1. From Method of Initial Rates to Integrated Rate Law
Rates of Reaction
From Method of Initial Rates to Integrated Rate Law

2. Method of Initial Rates
The initial rates listed in the following table were determined for the reaction: 2NO(g) + Cl2(g)  2NOCl(g)
What is the order of the reaction with respect to each reactant?
What is the rate law?
What is the value of the rate constant?
Experiment
Initial [NO] (M)
Initial [Cl2] (M)
Initial Rate of Consumption of Cl2 (M/s) 1
0.13
0.20
1.0 × 10-2 2
0.26
4.0 × 10-2 3
0.10
5.0 × 10-3
Complete as a quiz, then discuss/go over as a class while students correct their own work

3. Integrated Rate Laws N2O5 (g)  2NO2 (g) + ½ O2 (g) Time (s)
[N2O5] (M)
0.1000 50
0.0707
100
0.0500
200
0.0250
400
Integrated Rate Laws
N2O5 (g)  2NO2 (g) + ½ O2 (g)
Determine rate law for reaction from set of data consisting of concentration (or values of some function of concentration) versus time.
What is the order of the reaction with respect to each reactant?
What is the rate law?
What is the value of the rate constant?

4. Integrated Rate Laws The Common Integrated Rate Laws: A  products
First Order: rate = k[A]
ln [A] = ln[A]o – kt
Second Order: rate = k[A]2 (or rate = k[A][B])
𝟏 [𝐀] = 𝟏 [𝐀] 𝒐 +𝐤𝐭
Uses of Integrated Rate Laws
How long does it take?
What concentration remains after a given time?
What was the initial concentration?

5. Integrated Rate Laws Rate = k Zero Order First Order Second Order
Zero Order
First Order
Second Order
The graph that is linear indicates the order of the reaction with respect to A.

6. Integrated Rate Laws Rate = k[A] Zero Order First Order Second Order
Zero Order
First Order
Second Order
The graph that is linear indicates the order of the reaction with respect to A.

7. Integrated Rate Laws Rate = k[A]2 Zero Order First Order Second Order
Zero Order
First Order
Second Order
The graph that is linear indicates the order of the reaction with respect to A.

8. Integrated Rate Law: Summary Table
First Order
Second Order
Rate Law
Concentration-Time Equation
Linear Graph
Graphical Determination of k
Half-Life Equation

9. Integrated Rate Law: Summary Table
First Order
Second Order
Rate Law
Rate = −∆[R] ∆𝑡 = k[R]1
Rate = −∆[R] ∆𝑡 = k[R]2
Concentration-Time Equation
ln[R]t = -kt + ln[R]o
1 [R] =𝑘𝑡+ 1 [R] o
Linear Graph
ln[R] vs. t
1 [R] vs. t
Graphical Determination of k
k = -slope
k = slope
Half-Life Equation
𝑡 1/2 = 𝑘
𝑡 1/2 = 1 𝑘 [R] o