CBSE Class 12 Chemistry

Solutions and their types

A solution is a homogeneous mixture of two or more substances, meaning that its composition and properties are the same throughout. The component present in the largest amount is the solvent and determines the physical state of the solution; the others are solutes. A solution of two components is a binary solution.

Any of the three states of matter can act as solvent or solute, so there are nine combinations. The ones a student meets most often are these.

The notes that follow deal mostly with liquid solutions, in which the solvent is a liquid, because that is where concentration, vapour pressure and colligative properties are measured.

Expressing concentration

The concentration of a solution is the amount of solute present in a given amount of solution or solvent. It can be stated in several ways, and the choice depends on whether temperature will change.

Mass percentage

A solution that is 10% glucose by mass holds 10 g of glucose in every 100 g of solution, which means 90 g of water.

Volume percentage

This suits liquid in liquid solutions. A 35% (v/v) ethylene glycol antifreeze has 35 mL of ethylene glycol in 100 mL of solution.

Mass by volume percentage

This is the mass of solute in grams per 100 mL of solution, and it is the form used in medicine and pharmacy. A 0.9% (w/v) sodium chloride solution has 0.9 g of salt in 100 mL.

Parts per million

For a very dilute solution, where the solute is a trace, the concentration is given in parts per million (ppm):

The parts may be by mass, by volume or by number of moles. Dissolved oxygen in a lake or a pollutant in drinking water is usually quoted in mass ppm.

Mole fraction

The mole fraction of a component is its amount of substance divided by the total amount of substance in the solution. For components A and B,

For a solution with many components the mole fractions still sum to 1. Mole fraction has no unit and does not change with temperature, which is why it appears in Raoult's law and Henry's law.

Molarity

Molarity ($M$) is the amount of solute in moles in one litre (one $\pu{dm3}$) of solution:

Its unit is $\pu{mol L-1}$. Molarity changes with temperature, because the volume of the solution expands or contracts while the amount of solute stays the same.

Molality

Molality ($m$) is the amount of solute in moles per kilogram of solvent:

Its unit is $\pu{mol kg-1}$. Mass does not vary with temperature, so molality, like mole fraction, is independent of temperature. That makes it the natural choice for boiling point and freezing point calculations.

Worked examples

Molarity from a mass and a volume

A solution is made by dissolving 4.0 g of sodium hydroxide (molar mass $\pu{40 g mol-1}$) in water and making it up to 250 mL.

Molality and mole fraction

12.0 g of glucose (molar mass $\pu{180 g mol-1}$) is dissolved in 250 g of water.

For the mole fraction, 250 g of water is $250/18 = 13.9$ mol, so

A second case uses equal amounts. 46 g of ethanol (1.0 mol) and 36 g of water (2.0 mol) together give $x_\text{ethanol} = 1/(1+2) = 0.333$ and $x_\text{water} = 0.667$.

Converting between mass percentage and molarity

A bottle of concentrated hydrochloric acid is labelled 36.5% HCl by mass with a density of $\pu{1.18 g mL-1}$. Take 1000 mL of the acid.

The molarity is therefore $\pu{11.8 mol L-1}$. The density is the link: it turns the mass of solution into a volume.

Parts per million

Sea water of density $\pu{1.03 g mL-1}$ contains $\pu{6.0e-3 g}$ of dissolved oxygen in 1 L. One litre has mass 1030 g, so

Relating the units

For a solution in which the solute has molar mass $M_2$, the molarity and molality are related through the density $d$ (in $\pu{g mL-1}$) of the solution by

For a dilute aqueous solution the density is close to 1 and the mass of solute is small, so molarity and molality have nearly the same numerical value. For a concentrated solution the two differ noticeably, and the derivation above, which works from a fixed mass of solution, is safer than remembering the formula.