Page 33 - Instant notes

Liquids 19

Rather than measuring absolute viscosity, it is more convenient to measure the time taken
for a specific volume of a liquid standard to pass through a capillary, and to compare this
with the time required for the same volume of the fluid of interest, whence:

It is convenient to define a quantity known as the frictional coefficient, f, which is given
simply by f=Aη/d. This quantity can be measured relatively easily, but is directly related
to molecular shapes through Stoke’s law:
f=6πηr {F(a, b, c)}

r is the effective radius of the molecule, and represents the radius of a sphere with the
same volume as that of the molecule. F(a, b, c) is a complex shape-dependent function of
the molecule’s dimensions. Fitting of this expression to experimental data allows
determination of molecular shapes. For spherical molecules, F(a, b, c)=1.

Diffusion

When a solute is present in a solvent, then the tendency of that solute is to spread evenly
throughout the solvent in a series of small, random jumps. This thermally energized
process is known as diffusion. The fundamental law of diffusion is Fick’s first law. The
rate of diffusion of dn moles of solute, dn/dt, across a plane of area A, is proportional to
the diffusion coefficient, D, and the negative of the concentration gradient, −dc/dx, thus:

The diffusion coefficient for a spherical molecule, of radius r, is very simply related to
the viscosity of the solvent:
D=k BT/(6πηr)

where k B is the Boltzmann constant and T is the temperature. Alternatively, if it is
2
assumed that the molecules take steps of length λ in time τ, D is also given by D=λ /2τ. If
it is further assumed that the molecule makes random steps, then D also allows
calculation of the mean square distance, , over which a molecule diffuses in a time, t:

Surface tension

The effect of intermolecular forces in a liquid results in the free energy of a liquid
being minimized when the maximum number of molecules are completely surrounded by