PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 282

For the concentrations of the reactants we write

cA=cA0−x , cB=cB0−x , cC=cC0−x , (9.63)

wherexis obtained by the numerical solution of equation (9.62)

9.2.4.11 Reaction half-life

The reaction half-life is defined with respect to that component whose initial concentration is
the lowest. If, e.g. cA0≤cB0≤cC0, the half-life is defined with respect to component A and
we write

kτ 1 / 2 =

1

(cA0−cB0)(cA0−cC0)

ln 2

+

1

(cB0−cA0)(cB0−cC0)

ln

2 cB0

2 cB0−cA0

+

1

(cC0−cA0)(cC0−cB0)

ln

2 cC0

2 cC0−cA0

. (9.64)

9.2.4.12 Type.

aA +bB +cC→products. (9.65)

9.2.4.13 Kinetic equation

−

dcA

dτ

=kAcAcBcC =⇒ a

dx

dτ

=kA(cA0−a x)(cB0−b x)(cC0−c x). (9.66)

Similarly as in section9.2.3we rewrite this equation to

dx

dτ

=k′(c′A0−x)(c′B0−x)(c′C0−x), (9.67)

wherek′=kAbc, c′A0=cA0/a, c′B0=cB0/b, c′C0=cC0/c.