Colligative Properties

colligative properties: properties of a solution that depend on the number of particles dissolved, but not on the chemical properties of the particles.

vapor pressure reduction: solute particles get in the way of liquid solvent molecules trying to vaporize.

P_solvent = x_solvent

where:

P_solvent = partial pressure of the solvent

x_solvent = mole fraction of the solvent

= vapor pressure of the pure solvent

freezing point depression (ΔT_f): solute particles get in the way of liquid solvent molecules trying to freeze.

boiling point elevation (ΔT_b): solute particles get in the way of liquid solvent molecules trying to boil.

ΔT_f = i m K_f

ΔT_b = i m K_b

where:

i = van’t Hoff factor (# solute particles from each molecule)

m = molality of the solute

K_f = freezing point depression constant. For H₂O, K_f = 1.86 (degrees Celsius per molal)

K_b = boiling point elevation constant. For H₂O, K_b = 0.52 (degrees Celsius per molal)

osmotic pressure (π): pressure across a semi-permeable membrane from differences in solvent concentration due to solute.

πV = i n R T

where:

π = osmotic pressure (additional pressure due to osmosis)

V = volume of solution

i = van’t Hoff factor

n = moles of solute

R = gas constant

T = temperature (Kelvin)

Because molarity is the moles of solute (n) divided by the volume of solution (V), the above equation can be simplified to:

π = i M R T

where:

M = molarity of the solute

and everything else is as above.