Colligative Properties

Colligative Properties

Properties of solutions that depend only on the number of solute particles, not on the nature of the solute.

Collective Properties

Another term for colligative properties.

Colligative Properties Depend On

The number of solute particles present in solution.

Colligative Properties Do Not Depend On

The chemical identity of the solute.

Four Colligative Properties

Vapor-pressure lowering, boiling-point elevation, freezing-point depression, osmotic pressure.

Like Dissolves Like

Polar solutes dissolve in polar solvents; nonpolar solutes dissolve in nonpolar solvents.

Polar Solute

Usually dissolves in a polar solvent such as water.

Nonpolar Solute

Usually dissolves in a nonpolar solvent such as carbon tetrachloride.

Dilute Solution

A solution with concentration ≤ 0.2 M.

Nonvolatile Solute

A solute with negligible or no measurable vapor pressure.

Volatile Substance

A substance that evaporates readily and has measurable vapor pressure.

Pure Solvent

A solvent containing only one component.

Vapor Pressure

The pressure exerted by vapor molecules above a liquid at equilibrium.

Vapor-Pressure Lowering

The vapor pressure of a solution is lower than that of the pure solvent.

Reason for Vapor-Pressure Lowering

Solute particles reduce the number of solvent molecules escaping into the vapor phase.

Raoult's Law

The vapor pressure of a solvent over a solution equals the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent.

Raoult's Law Formula

Psolution = Xsolvent × P°solvent

Meaning of Psolution

Vapor pressure of the solution.

Meaning of P°solvent

Vapor pressure of the pure solvent.

Meaning of Xsolvent

Mole fraction of the solvent.

Mole Fraction Formula

X = moles of component / total moles of solution

Vapor-Pressure Lowering Formula

ΔP = P° − P

Meaning of ΔP

Decrease in vapor pressure.

Volatile Solution Formula

Ptotal = PA + PB

Partial Pressure Formula

PA = XA × P°A

Partial Pressure Formula

PB = XB × P°B

Dalton's Law of Partial Pressure

The total pressure is the sum of the partial pressures of each component.

Boiling Point

The temperature at which the vapor pressure equals the external atmospheric pressure.

Boiling-Point Elevation

The boiling point of a solution is higher than that of the pure solvent.

Boiling-Point Elevation Formula

ΔTb = Tb − Tb°

Boiling-Point Elevation Equation

ΔTb = Kb × m

Meaning of ΔTb

Increase in boiling point.

Meaning of Kb

Molal boiling-point elevation constant (°C/m).

Meaning of m

Molality of the solution.

Why Molality is Used

Molality does not change with temperature.

Freezing-Point Depression

The freezing point of a solution is lower than that of the pure solvent.

Reason for Freezing-Point Depression

Solute particles interfere with crystal formation.

Freezing-Point Depression Formula

ΔTf = Tf° − Tf

Freezing-Point Depression Equation

ΔTf = Kf × m

Meaning of ΔTf

Decrease in freezing point.

Meaning of Kf

Molal freezing-point depression constant (°C/m).

Pure Solvent During Freezing

The pure solvent crystallizes first.

Osmosis

The movement of solvent through a semipermeable membrane from a dilute solution to a concentrated solution.

Semipermeable Membrane

Allows solvent molecules to pass but blocks solute particles.

Osmotic Pressure (π)

The pressure required to stop osmosis.

Osmotic Pressure Formula

π = MRT

Alternative Osmotic Pressure Formula

π = (n/V)RT

Meaning of π

Osmotic pressure.

Meaning of M

Molarity of the solution.

Meaning of R

Gas constant = 0.0821 L·atm·mol⁻¹·K⁻¹.

Meaning of T

Absolute temperature in Kelvin.

Meaning of n

Number of moles of solute.

Meaning of V

Volume of solution in liters.

Hypertonic Solution

Higher solute concentration outside the cell; water leaves the cell.

Effect of Hypertonic Solution

Cells shrink.

Hypotonic Solution

Higher solute concentration inside the cell; water enters the cell.

Effect of Hypotonic Solution

Cells swell.

Isotonic Solution

Equal solute concentrations inside and outside the cell.

Effect of Isotonic Solution

No net movement of water.

Nonelectrolyte

A substance that dissolves without forming ions.

Electrolyte

A substance that dissociates into ions in solution.

Strong Electrolyte

Completely dissociates into ions in solution.

Weak Electrolyte

Partially dissociates into ions.

Reason Electrolytes Have Greater Colligative Effects

They produce multiple dissolved particles.

van't Hoff Factor (i)

The ratio of actual particles in solution to the number of dissolved formula units.

van't Hoff Factor Formula

i = Actual number of particles in solution / Number of formula units dissolved

Nonelectrolyte van't Hoff Factor

i = 1

NaCl van't Hoff Factor

i ≈ 2

KNO₃ van't Hoff Factor

i ≈ 2

CaCl₂ van't Hoff Factor

i ≈ 3

Na₂SO₄ van't Hoff Factor

i ≈ 3

Modified Vapor-Pressure Equation for Electrolytes

ΔP ∝ i

Modified Boiling-Point Elevation Equation

ΔTb = iKb m

Modified Freezing-Point Depression Equation

ΔTf = iKf m

Modified Osmotic Pressure Equation

π = iMRT

Ion Pair

A cation and anion held together by electrostatic attraction in solution.

Effect of Ion Pair Formation

Reduces the effective number of dissolved particles.

Electrolytes with Greater Ion Pair Formation

Those containing multivalent ions such as Mg²⁺, Al³⁺, SO₄²⁻, and PO₄³⁻.

Using Freezing-Point Depression to Find Molar Mass

Calculate molality, then moles, then molar mass.

Using Osmotic Pressure to Find Molar Mass

Calculate molarity, then moles, then molar mass.

Molality Formula

m = moles of solute / kilograms of solvent

Molarity Formula

M = moles of solute / liters of solution

Moles Formula

n = mass / molar mass

Molar Mass Formula

Molar Mass = mass / moles

Pressure Cooker Example

Increasing pressure raises the boiling point by decreasing vapor pressure.

Antifreeze Example

Ethylene glycol lowers freezing point and raises boiling point.

Salt Water Example

Dissolved salt lowers vapor pressure compared to pure water.

Salt on Roads Example

Salt lowers the freezing point of water, melting ice.

Aircraft De-icing Example

Ethylene glycol solutions lower the freezing point to prevent ice formation.

Spaghetti Example

Adding salt raises the boiling point of water but does not make it boil faster.

Jam and Jelly Preservation

High sugar concentration creates a hypertonic environment that dehydrates bacteria.

Brine and Cucumber Example

Water leaves cucumber cells by osmosis, causing shrinkage.

Why does vapor pressure decrease?

Fewer solvent molecules escape into the vapor phase.

Why does boiling point increase?

A higher temperature is needed for vapor pressure to equal atmospheric pressure.

Why does freezing point decrease?

Solute particles interfere with crystal formation.

Why does osmosis occur?

To equalize solvent concentration across a semipermeable membrane.

Why is molality used instead of molarity?

Molality is independent of temperature.

Why do electrolytes have larger colligative effects?

They dissociate into multiple particles.