Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
Reaction Half -life
Note:
[A]o = CAo
,
[A] = CA
1- Zero Order Reaction:
The t1/2 formula for a zero order reaction suggests the half-life
depends on the amount of initial concentration and rate
constant.
2- First Order Reaction:
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
The formula for t1/2 shows that for first order reactions, the
half-life depends solely on the reaction rate constant, k. We can
visually see this on the graph for first order reactions when we
note that the amount of time between one half life and the next
are the same. Another way to see it is that the half life of a first
order reaction is independent of its initial concentration.
3- Second Order Reaction:
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
The formula for t1/2 shows that for second order reactions, the
half-life only depends on the initial concentration and the rate
constant.
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
4 - nth Order Reaction:
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
Summary:
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
Problem: Calculate half-life for first-order reaction if 68% of a
substance is reacted within 66 s.
Solution:
1) 68% reacted means 32% remains:
ln A = -kt + ln Ao
ln 0.32 = - k (66 s) + ln 1
k = 0.0172642 s-1
2) for the half-life:
ln 0.5 = - (0.0172642 s-1) (t) + ln 1
t = 40. s
or:
t1/2 = (ln 2) / k
t1/2 = (ln 2) / 0.0172642 s-1
t1/2 = 40. S
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
Problem: The decomposition of hydrogen peroxide is a firstorder reaction. The half-life of the reaction is 17.0 minutes.
(a) What is the rate constant of the reaction?
(b) If you had a bottle of H2O2, how long would it take for 86%
to decompose?
(c) If you started the reaction with [H2O2] = 0.1 M, what would
be the hydrogen peroxide concentration after 15.0 minutes?
Solution:
Part (a)
k = (ln 2) / t1/2
k = (ln 2) / 17.0 min = 0.04077 min-1
Part (b)
86% decomposed means 14% remains.
ln A = -kt + ln Ao
ln 0.14 = - (0.04077 min-1) (t) + ln 1
t = 48.2 min
Part (c)
0.1 M is Ao
ln A = - (0.04077 min-1) (15.0 min) + ln 0.1
ln A = -2.914135
A = 0.0542 M
Comment: one half-life is 17.0 min, so the [H2O2] would be 0.05
M at the end of 17.0 min. Note that part c involves a time frame
Lec. 3…………………………………………………..……………………………………………………….Reaction Half-life
slightly less than one half-life, so the ending concentration is
slightly more than 0.05 M.
Q:
Liquid A decomposes by second-order kinetics, and in a batch reactor
50% of A is converted in a 5-minute run. How much longer would it take
to reach 75% conversion?
Solution:
Problem: The initial reactant concentration in a first-order
reaction was 7.30 x 10-2 M and 8.70 x 10-3 M after 20 s . What is
the rate constant for this reaction?
Solution:
ln A = -kt + ln Ao
ln 8.70 x 10-3 = - (k) (20. s) + ln 7.30 x 10-2
-4.74443 = - (k) (20. s) + (-2.61730)
2.12713 = (k) (20. s)
k = 0.106 s-1