The Mole Concept

Atoms and molecules are impossibly small — far too tiny to count or weigh individually. The mole is the bridge between the microscopic world of particles and the macroscopic quantities measured in the lab.

The Mole and Avogadro's Constant¶

A mole is the amount of substance that contains $6.02 \times 10^{23}$ particles. That number — $6.02 \times 10^{23}$ — is Avogadro's constant ($N_A$). The particles can be atoms, molecules, ions, or electrons, depending on the substance.

One mole of any substance contains the same number of particles, regardless of what the substance is. One mole of carbon atoms, one mole of water molecules, and one mole of sodium ions all contain $6.02 \times 10^{23}$ particles.

Molar Mass¶

Molar mass is the mass of one mole of a substance, expressed in g mol⁻¹. Numerically, the molar mass of an element equals its relative atomic mass in grams. For a compound, the molar mass equals the sum of the relative atomic masses of all atoms in one formula unit.

Calculations Involving the Mole¶

The fundamental relationship between moles, mass, and molar mass is:

$n = \frac{m}{M}$

where $n$ is the number of moles, $m$ is the mass in grams, and $M$ is the molar mass in g mol⁻¹.

Relative Formula Mass¶

The relative formula mass ($M_r$) of a compound is the sum of the relative atomic masses of all the atoms in one formula unit. For ionic compounds the term relative formula mass is used; for molecular compounds it is often called relative molecular mass. Neither is expressed in units — they are pure numbers relative to carbon-12.

Percentage Composition by Mass¶

The percentage by mass of each element in a compound is:

$\% \text{ by mass} = \frac{\text{mass of element in one mole}}{\text{molar mass of compound}} \times 100$

Empirical and Molecular Formulae¶

The empirical formula gives the simplest whole-number ratio of atoms in a compound. The molecular formula gives the actual number of atoms in one molecule. The molecular formula is always a whole-number multiple of the empirical formula.

To find the empirical formula from percentage composition:

1. Treat the percentages as masses in grams.
2. Divide each mass by its relative atomic mass to find moles.
3. Divide all mole values by the smallest to get the simplest ratio.
4. Round to the nearest whole number (or multiply through if fractions appear).

To find the molecular formula, divide the given molar mass by the empirical formula mass and multiply the subscripts.

Avogadro's Law and Gas Volumes¶

Avogadro's Law states that equal volumes of all gases, measured at the same temperature and pressure, contain equal numbers of molecules.

This leads directly to the concept of molar volume. At the conditions used in CSEC:

$n = \frac{V}{24} \text{ (at RTP)}$

Law of Conservation of Matter¶

The Law of Conservation of Matter states that matter is neither created nor destroyed in a chemical reaction. The total mass of reactants always equals the total mass of products. This is why chemical equations must be balanced — the same atoms must appear on both sides.

Balanced Equations and State Symbols¶

A balanced molecular equation shows the formulae of all reactants and products with state symbols, and has equal numbers of each type of atom on both sides.

State symbols:

• (s) — solid
• (l) — liquid
• (g) — gas
• (aq) — aqueous (dissolved in water)

Ionic equations show only the species that actually change in a reaction — spectator ions (ions present but unchanged) are omitted.

Applying the Mole Concept to Equations¶

The coefficients in a balanced equation are mole ratios — they tell you how many moles of each substance react or are produced. This allows calculation of reacting masses and volumes from any given starting quantity.

Method:

1. Write the balanced equation.
2. Identify the mole ratio between the substances of interest.
3. Calculate moles of the given substance.
4. Use the ratio to find moles of the unknown substance.
5. Convert to mass (using $m = nM$) or volume (using $V = n \times 24$) as required.

Concentration and Standard Solutions¶

Molar concentration is the number of moles of solute dissolved per cubic decimetre (litre) of solution:

$c = \frac{n}{V}$

where $c$ is in mol dm⁻³ and $V$ is in dm³. Note: 1 dm³ = 1000 cm³, so always convert cm³ by dividing by 1000.

Mass concentration is the mass of solute dissolved per unit volume, expressed in g dm⁻³.

A standard solution is a solution whose concentration is accurately known. Standard solutions are prepared by dissolving an accurately weighed mass of solute in a known volume of solvent using a volumetric flask.

Volumetric Analysis Calculations¶

In a titration, one solution of known concentration (the standard solution) reacts completely with another. The unknown concentration is calculated from the volume used and the mole ratio from the balanced equation.

General approach:

1. Calculate moles of the known solution: $n = cV$
2. Use the mole ratio from the balanced equation to find moles of the unknown.
3. Calculate the concentration of the unknown: $c = n/V$