The Foundations of Chemistry

(1 picosecond 10 ^12 second) or even femtoseconds (1 femtosecond 10 ^15 second).

Such studies have yielded information about very fast reactions, such as energy transfer

resulting from absorption of light in photosynthesis.

If the progress of a reaction causes a change in the total number of moles of gas present,

the change in pressure of the reaction mixture (held at constant temperature and constant

volume) lets us measure how far the reaction has gone. For instance, the decomposition

of dinitrogen pentoxide, N 2 O 5 (g), has been studied by this method.

2N 2 O 5 (g)88n4NO 2 (g)
O 2 (g)

For every two moles of N 2 O 5 gas that react, a total of five moles of gas is formed (four

moles of NO 2 and one mole of O 2 ). The resulting increase in pressure can be related by

the ideal gas equation to the total number of moles of gas present. This indicates the

extent to which the reaction has occurred.

Once we have measured the changes in concentrations of reactants or products with

time, how do we describe the rate of a reaction? Consider a hypothetical reaction.

aA
bB88ncC
dD

In this generalized representation, a represents the coefficient of substance A in the

balanced chemical equation, bis the coefficient of substance B, and so on. For example,

in an earlier equation given for the decomposition of N 2 O 5 , a2, A represents N 2 O 5 ,

c4, C represents NO 2 , and so on.

The amount of each substance present can be given by its concentration, usually

expressed as molarity (mol/L) and designated by brackets. The rate at which the reaction

proceeds can be described in terms of the rate at which one of the reactants disappears,

[A]/tor [B]/t,or the rate at which one of the products appears, [C]/tor

[D]/t.The reaction rate must be positive because it describes the forward (left-to-right)

reaction, which consumes A and B. The concentrations of reactants A and B decrease in

the time interval t.Thus, [A]/tand [B]/twould be negativequantities. The purpose

of a negative sign in the definition of a rate of reaction is to make the rate a positive

quantity.

If no other reaction takes place, the changes in concentration are related to one another.

For every amol/L that [A] decreases, [B] must decrease by bmol/L, [C] must increase by

cmol/L, and so on. We wish to describe the rate of reaction on a basis that is the same

regardless of which reactant or product we choose to measure. To do this, we can describe

the number of moles of reactionthat occur per liter in a given time. For instance, this is

accomplished for reactant A as






The units for rate of reaction are , which we usually shorten to 

L

m

ti

o

m

l

e

or

molL^1 time^1. The units 

m

L

ol

represent molarity, M,so the units for rate of reaction

can also be written as 

ti

M

me

or Mtime^1. Similarly, we can divide each concentration

change by its coefficient in the balanced equation. Bringing signs to the beginning of each

term, we write the rate of reaction based on the rate of change of concentration of each

species.

mol rxn



Ltime

[A]



t

1 mol rxn



amol A

rate of decrease



in [A]

1 mol rxn



amol A

In reactions involving gases, rates of
reactions may be related to rates of
change of partial pressures. Pressures
of gases and concentrations of gases
are directly proportional.

PVnRT or P RTMRT

where Mis molarity.

n



V

650 CHAPTER 16: Chemical Kinetics

The Greek “delta,” , stands for
“change in,” just as it did in
Chapter 15.