Lesson 12.2 Rate Laws
Suggested Reading

Zumdahl Chapter 12 Sections 12.2 & 12.3
Essential Question

What is a rate law?
Learning Objectives:


Analyze data from rate experiments.
Determine rate laws and rate constants.
Review & Preview:
Watch the following IsaacsTeach video to review reaction rates and preview
rate laws.
Watch the following YouTube Video:
https://www.youtube.com/watch?v=1jF6yOzZbws
The Rate Law
By now you know that reaction rate depends on concentration. Consider the
reaction of nitrogen dioxide with fluorine to give nitryl fluoride.
2NO2(g) + F2(g) → 2NO2F(g)
The rate of reaction is observed to be proportional to the concentration of
nitrogen dioxide. Thus, when the concentration of nitrogen dioxide is doubled,
the rate doubles. A rate law is an equation that relates the rate of a reaction
to the concentration of reactants raised to various powers. The following is the
rate law for the previous reaction:
Rate = k[NO2][F2]
In this rate law, both reactant concentrations have an exponent of 1. Please
not the exponents are not related to the coefficients in the balanced chemical
equations. Consider the reaction of substances A and B to give D and E,
according to the equation
aA + bB → cC + dD
You could write the rate law in the form
Rate = k[A]m[B]n
The exponents are often, but not always, integers. They must be determined
experimentally and they cannot be obtained from the chemical equation. Once
you know the rate law for a reaction and have found the value of the rate
constant, you can calculate the rate of a reaction for any values of reactant
concentrations.
The Rate Constant
The rate constant, k, is a proportionality constant in the relationship between
rate and concentrations. It has a fixed value at any given temperature. but it
varies with temperature. Whereas the units of rate are usually given as M/s,
the units of k depend on the form of the rat law. For the previous rate
law, Rate = k[NO2][F2],
from this you get the following units for k:
You are going to need your dimensional analysis skills to
study chemical kinetics!
Reaction Order
In chemical kinetics reactions are classified by their orders. The reaction
order with respect to a given reactant equals the exponent from the rate law.
For the reaction of nitrogen dioxide with fluorine to give nitryl fluoride, with
the rate law, Rate = k[NO2][F2]. The reaction is first order with respect to
nitrogen dioxide because the exponent of [NO2] in the rate law is 1.
Similarly, the reaction is first order with respect to F2.
The overall order of the reaction equals the sum of the orders of the
reactants in the rate law. In the example above, the overall order is 2, and
we say that the reaction is second order overall. Reactions display a variety
of orders. Lets look at some examples.
Example 1: When cyclopropane is heated the carbon ring opens up giving
propylene, C3H6(g) + Heat → CH2CHCH3(g). This reaction has the
following experimentally determined rate law, rate = k[C3H6]. The reaction is
first order in cyclopropane and first order overall.
Example 2: Nitric oxide, NO, reacts with hydrogen according to the
following equation, 2NO(g) + 2H2(g) → N2(g) + 2H2O(g). The rate law is
rate = k[NO]2[H2]. Thus, the reaction is second order with respect to NO,
first order with respect to H2, and third order overall.
Example 3: Acetone, CH3COCH3, reacts with iodine in acidic
solution, CH3COCH3(aq)+ I2(aq) + H+ → CH3COCH2I(aq) + HI(aq). The rate
law is rate = k[CH3COCH3][H+]. The reaction is first order in acetone, It is
zero order in iodine, which means it contains the factor [I2]0 = 1. Therefore,
the rate law does not depend on the concentration of iodine, as long as
some iodine is present. The reaction is first order in H+, which is a catalyst
in this reaction. When catalysts are present, they speed up the rate of
reaction and therefore must be included in the rate law. The reaction is
second order overall.
Determining the Rate Law
In order to determine the rate law by experiment, you must determine the
order of each reactant and any catalyst. The initial rate method is a simple
way to obtain reaction orders. If we are given data from two or more
experiments at the same temperature with different concentrations of
reactants and different rates we can determine the exponents in the rate
law for the reaction as follows:
1.
Write the rate law with the concentrations of all species in the equation.
Write the coefficients as unknowns: n, m, etc. For example, we might
have an equation such as, A + B → C, with the rate law.:
2.
Take ratios of the experimental data that give different rates.
3.
Cancel common terms and solve for the exponent that does not cancel.
An example will help make this clearer.
Example: Determining the rate law from initial rates.
If we have the following experimental initial rate data for the reaction, A + B →
2C.
[A], M
[B], M
experiment
rate = -d[A]/dt
1
0.50
0.50
1.2
2
1.0
0.50
4.8
3
2.0
1.0
38.4
We can write ratios for the data from experiments 1 and 2
Using the data from experiments 1 and 2, we see that the k's cancel as do the
concentrations of species B.
Solving this equation gives
0.25 = 0.5n , so n = 2 since 0.52 = 0.25
Now we use the known value of n and data from experiments 1 and 3 or from
experiments 2 and 3 and solve for m. Here we use experiments 1 and 3:
When we substitute the data we get:
0.031 = 0.06 x 0.5m
0.5 = 0.5m , so m = 1 since 0.51 = 0.5
Now that we know the exponents we can write the rate law can be written:
HOMEWORK: Finish practice exercises assigned in lesson 12.1 (practice
exercises 14.1-14.8)