1. Rate Laws

2. Rate Laws
Chemists conduct experiments to determine the rate law for a chemical reaction.
A RATE LAW is a mathematical equation that shows how the reaction rate is related to the concentration of the reactants.

3. Rate = k [reactant A]m [reactant B]n
Rate Constant (k)
From collision theory, you know that one way to speed up a reaction is to increase reactant concentrations.
For two reactants, a rate law has this form:
Rate = k [reactant A]m [reactant B]n
The term k is the rate constant
it is unique to each reaction; changes with catalyst
determined experimentally at specific temperature

4. Order of Reaction
The exponents m and n indicate the order of each reactant in the reaction.
For example, an exponent of 1 means the reaction is first order with respect to the given reactant.
Higher order, greater effect on reaction rate.
The sum of m + n gives the order of the overall reaction.

5. Reaction Order 2NO (g) + O2 (g)  2NO2 (g)
Has rate equation: rate = k[NO]1[O2]1
Describe reaction
Describe reactants

6. Reaction Order 2NO (g) + Cl2 (g)  2NOCl (g)
Has rate equation: rate = k[NO]2[Cl2]
Describe reaction
Describe reactants

7. CH3CHO (g)  CH4 (g) + CO (g)
Exp’t
[CH3CHO ]0
Initial Rate
(mole/l-s) 1
0.100 M
0.18 2
0.200 M
0.72 3
0.300 M
0.29
Exp't Data

8. Rate Law
Using the data from the decomposition of acetaldehyde, CH3CHO, the order fo the reaction is determined in the following way:
Rate = [CH3CHO]m
To determine the value of m, write a ratio of the rate expressions for two different concentrations.

9. NO (g) + ½ Cl2 (g)  NOCl (g)
Two Reactants
NO (g) + ½ Cl2 (g)  NOCl (g)
Exp’t
[NO]0
(moles/L)
[Cl2]0
Initial Rate
(moles/L-s) 1
0.250
1.43 X 10-6 2
0.500
2.86 X 10-6 3
11.4 X 10-6

10. NH4+ (aq) + NO2- (aq)  N2 (g) + 2 H2O (l)
Exp’t
[NH4+]0
[NO2-]0
Initial Rate
(M/s) 1
0.100 M M
1.35 X 10-7 2
0.010 M
2.70 X 10-7 3
0.200 M
5.40 X 10-7

11. Compare how the rate changes with concentration to find m, n
Compare expt’s 1 & 2
[NH4+] is constant, doubled [NO2-]
The rate doubled
Compare expt’s 2 & 3
[NO2-] is constant, doubled [NH4+]

12. Or, take Ratio of Rates Rate2 = k[NH4+]n[NO2-]m = k[0.100]n[0.010]m
2.70 X 10-7 = [0.010]m
1.35 X 10-7 = [0.005]m
2.00 = (2.0)m
m = 1

13. Write a Rate Law
Refer to balanced equation for the rate-determining step.
Write a rate constant, k.
Write the formula of each reactant in brackets.
Write the equation coefficient of each reactant as an exponent (only if a single event).

14. Example: Write a Rate Law
Step 1: NO + Cl2  NOCl2 (fast)
Step 2: NOCl2 + NO  2NOCl (slow)
Determine the overall balanced equation.
What is the intermediate?
Which step is rate-determining?
What is the rate law for the rate-determining step?
What is the order of the reaction with respect to NO and Cl2?