# Colligative Properties of Solutions | General Chemistry 2

Colligative properties of solutions are studied in this chapter: solution concentrations, solutions and solubility, gas solubility and Henry’s law, Raoult’s law, boiling point elevation, freezing point depression, osmotic pressure

## Solution Concentrations

Mass Percent:

% w/w = $\frac{{\mathrm{m}}_{\mathrm{solute}}}{{\mathrm{m}}_{\mathrm{solution}}}$ x 100

% w/v = $\frac{{\mathrm{m}}_{\mathrm{solute}}}{{\mathrm{V}}_{\mathrm{solution}}}$ x 100

% v/v = $\frac{{\mathrm{V}}_{\mathrm{solute}}}{{\mathrm{V}}_{\mathrm{solution}}}$ x 100

msolution = msolute + msolvent

Mole Fraction:

xsolute = $\frac{{\mathrm{n}}_{\mathrm{solute}}}{{\mathrm{n}}_{\mathrm{solution}}}$

n = number of moles (in mol)

Molarity M (in mol.L-1):

M = $\frac{{\mathrm{n}}_{\mathrm{solute}}}{{\mathrm{V}}_{\mathrm{solution}}}$

Molality m (in mol.kg-1):

m = $\frac{{\mathrm{n}}_{\mathrm{solute}}}{{\mathrm{m}}_{\mathrm{solution}}}$

## Solutions and Solubility

A solute dissolves in a solvent to make a solution

Solubility: maximum amount that dissolves in a given amount of solvent at a particular temperature
Substances with similar types of intermolecular forces dissolve in each other

H2O and CH3OH exhibit hydrogen bonding ⇒ they are miscible

Solids are more soluble at higher temperatures

## Gas Solubility and Henry’s Law

Gases become:

• less soluble as temperature increases
• more soluble at higher pressure

Henry’s Law:

Solubility of a gas is proportional to its pressure:

Pgas = k x Mgas

Pgas = partial pressure of the gas (in atm)
Mgas = molarity of the dissolved gas (in mol.L-1)
k = proportionality constant (Henry’s law constant) ⇒ depends upon the gas, the solvent and T

## Raoult’s Law

Psolvent = xsolvent P0solvent

Psolvent = vapor pressure of the solvent
P0solvent = vapor pressure of the pure solvent
xsolvent = mole fraction of solvent in the solution
(0 ≤ xsolvent < 1 ⇒Psolvent < P0solvent)

## Boiling Point Elevation

Vapor pressure of the solution < Vapor pressure of the pure solvent
⇒ more energy is required to convert solution from liquid to gas
⇒ boiling point elevation

The magnitude of the boiling point elevation ΔTb (in K) is:

ΔTb = i x Kb x m

ΔTb = Tb solution – Tb solvent
i = van’t Hoff i-factor = number of ions produced per formula unit
m = solution molality (in mol.kg-1)
Kb = proportionality constant (boiling point elevation constant) ⇒ depends upon the solvent

## Freezing Point Depression

At the freezing temperature:
vapor pressure of the solid (pure solvent) = vapor pressure of the solution

BUT the vapor pressure of the solution has been lowered by the solute
⇒ freezing point is also lower
⇒ solid solvent has a smaller vapor pressure
⇒ freezing point depression

The magnitude of the freezing point depression ΔTf (in K) is:

ΔTf = - i x Kf x m

ΔTf = Tf solution – Tf solvent
i = van’t Hoff i-factor = number of ions produced per formula unit
m = solution molality (in mol.kg-1)
Kf = proportionality constant (freezing point depression constant) ⇒ depends upon the solvent

## Osmotic Pressure

Osmosis: movement of solvent particle through a semipermeable membrane while the solute particles stay within their respective solutions
Solvent particles move from the solution of lower concentration to the solution of higher concentration

Osmotic pressure Π: amount of pressure that must be applied to the higher concentration solution to prevent the osmosis

Π = i x x R x T

i = van’t Hoff i-factor = number of ions produced per formula unit
M = molarity (in mol.L-1)
R = ideal gas constant = 8.314 (in J.K-1.mol-1)
T = temperature (in K)