Half Life (t1/2)
Half Life of a reaction is time required to reduce the initial concentration to half. The half-life of a reaction depends on the order of reaction. The variation of half-life with order is given as
t1/2 ∝ [A0]1-n
Where, [A0] = initial concentration
n = Order of reaction
for, Zeroth order reaction
t1/2 ∝ [A0]
for first order reaction,
t1/2 is independent of initial concentration
for second order reaction,
t1/2 ∝ [1/A0]
Integrated rate law expression
For Zeroth order reaction
A → product
Initially a o
at t = t1 (a -x) x
The rate of reaction at time ‘t’
Integrating on both sides, we get,
when t = 0, x = 0
c = 0
x = kt
k = x/t
When t = t1/2, x = a/2
k = a/2t1/2
t1/2 = a/2k
For first Order Reaction
A → product
Initially a o
At, t = t (a -x) x1
The rate of reaction at time ‘t’
Integrating on both sides, we get,
when t = 0, x = 0
-ln a = c
-ln (a-x) = kt – ln a
When t = t1/2,
x = a/2
i.e. (a-x) = a/2
So, half-life of first order reaction is independent of initial concentration.
Numerical
The half-life of a first order reaction is 50 mins. Calculate the time required to complete 75% of the reaction.
Given,
Half Life (t1/2) = 50 mins
Then,
Rate constant (k)
= 0.01386 min-1
Again,
initial concentration (a) = 100 (let) then
at time t,
Concentration left (a-x) = 100-75 = 25
We have,
Calculate the half period of first order reaction when rate constant is 5 year-1.
We have,
For 1st order reaction
t1/2 = 0.693/5
= 0.1386 year
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