Chapter 13 Worksheet 3 (ws13.3)
Rate Laws – The Effect of Concentration of Reactants on Reaction Rate
Rate laws (or rate equations)
A rate law describes the dependence of the (forward) rate on the concentrations of reactants.
1. For an elementary reaction (and ONLY for an elementary reaction), the rate law can be
determined by simply looking at the balanced equation and using common sense. Below is a
list of every possible elementary reaction. Write the rate law for each reaction.
Unimolecular
A = products
Rate = k[A]
Bimolecular
A + B = products
Rate = k[A][B]
Bimolecular
2A = products
Rate = k[A]2
Termolecular
A + B + C = products
Rate = k[A][B][C]
Termolecular
2A + B = products
Rate = k[A]2[B]
Termolecular
3A = product
Rate = k[A]3
2. For a reaction with two reactants (A and B), the rate law is:
Rate = k[A]x[B]y
k is the rate constant
x is the order of the reaction with respect to A
y is the order of the reaction with respect to B
x + y is the overall order of the reaction.
Most reactions are zeroth, first, or second order with respect to a given reactant.
Complete the table for the elementary reactions above:
Order with respect to . . .
Elementary Reaction
A
B
C
A = products
First
--------------------- --------------------A + B = products
First
First
--------------------2A = products
Second
--------------------- --------------------A + B + C = products
First
First
First
2A + B = products
Second
First
--------------------3A = product
Third
--------------------- ---------------------
Overall Order
First
Second
Second
Third
Third
Third
3. What information is provided by the overall order of an elementary reaction?
The overall order tells you the molecularity. The overall order for a reaction that occurs
in multiple steps tells you the number of molecules involved in the rate-determining step
and all of the steps preceding the rate-determining step. (You’ll see this later.)
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4. List the 4 factors that affect the rate of a homogenous reaction and the one additional factor
that affects the rate of a heterogeneous reaction that contains a solid.
1. The properties of reactants and products – in particular, their molecular structure and
bond strengths
2. The concentrations of reactants
3. The temperature
4. The presence of a catalyst and its concentration (more catalyst = faster reaction)
The rate of a heterogeneous reaction with a solid phase is affected by the surface area of the
solid phase. The rate increases as the surface area increases.
5. Which of the factors above affect the magnitude of the rate constant for a reaction (k)?
All except number 2. Notice that the effect of concentration is shown explicitly in the rate law.
The other effects are hiding in the rate constant.
6. The unit for a rate constant depends on the overall order of a reaction. Complete the following
table assuming that the unit for rate is M-s-1.
Overall order
Zeroth
First
Second
Third
Unit for k
M-s-1
s-1
M-1-s-1
M-2-s-1
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7. Recall that the rate of a reaction is identical to the rate of the slowest elementary step in
the mechanism. For any reaction, there are many possible mechanisms. The actual mechanism
must be determined experimentally.
Below are two proposed mechanisms for the destruction of ozone.
O3(g) = O2(g) + O(g)
O(g) + O3(g) = O2(g) + O2(g)
2O3(g) = 3O2(g)
SLOW
FAST
O3(g) + O3(g) = O2(g) + O4(g)
O4(g) = O2(g) + O2(g)
SLOW
FAST
2O3(g) = 3O2(g)
Determine the net reaction for both mechanisms above.
Identify the intermediate(s) in mechanism 1. ____ O(g)____
Identify the intermediate(s) in mechanism 2. ____ O4(g)____
What is the molecularity of the rate limiting step in the above mechanisms?
Mechanism 1 ________unimolecular____________
Mechanism 2 _________bimolecular___________
Write the rate law for each of the net reactions based on the given mechanisms.
Mechanism 1 _________ rate = k[O3] ___________
Mechanism 2 _________ rate = k[O3]2 ___________
The experimentally determined rate law for the destruction of ozone is as follows : Rate = k [O3].
Which mechanism is consistent with the experimental rate law? ___mechanism 1____
Note: A mechanism must be consistent with the experimentally determined rate law. However, this
does not prove that a mechanism is correct.
8. True or false (Explain your answer. THIS IDEA IS VERY IMPORTANT!!)
For the generalized reaction, aA + bB = products, the rate equation is: Rate = k[A]a[B]b.
FALSE! The rate law for a reaction is the same as the rate law for the rate determining
(slowest) step in the mechanism. The reaction in problem 6 is a good example. If the statement
above was true, then the reaction would be second order with respect to ozone. In reality it is
first order because the slowest step in the mechanism involves only one molecule of ozone rather
than two molecules. RATE CONSTANTS AND REACTION ORDERS MUST BE
DETERMINED EXPERIMENTALLY! COEFFICIENTS IN BALANCED EQUATIONS
CORRESPOND TO REACTION ORDERS ONLY IF THE REATION IS AN ELEMENTARY
REACTION!!
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9. Determine the rate law for the net reaction based on the given mechanism.
Net:
H2(g) + ICl(g) → HClI(g) + H(g)
(Slow)
H(g) + ICl(g) → HCl(g) + I(g)
(Fast)
HClI(g) → HCl(g) + I(g)
(Fast)
I(g) + I(g) → I2(g)
(Fast)
H2(g) + 2 ICl(g) → 2 HCl (g) + I2(g)
rate = k[H2][ICl]
Notice that the reaction is first order with respect to ICl (not second order) because the slow
step involves only one molecule of ICl.
For all of the mechanisms in this worksheet, the first step is the rate determining step. This
certainly is not always the case. Read about the hydrogen iodide reaction on pages 590-591
in your textbook to learn how to handle mechanisms with a fast initial step.
10. The experimentally determined rate law for the reaction, 2NO2 + F2 = 2NO2F, is:
rate = k[NO2][F2]
Write a two step mechanism that is consistent with this rate law. (Make the first step ratelimiting.)
NO2(g) + F2(g) → NO2F(g) + F(g) (slow)
NO2(g) + F(g) → NO2F(g) (fast)
11. How is it possible for a reaction to be zeroth order with respect to a reactant?
A reaction can be zeroth order with respect to a reactant if that reactant is not involved in the
rate determining step.
Note: If the first step is not the slowest step, then, to be zeroth order, a reactant must also not be
involved in any of the steps that precede the rate determining step.
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