92168.pdf

26 Kinetic properties

Table 2.1 Diffusion coefficients and Brownian displacements calculated for uncharged

spheres in water at 20°C

Radius D 2 o°c/m2s~^1 He after I h

10~^9 m (1 nm)

10~^8 m (10 nm)

Hr^7 rn(100nm)

10~^6 (1 fxm)

2.1 x 10~^10

2.1 x 10~ n

2.1 x 10-^12

2.1 x KT^13

1.23 x 10~^3 m (1.23 mm)

3.90 x 10~^4 m (390 jim)

1.23 x 10~^4 m (123 pm)

3.90 x 10~^5 m (39 jutn)

yielded values of NA closer to the accepted 6.02 x 1023 mol *; for

example, Svedberg (1911) calculated NA = 6.09 x 1023 moP^1 from

observations on monodispersed gold sols of known particle size in the

ultramicroscope. The correct determination of Avogadro's constant

from observations on Brownian motion provides striking evidence in

favour of .the kinetic theory

As a icsult of Brownian motion, continual fluctuations of

concentration take place on a molecular or small-particle scale. For

this reason, the second law of thermodynamics is only valid on the

macroscopic scale.

Translational diffusion

Diffusion is the tendency for molecules to migrate from a region of
high concentration to a region of lower concentration and is a direct
result of Brownian motion.
Pick's first law of diffusion (analogous with the equation of heat
conduction) states that the mass of substance dm diffusing in the x
direction in a time At across an area A is proportional to the
concentration gradient dc/dx at the plane in question:
dc
dm = -DA—, \dt (2.8) /
dx
(The minus sign denotes that diffusion takes place in the direction of
decreasing concentration.)
The rate of change of concentration at any given point is given by
an exactly equivalent expression, Pick's second law:

dc d^2 c

= D r- (2 Q)

dt dx^2 lz-v;