1. Kinetics Part II: Rate Laws & Order of Reaction
Jespersen Chap. 14 Sec 3
Dr. C. Yau
Fall 2013 1

2. Rate law is a rate expression that includes all reactants.
Rate of Rxn vs. Rate Law
Rate of reaction is based on one component (reactant or product) of the reaction: disappearance of a reactant or formation of a product.
Rate law is a rate expression that includes all reactants.
LEARN THESE TERMS SO YOU KNOW WHAT IS BEING ASKED FOR!! 2

3. The Rate Law Depends On The Concentrations Used
Rate= k [reactant]order
k is a reaction rate constant, a measure of time efficiency (not to be confused with “Rate”).
High values of k mean high efficiency.(Reaction goes fast.)
k must be determined experimentally.
Each experiment has its own rate law.
Rate law must be determined experimentally.
Chem FAQ: How do I calculate reaction rate using a rate law?

4. A + B products
Rate = k [A]m[B]n where m and n are the "orders of reaction" and are found by experiment, NOT based on the coefficients of the chemical equation, and k is the "rate constant." This expression is called the "rate law."

5. H2SeO3 + 6I- +4H Se + 2I3- + 3H2O
Rate = 5.0x105 L5mol-5 s-1 [H2SeO3] [I-]3[H+]2 5.0x105 mol-5 s-1 is the rate constant (k). We speak of the reaction as being… first order with respect to H2SeO3, third order with respect to I-(Nothing to do with 6 in eqn) second order with respect to H+, and the overall order of reaction is 6 (sum of all the orders). Learn this terminology! What is the unit of Rate in the equation shown above?
Do Practice Exercises 7, 8 & 9 on p.648.

6. What is a rate law used for?
Rate changes with concentrations. The rate law allows us to determine the rate for various concentrations of the reactants.
Example: The rate law for the reaction 2A +B→3C is Rate = 0.045M-1s-1 [A][B] If the concentration of A is 0.2M and that of B is 0.3M, what will be the reaction rate?
Chem FAQ: How do I calculate reaction rate using a rate law?
rate = M-1 s-1 [0.2M][0.3M]
rate = M/s
Do Practice Exercises 5 & 6 p.646

7. Chlorine dioxide, ClO2, is a reddish-yellow gas that is soluble in water. In basic solution it gives ClO3- and ClO2- ions.
ClO2(aq) + OH(aq)  ClO3(aq) + ClO2(aq) + H2O (l)
The rate law is Rate=k[ClO2]2[OH-]. What is the value of the rate constant given that when [ClO2]=0.060M, [OH-] = 0.030M, the reaction rate is M/s
0.02 M-1 /s
0.02 M/s
0.02 s-
None of these
2.3x102 M-2 s-1

8. Orders… are indicated for each reactant,
the overall reaction order is the sum of individual reactant orders,
may be zero, negative, fractional or integers, but in this course we will usually encounter positive integers, and
must be determined from experimental data.
Chem FAQ: What is the order of a reaction?

9. Determining The Rate Law:
Run reaction under the same conditions, varying only the concentrations of reactants (not the temperature).
A ratio of rate laws for each experiment allows us to determine the order of each reactant.
The rate law is unique to temperature and concentration conditions. Therefore, when a rate law is stated, it must include the temperature at which it is determined.

10. Use Rate Laws To Determine Orders :
2NO(g) + O2(g) → 2NO2(g)
Select 2 rate laws that vary in concentration for only one of the substances (NO).
exp
[NO]
[O2]
RNO2 M/s 1
.015
.048 2
.030
.192 3
.096
Hint: Write the fractions with the larger R on top.

11. Use Rate Laws To Determine Orders :
2NO(g) + O2(g) → 2NO2(g)
Next choose 2 rate laws where the concentration for the other component
(O2) changes.
exp
[NO]
[O2]
RNO2 M/s 1
.015
.048 2
.030
.192 3
.096
x=2, y = 1
so…..
Rate = k [NO]2[O2]

12. Determining The Value Of k
Finally we can solve for k. Use any rate law and the orders that we have determined.
exp
[NO]
[O2]
RNO2 M/s 1
.015
.048 2
.030
.192 3
.096
rate = k[NO]2[O2]
Substitute orders into the rate laws.
Note that the units on k are always M(1-order)s-1.
0.048M/s =k [0.015M]2[0.015M]
1.4×104 M-2s-1 =k
Do Example 14.5, 14.6 p.651, Exercises 10 thru 14p.651+.

13. Determine The Rate Law From Given Data
[B]
[C]
Rate M/s
0.01
0.02
0.15
0.0002
0.0004
0.0001
0.3
x=1
y=1
z=0
rate=k[A][B]
Note that changing the concentration of C had no effect on the rate. We say it is “zero order with respect to C.”

14. Effect of Order of Rxn on Rate
Consider Rate = k[A]n If n = 0, change in conc has no effect on rate. If n = 1, Rate = k[A]1 and when conc is 2x, rate is 2x. If n = 2, Rate = k[A]2 and when conc is 2x, rate is 4x If n = 2, when conc is tripled, rate is …? rate is 9x If n = 3, and conc is doubled, rate is…? rate is 8x

15. Visual Determination of Reaction Order
Once you understand how you can predict effect of a change in concentration on rates (as in the previous slide), you can often determine the rxn order visually without doing complicated calculations.
HOWEVER, that is only if the conc were neatly doubled or tripled, etc.
(See next 2 slides.)

16. p. 648
What is the rate law?
Rate = k[A]?[B]?
Rate = k[A]1[B]2

17. For the following data, determine the order of NO2 in the reaction at 25°C
2 NO2(g) + F2(g)→ 2 NO2F(g):
Exp
[NO2]
[F2]
Rate NO2 disappearance (M/s) 1
0.001
0.005
2 x10-4 2
0.002
4 x10-4 3
0.006
4.8 x10-4 1 2 3
not enough information given

18. When Visual Determination Fails...
We cannot always determine the rxn order visually. For example, if we ended with 32.1=3.18x How do we determine what x is? In high-level chemistry courses, x might even be a fraction!