PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 58

2.4 State behaviour of mixtures

We may estimate the state behaviour of gaseous mixtures based on the knowledge of the state
behaviour of their pure components using the following methods.

2.4.1 Dalton’s law.

According to Dalton’s law, the pressure of ak-component mixture at temperatureT,volume
V, and amount of substancen=

∑k
i=1niequals the sum of the pressures of its individual pure
components

p(T, V, n) =

∑k

i=1

p(T, V, ni) =p(T, V, n 1 ) +p(T, V, n 2 ) +···+p(T, V, nk), (2.37)

wherep(T, V, ni) is the pressure ofnimoles of a pure substanceiat temperatureTand volume
V.
Dalton’s law applies exactly for an ideal gas. The pressure of a pure substance equals the
partial pressurepiof componentiin the mixture.

p(T, V, ni) =pi≡pxi. (2.38)

Dalton’s law applies only approximately for real gases.

Example

At a certain temperature, the pressure in an autoclave (a system of a fixed volume) containing

2 moles of substance A equals 2.55 MPa. At the same temperature, the pressure in the same

autoclave containing 3 moles of substance B equals 4.05 MPa. Using Dalton’s law estimate the

pressure in the same autoclave containing a mixture consisting of 2 moles of substance A and

3 moles of substance B.

Solution

It follows from the specification thatp(T, V, nA) = 2. 55 MPa, andp(T, V, nB)= 4.05 MPa,

whereV is the volume of the autoclave andTis the considered temperature. For the pressure of

the mixture we have from equation (2.38)p= 2.55 + 4.05 = 6. 60 MPa