Solutions | Your Answer

1. What Is a Solution?

A solution is a homogeneous mixture of two or more substances. Its composition is uniform throughout the mixture.

Solvent

The component that dissolves the solute. It is often the component present in the larger amount.

Solute

The substance dissolved in the solvent. For salt water, salt is the solute and water is the solvent.

Types of solutions

Solute	Solvent	Example
Gas	Gas	Air
Gas	Liquid	Carbon dioxide in a fizzy drink
Solid	Liquid	Salt in water
Liquid	Liquid	Ethanol in water
Solid	Solid	Many metal alloys

2. Expressing Concentration

Concentration describes how much solute is present in a given amount of solution or solvent. Different units are useful for different types of calculations.

Mass percentage

Mass % = (Mass of solute / Mass of solution) × 100

Volume percentage

Volume % = (Volume of solute / Volume of solution) × 100

Mass-by-volume percentage

Mass-by-volume % = (Mass of solute in g / Volume of solution in mL) × 100

Molarity (M)

Molarity = Moles of solute / Volume of solution in litres

Molality (m)

Molality = Moles of solute / Mass of solvent in kilograms

Mole fraction

Mole fraction of A, xA = Moles of A / Total moles of all components

Mole fractions have no units. For a solution containing only components A and B, xA + xB = 1.

Worked example: Molarity

Suppose 0.5 mol of a solute is present in 2.0 L of solution.

M = 0.5 / 2.0 = 0.25 mol L⁻¹

The solution has a molarity of 0.25 M.

Dilution

When a solution is diluted, solvent is added without changing the amount of solute. The concentration decreases.

M₁V₁ = M₂V₂

This relationship applies when the same solute is diluted and volumes are expressed in consistent units.

3. Solubility

Solubility is the maximum amount of a substance that can dissolve in a specified amount of solvent under given conditions.

Unsaturated solution

Contains less dissolved solute than the amount needed to reach saturation under the stated conditions.

Saturated solution

Contains the maximum equilibrium amount of dissolved solute under the stated conditions.

Supersaturated solution

Contains more dissolved solute than is normally present in a saturated solution at the same conditions. It is often unstable.

Factors affecting solubility

Nature of solute and solvent: their intermolecular interactions matter.
Temperature: the solubility of many solids in liquids increases with temperature, but there are exceptions.
Pressure: has a major effect on the solubility of gases in liquids.

Stirring and crushing a solid can speed up dissolving, but they do not necessarily increase the equilibrium solubility.

4. Henry's Law

At a constant temperature, the concentration of a dissolved gas in a liquid is proportional to the partial pressure of that gas above the liquid, provided the system behaves suitably.

p = Kₕx

Here, p is the gas's partial pressure, x is its mole fraction in the solution, and Kₕ is Henry's law constant in this convention.

Everyday example

Carbon dioxide is dissolved in soft drinks under elevated pressure. When the container is opened, the pressure drops and gas escapes as bubbles.

5. Raoult's Law

For an ideal solution, the partial vapour pressure of a volatile component is equal to its mole fraction in the liquid multiplied by the vapour pressure of the pure component at the same temperature.

pA = xA pA°

For a solution containing two volatile components:

Ptotal = pA + pB
Ptotal = xA pA° + xB pB°

Here, pA° is the vapour pressure of pure A, and xA is its mole fraction in the liquid solution.

Real solutions may show positive or negative deviations from Raoult's law when interactions between unlike molecules differ from those in the pure liquids.

6. Colligative Properties

Colligative properties depend primarily on the number of dissolved solute particles, rather than their chemical identity, for sufficiently dilute solutions.

Relative lowering of vapour pressure

For an ideal solution with a non-volatile solute, the relative lowering of vapour pressure equals the solute's mole fraction.

(p° − p) / p° = xsolute

Elevation of boiling point

ΔTb = i Kb m

The boiling point increases when a suitable non-volatile solute is dissolved in a solvent. Kb is the ebullioscopic constant, m is molality, and i is the van't Hoff factor.

Depression of freezing point

ΔTf = i Kf m

The freezing point decreases. Kf is the cryoscopic constant.

Osmotic pressure

π = iCRT

For dilute solutions, π is osmotic pressure, C is molar concentration, R is the gas constant, and T is absolute temperature in kelvin.

What does the van't Hoff factor mean?

The factor i accounts for the effective number of solute particles in solution. Dissociation can increase the particle count, while association can decrease it. In real solutions, deviations from ideal behaviour may also affect the observed value.

7. Abnormal Molar Mass

Molar mass calculated from colligative properties may differ from the expected value when solute particles associate or dissociate in solution.

Dissociation: one solute unit forms multiple particles, as with many ionic compounds.
Association: multiple solute units combine into larger particles.

The van't Hoff factor helps account for these changes when interpreting colligative-property measurements.

8. Quick Revision

A solution is a homogeneous mixture of solute and solvent.
Molarity uses litres of solution; molality uses kilograms of solvent.
Henry's law relates gas solubility to partial pressure.
Raoult's law describes vapour pressure in ideal solutions.
Colligative properties depend primarily on the number of dissolved particles.
Boiling-point elevation: ΔTb = iKbm.
Freezing-point depression: ΔTf = iKfm.
Osmotic pressure for dilute solutions: π = iCRT.