1. Reaction Rates and Rate Laws
Chapter 14

2. Reaction Rates
Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time. 2

3. Reaction Rates
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
In this reaction, the concentration of butyl chloride, C4H9Cl, was measured at various times. 3

4. Reaction Rates
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
The average rate of the reaction over each interval is the change in concentration divided by the change in time:
Average rate =
[C4H9Cl] t 4

5. Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Note that the average rate decreases as the reaction proceeds.
This is because as the reaction goes forward, there are fewer collisions between reactant molecules because there are not as many reactants left to collide 5

6. Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
A plot of concentration vs. time for this reaction yields a curve like this.
The slope of a line tangent to the curve at any point is the instantaneous rate at that time.
Instantaneous rate = change in conc./change in time 6

7. Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
All reactions slow down over time.
Therefore, the best indicator of the rate of a reaction is the instantaneous rate near the beginning. 7

8. Reaction Rates and Stoichiometry
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
In this reaction, the ratio of C4H9Cl to C4H9OH is 1:1.
Thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH.
Rate =
-[C4H9Cl] t =
[C4H9OH] 8

9. Reaction Rates and Stoichiometry
What if the ratio is not 1:1?
2 HI(g)  H2(g) + I2(g)
Therefore,
Rate = − 1 2
[HI] t =
[I2]
To generalize, then, for the reaction
aA + bB
cC + dD
Rate = − 1 a
[A] t
= − b
[B] = c
[C] d
[D] 9

10. Rate= -1/2*Δ[O3]/ Δt = 1/3 Δ[O2]/ Δt
Practice Problem
How is the rate at which ozone disappears related to the rate at which oxygen appears in the reaction:
2O3(g)  3O2(g)
Rate= -1/2*Δ[O3]/ Δt = 1/3 Δ[O2]/ Δt
Rate = − 1 a
[A] t
= − b
[B] = c
[C] d
[D]

11. Practice Problem 2
If the rate at which O2 appears, Δ[O2]/ Δt, is 6.0 x 10-5 M/s at a particular instant, at what rate is O3 disappearing at this same time, -Δ[O3]/ Δt ? Rate= -1/2*Δ[O3]/ Δt = 1/3 Δ[O2]/ Δt Rate = - Δ[O3]/ Δt = 2/3 * (6.0 x 10-5) Rate = 4.0 x 10-5 M/s

12. Concentration and Rate
One can gain information about the rate of a reaction by seeing how the rate changes with changes in concentration for each reactant. 12

13. Concentration and Rate
NH4+(aq) + NO2−(aq)
N2(g) + 2 H2O(l)
Comparing Experiments 1 and 2, when [NH4+] doubles, the initial rate doubles. 13

14. Concentration and Rate
NH4+(aq) + NO2−(aq)
N2(g) + 2 H2O(l)
Likewise, comparing Experiments 5 and 6, when [NO2−] doubles, the initial rate doubles. 14

15. Concentration and Rate
This means
Rate  [NH4+]
Rate  [NO2−]
Rate  [NH+] [NO2−] or
Rate = k [NH4+] [NO2−]
This equation is called the rate law, and k is the rate constant.
Rate = k[A]m[B]n 15

16. Rate constant, k
k is temperature dependent, k increases with increasing temperature (reaction rates increase with temperature)
Rate constants can vary over many orders of magnitude because reaction rates vary widely

17. Rate Laws
A rate law shows the relationship between the reaction rate and the concentrations of reactants.
The exponents tell the order of the reaction with respect to each reactant.
Rate = k [NH4+] [NO2−]
This reaction is
First-order in [NH4+]
First-order in [NO2−] 17

18. Rate Laws
The overall reaction order can be found by adding the exponents on the reactants in the rate law.
Rate = k [NH4+] [NO2−]
This reaction is second-order overall. 18

19. Rate Laws
Although the exponents in rate laws are sometimes the same as the coefficients in the balanced equation, this is not necessarily the case.
If the reaction occurs in more than one step the rate law cannot always be expressed this way
The values of these exponents must be determined experimentally by looking at the rate at which that reactant changes over time

20. What is the overall rate reaction orders for each reaction?
2 N2O5(g)  4NO2(g) + O2(g) Rate= K[N2O5]
First order
CHCl3 + Cl2  CCl4(g) + HCl(g) Rate= k[CHCl3][Cl2]1/2
3/2 order
H2(g) + I2(g)  2HI(g) Rate= k[H2][I2]
Second order

21. Determining a Rate Law from Initial Rate Data
The initial rate of a reaction A + B  C was measured for several different starting concentrations of A and B, and the results are as follows:
Experiment Number
[A] (M)
[B] (M)
Initial Rate (M/s) 1
0.100
4.0 x 10-5 2
0.200 3
16.0 x 10-5
Using these data, determine (a) the rate law for the reaction (b) the rate constant (c) the rate of the reaction when [A] = M and [B] = M

22. Experiment Number
[A] (M)
[B] (M)
Initial Rate (M/s) 1
0.100
4.0 x 10-5 2
0.200 3
16.0 x 10-5
Determine the rate law for the reaction Rate = k[A]m[B]n Experiment 1 and 2: [A] stays the same, [B] doubles but has no effect on the rate (so zero order for [B]) Experiment 1 & 3: [A] doubles, and rate quadruples while [B] remains the same, so therefore A is a second order reaction [A]2 Therefore, rate= k[A]2, so second order overall

23. Experiment Number
[A] (M)
[B] (M)
Initial Rate (M/s) 1
0.100
4.0 x 10-5 2
0.200 3
16.0 x 10-5
Determine the rate constant Rate = k[A]2 k= (4.0 x 10-5 M/s)/ (0.100 M)2 k= 4.0 x 10-3 M-1s-1

24. Experiment Number
[A] (M)
[B] (M)
Initial Rate (M/s) 1
0.100
4.0 x 10-5 2
0.200 3
16.0 x 10-5
Determine the rate of the reaction when [A] = M and [B] = M Rate = 4.0 x 10-3 M-1s-1 x (0.050) 2 Rate = 1.05 x 10-5 M/s