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Rate laws can be converted into equations
that tell us what the concentration of the
reactants or products are at any time
Calculus required to derive the equations
but not to use them
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Rate = k
With calculus it can be changed to an
equation that relates the starting conc ([A]o)
to the conc at any other time (t)
[A] = -kt + [A]o
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Plot of [A] vs t is linear with a slope equal to k
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Find the conc of a reactant at some time after
the reaction started
Find the time required for a given fraction of
a sample to react
Find the time required for a reactant to reach
a certain concentration
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Rate = k[A]
ln[A] = - kt + ln[A]o
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Plot of ln[A] vs t is linear
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The first order constant for the hydrolysis
of a certain insecticide in water at 12°C is
1.45/yr. A quantity of this insecticide is
washed into a lake in June, leading to an
overall concentration of 5 x 10-7 g/cm3 of
water. Assume that the effective temp of
the lake is also 12°C. A) what is the conc of
the insecticide in June of the following year?
B) How long will it take for the conc of the
insecticide to drop to 3.0 x 10-7 g/cm3 ?
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The decomposition of dinitrogen pentoxide is
studied over time and the results are given in
in the table on pg.573.
a) Verify if this is a first order reaction.
b) Calculate the value of the rate constant
c) Find the concentration after 150 sec.
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Time required for the concentration of a
reactant to decrease to halfway between its
initial and final values
Time when [A]= ½ [A]o
t1/2 = .693/k
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What is the half life of the insecticide in the
lake from the previous example?
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Rate = k[A]2
1/[A] = kt + 1/[A]o
Plot of 1/[A] vs t is linear
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Plot of 1/[A] vs t is linear
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The following data was obtained for the
decomposition of nitrogen dioxide. Is the
reaction first or second order? What is the
rate constant?
Time (s)
[NO2]
0
.0100
50
.0079
100
.0065
200
.0048
300
.0038