The Chemistry Maths Book, Second Edition

11.4 Separable equations in chemical kinetics 323

and theH

2

2 O

2

equation is

01 = 1 −2H

2

1 − 1 O

2

1 + 1 2H

2

O

Rate of reaction

Letn

A0

be the initial amount of species A, at timet 1 = 10 , and letn

A

be the amount at

timet. The ‘amount’ of reaction that has occurred in time tis given by the extent of

reaction ξ, defined by

n

A

1 = 1 n

A0

1 + 1 ν

A

1 ξ (11.23)

and a measure of the rate of a reaction is then the rate of change of the extent of

reaction, or rate of conversion,

(11.24)

This rate can also be expressed in terms of the rate of change of the amount of each

species taking part in the reaction; differentiating (11.23),

(11.25)

(since n

A0

and ν

A

are constants), so that

(11.26)

For many purposes in physical chemistry it is more convenient to express the rate

in terms of concentrations instead of amounts.*The concentration of species Ain

volume Vis given by[A] 1 = 1 n

A

2 V, and division of equation (11.26) by the volume gives

the rate of reaction (in terms of the concentration of A)

(11.27)

For the general reaction written in the form (11.21) we have

(11.28)

v=− =− = = =

1111

a

d

dt b

d

dt p

d

dt q

d

dt

[] [] [] []ABPQ



v==

r

V

d

dt

1

ν

A

[]A

r

d

dt

dn

dt

==

ξ

ν

1

A

A

dn

dt

d

dt

A

A

=ν

ξ

r

d

dt

=

ξ

*By convention, the symboln

A

is the amount of species A in the (SI) unit mol, and this is also the unit of ξ.

Other quantities used instead of amount are the concentration [A], the partial pressurep

A

for a gas, and the

dimensionless mole fractionx

A

. We follow the normal practice in physical chemistry texts of using concentrations

for our discussion of kinetics, but omit the units.