PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 268

The concentrations of substances reacting according to equation (9.1) are bound by the
material balance equations

cA = cA0−a x ,

cB = cB0−b x ,

..

. [V] (9.10)
cR = cR0+r x ,
cS = cS0+s x ,
..
.

whereci 0 are the initial concentrations, i.e. the concentrations at timeτ= 0.
For a chemical reaction written in a compact form,

0 =

∑n

i=1

νiRi,

we may summarize equations (9.10) into:

ci=ci 0 +νix , i= 1, 2 ,... , n , (9.11)

wherenis the number of the reacting components andνiare their stoichiometric coefficients
(negative for the reactants and positive for the products).

Note: The material balance equations are an analogy to equations (8.4) in Chapter 8,
which was devoted to chemical equilibrium. The formal difference between them is that
here they are written for concentrations (i.e. amounts of substance in unit volume) and
not for amounts of substance.
Using material balance equations we may rewrite the kinetic equation of a simple reaction
(9.9) into the form

a

dx

dτ

=kA(cA0−ax)α(cB0−bx)β.... (9.12)

Thus we obtain a differential equation between a single dependent variablexand an independent
variableτ. The initial condition isx= 0 at timeτ= 0.