1. Integrated Rate Law: First-Order
Given information - concentration and time
ln[A] = -kt + ln[A]o
Y = mx + b
[A] = concentration of A at time t
K = rate constant
T = time
[A]o = initial concentration of A
First order: ln[A] varies linearly with time, rate = k[A]

2. Example 2N2O5(g) -> 4NO2(g) + O2(g)
[N2O5] (mol/L)
Time (s)
0.1000
0.0707 50
0.0500
100
0.0250
200
0.0125
300
400
Example
2N2O5(g) -> 4NO2(g) + O2(g)
Verify first order in [N2O5], and collect value of the rate constant, where
rate = -[N2O5]/t
2. Calculate [N2O5] at 150s after the start of the reaction

3. Half-Life
Definition: Amount of time required for a reactant to reach half of its original concentration (t1/2)
For first order reactions, the general equation is
t1/2 = 0.693/k
Does not depend on the concentration

4. Example
A certain first-order reaction has a half-life of 20.0 minutes.
Calculate the rate constant for this reaction
Answer: 3.47 X 10-2 min-1
2. How much time is required for this reaction to be 75% complete?
Answer: 40. min

5. Integrated Rate Law: Second-Order
1/[A] = kt + 1/[A]0
1/[A] versus t will be linear with slope equal to k
Rate = k[A]2
Half Life equation: t1/2 = 1/k[A]0
Each successive half-life is double the preceding one (when A0 is halved, t1/2 doubles)

6. Example 2C4H6(g) -> C8H12(g)
[C4H6] (mol/L)
Time (±1 s)
1000
1800
2800
3600
4400
5200
6200
2C4H6(g) -> C8H12(g)
Is this reaction first or second order?
Answer: second order
2. What is the value of the rate constant?
Answer: 6.14 X 10-2 L/mol s
3. What is the half-life under these conditions?
Answer: 1.63 X 103 s

7. Zero-Order [A] = -kt + [A]0
The rate is constant and does not change with concentration
[A] versus t is a straight line
Rate = k (rate is constant)
Half-Life Equation: t1/2 = [A]0/2k

8. More Than One Reactant
When there are large initial concentrations of all reactants but one, the rate law can be assumed to only be controlled by the one reactant
Pseudo-first-order rate law

9. Summary – Memorize!!
Pages may help

10. 2I(g) -> I2(g) Rate = k[I]2, where k = 7.0 X 109
Example
2I(g) -> I2(g) Rate = k[I]2, where k = 7.0 X 109
What are the proper units for k?
If [I]0 = 0.40 M, calculate [I] at t=2.5 X 10-7 sec
If [I]0 =0.40 M, calculate t1/2
If [I]0 =0.80 M, how much time would it take for 75% of the iodine atoms to react?