Chemistry Reference
In-Depth Information
solution density (
) and solute concentration (c
w
) (w/w), the specific refraction
increment (r) can be defined as
r
¼
n
n
0
c
w
¼
n
c
w
(7)
where n and n
0
are the refractive indices of the solution and the solvent,
respectively, measured under the same conditions. Since refraction is an
additive property, the refractive index increment (n) for a multicomponent
system is given by
n
¼
n
solution
n
solvent
¼
ð
mr
Þ
(8)
where m is the mass fraction of a solute, r is the specific refraction increment
and
is the density of the solution. Goulden (1963) reported the following
specific refraction increments (ml g
1
): casein micelles, 0.207; whey proteins,
0.187; lactose, 0.140. Refractive index measurements can be used satisfacto-
rily to estimate the solids-not-fat (SNF) content of milk and condensed milk.
Generally, there is a linear relationship between solids content (based on
weight per unit volume) and refractive index, but this relation varies between
lots of milk, owing mainly to variations in the lactose/protein ratio. The
refractive index can be determined quickly and accurately and can be used
as a rapid method of checking the SNF content and purity of butter fat.
15.6.
Freezing Point
The freezing point of water is directly related to the concentrations of water-
soluble constituents. The addition of solute to water lowers the freezing point,
the degree of depression of the freezing point being proportional to the
molality of the solution. The Raoult (1884) equation reflects the relationship
between the depression of the freezing point (T
f
) and the molality of an
aqueous solution (M):
T
f
¼
K
f
M
(9)
where K
f
is the molar depression constant (1.868C for an ideal aqueous
solution). This relationship applies only to very dilute solutions.
Milk is a complex aqueous solution and Raoult's law can therefore be used
only for a rough calculation of the relation between the concentration of milk
constituents and freezing point. The freezing point of milk is lower than that of
water
and
is
proportional
to
the
concentration
of
milk's
water-soluble
