Kinetics ❮ 197The Rate Equation
The rate of reaction may depend upon reactant concentration, product concentration, and
temperature. Cases in which the product concentration affects the rate of reaction are rare
and are not covered on the AP exam. Therefore, we will not address those reactions. We will
discuss temperature effects on the reaction later in this chapter. For the time being, let’s just
consider those cases in which the reactant concentration may affect the speed of reaction. For
the general reaction: a A + b B +... → c C + d D +... where the lowercase letters are the
coefficients in the balanced chemical equation; the uppercase letters stand for the reactant; and
product chemical species and initial rates are used, the rate equation (rate law) is written:
Rate = k[A]m[B]n...
In this expression, k is the rate constant—a constant for each chemical reaction at a
given temperature. The exponents m and n, called the orders of reaction, indicate what
effect a change in concentration of that reactant species will have on the reaction rate.
Say, for example, m = 1 and n = 2. That means that if the concentration of reactant A is
doubled, then the rate will also double ([2]^1 = 2), and if the concentration of reactant B
is doubled, then the rate will increase fourfold ([2]^2 = 4). We say that it is first order
with respect to A and second order with respect to B. If the concentration of a reactant is
doubled and that has no effect on the rate of reaction, then the reaction is zero order with
respect to that reactant ([2]^0 = 1). Many times the overall order of reaction is calculated; it
is simply the sum of the individual coefficients, third order in this example. The rate equa-
tion would then be shown as:
Rate = k[A][B]^2 (If the exponent is 1, it is generally not shown.)
It is important to realize that the rate law (the rate, the rate constant, and the orders of
reaction) is determined experimentally. Do not use the balanced chemical equation to
determine the rate law.
The rate of reaction may be measured in a variety of ways, including taking the slope
of the concentration versus time plot for the reaction. Once the rate has been determined,
the orders of reaction can be determined by conducting a series of reactions in which the
reactant species concentrations are changed one at a time, and mathematically determining
the effect on the reaction rate. Once the orders of reaction have been determined, it is easy
to calculate the rate constant.
For example, consider the reaction:
2 NO(g) + O 2 (g) → 2 NO 2 (g)
The following kinetics data were collected:Experiment Initial [NO] Initial [O 2 ] Rate of NO 2 formation (M/s)
1 0.01 0.01 0.05
2 0.02 0.01 0.20
3 0.01 0.02 0.10
There are a couple of ways to interpret the data to generate the rate equation. If the
numbers involved are simple (as above and on most tests, including the AP exam), you
can reason out the orders of reaction. You can see that in going from experiment 1 to
experiment 2, the [NO] was doubled, ([O 2 ] held constant), and the rate increased fourfold.
This means that the reaction is second order with respect to NO. Comparing experiments 1
and 3, you see that the [O 2 ] was doubled, ([NO] was held constant), and the rate doubled.KEY IDEA
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