Question

Calculate the osmotic pressure of low-fat milk with 9% total solids at 20°C and a gas constant of 8.134 m³ kPa / Kg mol K

Answer 1

Temperature (T) = 20^oC = 293K

% of Total solids = 9% Kg solids / Kg product

Gas constant (R) = 8.134 m³.KPa/Kg.mol.K

The osmotic pressure can be found by using Vant Hoff's equation

where, = osmotic pressure, C= concentration of total solutes, R= gas constant, T= temperature, M= molecular weight of solutes

we know, Density of milk solids at 20^oC = 1034 Kg/m³ , Density of water at 20^oC = 998.2 Kg/m³

Density of low fat milk () = 0.09(density of milk solids at 20^oC) + 0.91(density of water at 20^oC)

Density of low fat milk () = 0.09(1034) + 0.91(998.2) = 1001.422 Kg/m³

So. the concentration of total solids (C) = 0.91* = 0.91*1001.422 = 911.294 Kg solids/ m³ product

Milk is composed of lactic acids, fats, lipids, proteins, fatty acids, triglycerides, galactose, etc. So on an average the molecular mass of the milk combined (M) = 3217 Kg/mol

Osmotic pressure = (911.294*8.134*293) / 3217

= 675 KPa is the osmotic pessure