Page 171 - Essentials of physical chemistry

7 Basic Chemical Kinetics

INTRODUCTION

We have taken a quick trip through what we consider essential thermodynamics and for those
students who are only going to take one semester of physical chemistry we have to make sure we
treat the basics of chemical kinetics. A glance at the table of contents’ chapter headings will reveal that
we can continue to do more with kinetics in an additional chapter or skip to some basic spectroscopy
and then return to more kinetics in the second semester with an emphasis on the molecular level. Here,
we want to make sure we establish the mathematical basis for the time dependence of chemical
reactions at a macroscopic level. Once again we are giving what we believe are the essential aspects of
kinetics here and then visit more advanced kinetics in the second semester.
The main concept we need to develop is the ‘‘Extent of Reaction.’’ The extent of the reaction is
related to the mole quantity change during the reaction and is based on 1 mol so that we can relate
to whatever the coefficients are in the balanced reaction. On a macroscopic scale as used in kinetics
we consider the extent of the reaction related to the process of ‘‘moles in and moles out.’’ So, even if
there is a detailed treatment of a reaction mechanism, the extent of reaction is a mole quantity related
to progress of the reaction toward the product. Consider the reaction

A þ 2B ! C þ 3D

Let ‘‘x’’ be the extent of reaction. We are interested in the rate of the overall reaction but what do we
mean by ‘‘rate’’? We can measure the rate by the appearance of species C or D or we can measure
the rate of disappearance of A or B.

d[C] 1 d[D] d[A] 1 d[B]
:
Rate ¼þ ¼þ ¼ ¼
dt 3 dt dt 2 dt
When it comes to measuring a rate, we can use a variety of techniques but they must be quantitative.
Note that we can measure the rate as an appearance of a product or as a disappearance of a reactant
relative to the 1 mol extent of reaction. A rate can be measured by a count of events per unit time as
appearance=disappearance of individual molecules or converted to moles using Avogadro’s number.
As a practical matter, a student should be alert to any physical variable which changes in time during
a reaction and can be related quantitatively to moles of the reacting species. Another clue to how
to proceed is the fact that we show the rate as a derivative which will lead to the need to solve
differential equations by integrating the rate equation.

FIRST-ORDER REACTIONS
The most basic type of rate equation is the first-order decay and we will give complete details of the
mathematics here. There are a number of spontaneous reactions in nuclear chemistry and organic
chemistry. A basic characteristic of any reaction is that the more reactant there is, the more the
reaction will proceed but as the amount of reactant decreases the reaction will be slower. Thus, the
rate of the reaction is proportional to the concentration of the reactant.

d[A]
A ! B, ¼ k 1 [A]
dt

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