(Adapted from Barbosa-Cánovas and Vega-Mercado, 1996)
3.1.4.2 Freezing point depression and freezing point elevation
This method is accurate for liquids in the high water activity range but is not suitable for solid foods (Barbosa-Cánovas and Vega-Mercado, 1996). The water activity can be estimated using the following two expressions:
Freezing point depression:
-log aw = 0.004207 DTf + 2.1 E-6 DT2f (1)
where DTf is the depression in the freezing temperature of water
Boiling point elevation:
-log aw = 0.01526 DTb - 4.862 E-5 DT2b (2)
where DTb is the elevation in the boiling temperature of water.
3.1.4.3 Osmotic pressure
Water activity can be related to the osmotic pressure (p) of a solution with the following equation:
p = RT/Vw ln(aw) (3)
where Vw is the molar volume of water in solution, R the universal gas constant, and T the absolute temperature. Osmotic pressure is defined as the mechanical pressure needed to prevent a net flow of solvent across a semi-permeable membrane. For an ideal solution, Equation (3) can be redefined as:
p = RT/Vw ln(Xw) (4)
where Xw is the molar fraction of water in the solution. For non-ideal solutions, the osmotic pressure expression can be rewritten as:
p = RTfnmb(mwVw) (5)
where n is the number of moles of ions formed from one mole of electrolyte, mw and mb are the molar concentrations of water and the solute, respectively, and f the osmotic coefficient, defined as:
f = -mw ln(aw)/nmb (6)