1. Rate Laws

2. Determine the rate law and order of a chemical reaction from experimental data.
Include: various reaction orders, rate versus concentration graphs.
Additional KEY Terms
Ratio

3. Rate is proportional to changes in A and B
A + B C
Rate is proportional to changes in A and B
Rate Law helps us calculate the rate of a REACTION not a reactant.

4. It is an expression that shows the quantitative effect of concentration changes on reaction rate.
Rate = k[A]x
where: k rate constant
[A] concentration of A
x reaction order
**The rate constant (k) and the order (x) can only be determined experimentally**

5. Temperature is the only factor to affect
The rate constant (k) is specific for each reaction at a specific temperature.
Temperature is the only factor to affect
the rate constant.
Rate = k[A]x

6. Reaction
Order

7. Each reactant can affect the rate differently
A + B
Products
Rate = k[A]x[B]y
Each reactant can affect the rate differently
The orders of a reaction (x and y) indicate how much each [reactant] affects the rate of a reaction.

8. Rate = k[A] 1 x First order reaction ( x = 1)
The reaction rate is directly proportional to changes in reactant concentration.
[A] is doubled - rate doubles 2 = 21
[A] is tripled - rate triples 3 = 31 x
Rate = k[A] 1

9. Rate = k[A]2 Second order reaction (x = 2)
The reaction rate is proportional to changes in reactant concentration squared.
Rate = k[A]2
Doubling [A] - increase rate 4x 4 = 22
Tripling [A] - rate increase 9x = 32

10. **NOT included in the rate law if determined
Third order reaction (x = 3)
The reaction rate is proportional to changes in reactant concentration cubed.
Rate = k[A]3
Zero order reaction (x = 0)
The rate does not depend on the [A].
Changing [A] does NOT change the rate.
Rate = k
**NOT included in the rate law if determined
to be zero order**

11. Rate = k[A][B]2 1st order + 2nd order = 3rd order overall
Overall order of reaction is the sum of the orders:
x + y = overall reaction order
1st order + 2nd order = 3rd order overall

12. Calculating Rate Law

13. Several ways to determine the rate law:
differential rate law - uses calculus
integrated rate law – uses graphing software
initial rates method – uses data tables
Determining rate law:
Measure the effect of changes in concentration of one reactant on rate, while
keeping the other reactant constant.

14. Ratio Approach
8 = 2  4
2 = 

15. = Using ratios: A + B → products same Rate = k[A]x[B] y
Trial
[A] (mol/L)
[B] (mol/L)
Initial Rate (mol/Ls) 1
0.10
0.20
2.0 2
0.30
18.0 3
0.40
16.0
same
Rate = k[A]x[B] y
Rate = k[A]x[B] y
Rate2 k [A]2x  [B]2y
Rate1 k [A]1x  [B]1y = α
9.0 α [3]x  1
9.0 α [3]x
18.0 α x  0.2 y
 0.2
x = second order

16. = Using ratios: A + B → products 2 Rate = k[A]2[B] y 1
Trial
[A] (mol/L)
[B] (mol/L)
Initial Rate (mol/Ls) 1
0.10
0.20
2.0 2
0.30
18.0 3
0.40
16.0
Rate = k[A]2[B] y 1
Rate = k[A]x[B] y
Rate3 k [A]3x  [B]3y
Rate1 k [A]1x  [B]1y = α
8.0 α [2]2  [2]y
8.0 α  [2]y
2.0 α [2]y
16.0 α  0.4 y
 0.2
y = first order

17. Can’t have multiple answers…pick new trials.
Using ratios:
A + B → products 2
Trial
[A] (mol/L)
[B] (mol/L)
Initial Rate (mol/Ls) 1
0.10
0.20
2.0 2
0.30
18.0 3
0.40
16.0
Rate = k[A]2[B] y
You might pick bad trials
Can’t have multiple answers…pick new trials.
Rate2 α [A]2x  [B]2y
9.0 α [3]  [1]y 2
Rate [A]1x  [B]1y
9.0 α 9  [1]y
1 α [1]y
18.0 α x  0.2 y
 0.2
y = 0 or 1 or 2…..

18. Common Sense Approach

19. x y 1 1 rate = k[H2O2] [HI] rate = k[H2O2] [HI] = 2x 2 same same
Rate2 k [H2O2]2x  [HI]2y
Rate1 k [H2O2]1x  [HI]1y
2.0 α 1 ּ [2]y = x y 1 1
rate = k[H2O2] [HI]
2.0 α [2]y
α x  0.2 y
 0.1
rate = k[H2O2] [HI]
x = first order

20. x 1 y Rate = k[A] [B] 8.0 α [2]x  [4]1 Rate α [A]x  [B]yTl
[A]i
mol/L
[B]i
Initial Rate
(mol/Ls) 1
0.0100
0.0240
1.45 x 10−4 2
0.0120
7.25 x 10−5 3
0.0200
0.0480
5.80 x 10−4 x y
Rate = k[A] [B] 1
8.0 α [2]x  [4]1
Rate α [A]x  [B]y
8.0 α [2]x  4
Rate3 α [A]3x  [B]3y
Rate [A]2x  [B]2y
2.0 α [2]x
x = first order
α x 
 0.012

21. 3 A (g) + B (g) + 2 C (g) 2 D (g) + 3 E (g)
a. Write the rate law for this reaction.
b. Calculate the value of the rate constant (k).
c. Calculate the rate for Trial #5.
d. Calculate the concentration of A in Trial #6.

22. rate = k[A][B]2 = = 1 2 same same same same same same
same
same
same
same
same
same
a. Write the rate law for this reaction.
Rate2 k [A]2x  [B]2y  [C]2z
Rate1 k [A]1x  [B]2y  [C]2z =
Rate2 [A]2x
Rate1 [A]1x =
rate = k[A][B]2

23. rate = k[A][B]2 b. Calculate the value of the rate constant (k).
To find the value of k, we use that data from ANY trial.
Don’t include units for k.

24. rate = (200)(0.50 mol/L)(0.40 mol/L)2 rate = 16 mol/Ls
c. Calculate the rate for Trial #5.
rate = k[A][B]2
rate = (200)(0.50 mol/L)(0.40 mol/L)2
rate = 16 mol/Ls

25. d. Calculate the concentration of A in Trial #6.
rate = k[A][B]2

26. Conclusion: Everything in the Rate Law must be determined experimentally:
1. Write a basic rate law with all reactants
2. Determine the order for each reactant (1, 2, 0)
3. Re-write the rate law with the determined order of reaction for each
4. Solve any problems

27. CAN YOU / HAVE YOU?
Determine the rate law and order of a chemical reaction from experimental data.
Include: various reaction orders, rate versus concentration graphs.
Additional KEY Terms
Ratio