1. Lecture 1402 Concentration and Rate The Rate Laws
Chemistry, The Central Science, 11th edition
Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten
Lecture 1402 Concentration and Rate The Rate Laws
John D. Bookstaver
St. Charles Community College
Cottleville, MO
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2. Concentration and Rate
Rate Laws
Experimental Determination of Rate
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3. RATE LAW Mathematical model Specific information
Which reactants determine the rate
How the rate is controlled

4. The Initial Rate Method is used to establish the exact rate law

5. Concentration and Rate
One can gain information about the rate of a reaction by seeing how the rate changes with changes in concentration.
Let’s consider the experimental data for the following reaction…
NH4+(aq) + NO2−(aq)
N2(g) + 2 H2O(l)
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6. Concentration and Rate
NH4+(aq) + NO2−(aq)
N2(g) + 2 H2O(l)
If we compare Experiments 1 and 2, we see that when [NH4+] doubles, the initial rate doubles (initial [NO2-] is the same).
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7. Concentration and Rate
NH4+(aq) + NO2−(aq)
N2(g) + 2 H2O(l)
Likewise, when we compare Experiments 5 and 6, we see that when [NO2−] doubles, the initial rate doubles (initial [NH4+] is the same).
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8. Concentration and Rate
This means
Rate  [NH4+]1
Rate  [NO2−]1
Rate  [NH4+]1 [NO2−]1
which, when written as an equation, becomes
Rate = k [NH4+]1 [NO2−]1 =
k [NH4+] [NO2−]
Therefore,
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9. Concentration and Rate
Rate = k [NH4+] [NO2−]
This equation is called the rate law, and k is the rate constant.
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10. 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.
Since the rate law is
Rate = k [NH4+] [NO2−]
the reaction is
First-order in [NH4+] and
First-order in [NO2−].
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11. Rate Laws Rate = k [NH4+] [NO2−]
The overall reaction order can be found by adding the exponents on the reactants in the rate law.
This reaction is second-order overall.
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12. More Generically
R0 = k[A0]m[B0]n

13. Where:
m = order with
respect to A
n = order wrt B
and
n + m = order of
reaction

14. Let’s Look at Another Set of Data
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15. Use ratio method to solve for m and n
R0 = k[A0]m[B0]n

16. Exp Rate [A0] [B0]

17. R0 = k[A0]m[B0]n

18. Exp Rate [A0] [B0]

19. R0 = k[A0]m[B0]n

20. Thus, rate = k[A]0[B]1 or rate = k[B]
Order wrt [A]?
Order wrt [B]?
Order of the Reaction?

21. Where k is the rate constant.

22. So, if you have the rate law and concentration data you can calculate k, the rate constant in the appropriate units.

23. rate = k[B]
Using Exp 1:

24. A + B + C  products Exp [A] [B] [C] Initial Rate 1 1.25 8.7 2 2.50
17.4 3
3.02
50.8 4
3.75
457 5
3.01
1.00
1.15 ??