PHYSICAL CHEMISTRY IN BRIEF

CHAP. 14: DISPERSION SYSTEMS [CONTENTS] 462

expressed by the relation

ln

ch 2

ch 1

=−

mNAg

RT

(

1 −

ρ 0

ρ

)

(h 2 −h 1 ) =−

4 π r^3 NAg

3 RT

(ρ−ρ 0 ) (h 2 −h 1 ) (14.6)

wherech 2 andch 1 represent the number of particles of the massmin unit volume, at the height
h 2 andh 1. Other symbols have their usual meanings.

Example

Calculate the concentration ratio of quartz particles of the radiusr= 5× 10 −^6 m scattered in

water as established at equilibrium in layers distant 1 cm from one another. The density of water

and quartz isρ 0 = 1g cm−^3 andρ= 2. 6 g cm−^3 , respectively.

Solution

Substituting into (14.6) yields

ln

ch 2

ch 1

= −

4 × 3. 146 ×(5× 10 −^6 )^3 × 6. 022 × 1023 × 9. 81

3 × 8. 314 × 298. 15

(2. 6 −1)× 103 × 0. 01

= − 7. 625 × 104.

These particles will sediment practically completely.

In the centrifugal field of the ultracentrifuge, a sedimentation equilibrium is attained which
is described by the relation

ln

ch 2

ch 1

=

mNAω^2

2 RT

(

1 −

ρ 0

ρ

)

(h^22 −h^21 ) =

2 π r^3 NAω^2

3 RT

(ρ−ρ 0 ) (h^22 −h^21 ), (14.7)

wherech 2 denotes the number of particles of the massmor radiusrin unit volume, and at the
distanceh 2 from the axis of rotation.

14.2.3 Membrane equilibria

Different properties of colloid systems are also evident when we observe those comprised of two
subsystems separated by a semipermeable membrane.