CK-12-Chemistry Intermediate

18.2. Rate Laws http://www.ck12.org

Since the rate of a reaction generally depends upon collision frequency, it stands to reason that as the concentration
of A increases, the reaction rate increases. Likewise, as the concentration of A decreases, the reaction rate decreases.
The expression for the rate of the reaction can be shown as follows:

rate=−

∆[A]

∆t

or rate = k[A]

The proportionality between the rate and [A] becomes an equal sign by the insertion of a constant (k). Arate lawis
an expression showing the relationship of the reaction rate to the concentrations of each reactant. Thespecific rate
constant (k)is the proportionality constant relating the rate of the reaction to the concentrations of the reactants.
The rate law and the specific rate constant for any chemical reaction must be determined experimentally. The value
of the rate constant is temperature dependent. A large value for the rate constant means that the reaction is relatively
fast, while a small value means that the reaction is relatively slow.

In the reaction described above, the rate of the reaction is directly proportional to the concentration of A, which can
also be written as A raised to the first power. That is to say, [A] = [A]^1. Afirst-order reactionis a reaction in which
the rate is directly proportional to the concentration a single reactant. As a first-order reaction proceeds, the rate of
the reaction decreases because the concentration of the reactant also decreases (Figure18.8). Thus, the graph of
concentration versus time is curved. The reaction rate (∆[A]/∆t) at any given time can be determined graphically by
the slope of a line that is tangent to the curve at that point. For example, the rate of the reaction at the time where
the red line intersects with the black curve is given by:

rate=−

[A]final−[A]initial

∆t

=−

0 .35 M− 0 .63 M

3 .0 s− 1 .0 s

= 0 .14 M/s

FIGURE 18.8

This graph shows how the concentration

of a reactant changes as a reaction pro-

ceeds. The rate of the reaction is deter-

mined at any point by measuring the slope

of a tangent to the curve.

The rates of some reactions depend on the concentrations of more than one reactant. Consider a reaction in which a
molecule of A collides with a molecule of B to form product C.

A+B→C

Doubling the concentration of A alone would double the reaction rate. Likewise, doubling the concentration of B
alone would also double the rate. The rate law must reflect this dependence on the concentrations of both reactants.

rate=k[A][B]

This reaction is said to be first order with respect to A, and first order with respect to B. Overall, it is a second-order
reaction. We have again derived this rate law based on the assumption that the reaction proceeds by a single-step
mechanism. With real reactions, where we cannot necessarily make this type of assumption, the rate law and the
order of a reaction must be determined experimentally.