 2 303/k(log103)
t 99 9 = (2 303/k)××3 = 6 909/k = 10(0
6909/k) ≈≈ 10(t1 /2)

show that in a first order reaction the time required for completion of 99.9% of the reaction is 10 tomes of the half life of the first order reaction.