1. Half-Life

2. Half-life is the time it takes for the concentration of a reactant to be cut in half.

3. The longer the half-life, the slower the reaction.
A reaction that takes 2 hours to reach
its half-life, is slower than a reaction
that only takes 1 hour to reach its
half-life.

4. Zero-Order Reaction
Integrated Rate Law: [A]t = -kt + [A]o
For half-life, [A]t = 1/2[A]o
and t = t1/2
Substitute: 1/2[A]o = -kt1/2 + [A]o
Rearrange: kt1/2 = 1/2[A]o
Solve for t1/2: t1/2 = [A]o 2k

5. Half-life for t1/2 = [A]o
Zero-Order 2k
Half-life and initial concentration are
directly related.
When initial concentration falls, half-life
falls.

6. Let’s look at a graph of [A] v. time
for a zero-order.
Starting at the initial concentration of
0.200 M, let’s see how long it takes for
the concentration to fall to M.
0.200 M
0.100 M

7. 1st Half-life:
260 Seconds

8. For the second half-life, the “initial concentration” is 0.100 M.
Use the final concentration from the
first half-life to be the
“initial concentration” or [A]o for
the second half-life.
0.200 M
1st
0.100 M
2nd M

9. 1st Half-life:
260 Seconds
2nd Half-Life:
130 Seconds
65 s

10. Zero-Order Reaction
Integrated Rate Law: [A]t = -kt + [A]o
Half-Life for t1/2 = [A]o
Zero-Order 2k
Each successive half-life is shorter than
the previous half-life.

11. First-Order Reaction Integrated Rate Law: ln[A]t = -kt + ln[A]o
For half-life, [A]t = 1/2[A]o
and t = t1/2
Substitute: ln 1/2[A]o = -kt1/2 + ln[A]o
Rearrange: ln 1/2[A]o - ln[A]o = -kt1/2
ln 1/2[A]o /ln[A]o = -kt1/2
ln 1/2 [A]o /[A]o = -kt1/2
ln 1/2= -kt1/2
= -kt1/2
Solve for t1/2: = t1/2 k

12. Half-life for = t1/2
First-Order k
Half-life and initial concentration are
NOT related.
When initial concentration falls, no effect
on half-life is observed.

13. 180 s
180 s
180 s

14. First-Order Reaction
Integrated Rate Law: ln[A]t = -kt + ln[A]o
Half-Life for t1/2 = 0.693
First-Order k
Each successive half-life is the same length
as the previous half-life.

15. Second-Order Reaction
Integrated Rate Law: 1/[A]t = kt + 1/[A]o
For half-life, [A]t = 1/2[A]o
and t = t1/2
Substitute: 1/1/2[A]o = kt1/2 + 1/[A]o
Solve for t1/2: = t1/2
k[A]o

16. Half-life for: = t1/2
Second-Order k[A]o
Half-life and initial concentration are
inversely related.
When initial concentration falls, half-life
gets longer.

17. 130 s
260 s
520 s

18. Second-Order Reaction
Integrated Rate Law: 1/[A]t = kt + 1/[A]o
Half-Life for t1/2 = 1
Second-Order k[A]o
Each successive half-life is longer than
the previous half-life.

19. To determine half-life, you need to know:
1. the order of the reaction
2. the rate constant
3. the initial concentration