Physical Chemistry of Foods

dissociate into two species—commonly ions—have an effective molarity
that is about twice the nominal one, etc.; this effective concentration is
called theosmolarity. We will here only consider water as the solvent and
assume the solution to be ideally dilute. Subscript 1 refers to the solvent
(water), 2 to the solute.
The lowering of vapor pressure at any temperature then follows from
Raoult’s law,

p 1 ¼x 1 po 1 ¼ð 1 
x 2 Þpo 1 ð 2 : 14 Þ

wherepis vapor pressure andpo 1 is that of pure water.
The change inboiling pointat standard pressure (1 bar) is given by

DTb¼

Tb^2 ; 1

DHv; 1

Rlnx 1 &
28 lnx 1 & 28 x 2 & 0 : 51 m 2 ðKÞð 2 : 15 Þ

whereTb; 1 is the boiling point of the pure solvent,DHvis the enthalpy of
vaporization ð 40 :6kJ?mol
^1 for water at 100CÞ, and m is the solute
concentration in moles per liter. The approximations successively made,
when going from the first to the last righthand term in the equation, all
apply at infinite dilution. The boiling point elevation is often given as
Kb?m 2 , where for waterKb¼ 0 :51 K?L?mol
^1. It should be noted that its
magnitude significantly depends on ambient pressure.
The change infreezing pointis similarly given by

DTf¼

Tf^2 ; 1

DHf; 1

Rlnx 1 &103 lnx 1 &
 103 x 2 &
 1 : 86 m 2 ðKÞð 2 : 16 Þ

whereDHfis the enthalpy of fusion, 6020 J?mol
^1 for water. Note that the
freezing point depression is considerably greater than the boiling point
elevation, because the molar enthalpy of fusion is far smaller than the
enthalpy of vaporization.
The osmotic pressure ðPÞof a solution can be interpreted as the
pressure that has to be applied to the solution to increase the chemical
potential of the solvent to the value of the pure solvent at standard pressure.
Pis thus higher for a higher solute concentration. If local differences in
concentration exist, solvent (i.e., liquid) will move to the regions wherePis
highest, to even out concentration gradients; this means that osmotic
pressure is in fact a negative pressure.
The osmotic pressure becomes manifest and can thus be measured in a
situation as depicted in Figure 2.4, where solvent and solution are separated
by asemipermeable membranethat lets the solvent pass but not the solute(s).
Solvent now moves to the solution compartment until the osmotic pressure