General Chemistry Principles, Patterns, and Applications, 2011

synthesis of drugs. Like the first-order reactions studied previously, it can be analyzed using either the differential
rate law (Equation 14.22) or the integrated rate law (Equation 14.23).
To determine the differential rate law for the reaction, we need data on how the reaction rate varies as a
function of monomer concentrations, which are provided in Table 14.3 "Rates of Reaction as a Function of
Monomer Concentration for an Initial Monomer Concentration of 0.0054 M". From the data, we see that
the reaction rate is not independent of the monomer concentration, so this is not a zeroth-order reaction.
We also see that the reaction rate is not proportional to the monomer concentration, so the reaction is not
first order. Comparing the data in the second and fourth rows shows that the reaction rate decreases by a
factor of 2.8 when the monomer concentration decreases by a factor of 1.7:
5.0 ´10 - 5 M / min1.8 ´10 - 5 M / min = 2.8
and 3.4 ´10 - 3 M 2.0 ´10 - 3 M = 1.7
Table 14.3 Rates of Reaction as a Function of Monomer Concentration for an Initial Monomer
Concentration of 0.0054 M
Time (min) [Monomer] (M) Instantaneous Rate (M/min)
10 0.0044 8.0 × 10 −5
26 0.0034 5.0 × 10 −5
44 0.0027 3.1 × 10 −5
70 0.0020 1.8 × 10 −5
120 0.0014 8.0 × 10 −6
Because (1.7) 2 = 2.9 ≈ 2.8, the reaction rate is approximately proportional to the square of the monomer
concentration.
rate ∝ [monomer] 2
This means that the reaction is second order in the monomer. Using Equation 14.22and the data from any
row in Table 14.3 "Rates of Reaction as a Function of Monomer Concentration for an Initial Monomer
Concentration of 0.0054 M", we can calculate the rate constant. Substituting values at time 10 min, for
example, gives the following:
rate8.0 ´10 - 5 M / min4.1 M -1×min -1
= k[ A]2 = k(4.4 ´10 - 3 M )2 = k
We can also determine the reaction order using the integrated rate law. To do so, we use the decrease in
the concentration of the monomer as a function of time for a single reaction, plotted in part (a) in Figure
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