Moles + gas laws

exact definition of a mole

The amount of substance that contains the same number of particles as there are atoms in 12 g of carbon-12.

n

Number of moles of a substance.

N

Number of particles (atoms, molecules, or ions) present.

Nᴀ (Avogadro's constant)

6.022 × 10²³ mol⁻¹ — the number of particles in one mole of a substance.

Relationship between n, N, and Nᴀ

n = N ÷ Nᴀ.

Molar mass (M)

Mass of one mole of a substance, measured in g mol⁻¹.

Relative molecular mass (Mᵣ)

Sum of the relative atomic masses of all atoms in a molecule (no units).

Molecular mass

Mass of one molecule in atomic mass units (u); numerically equal to Mᵣ.

Relative formula mass

Sum of the relative atomic masses of the atoms in an ionic compound's formula unit.

Empirical formula

Simplest whole-number ratio of atoms of each element in a compound.

Molecular formula

Actual number of atoms of each element in a molecule; always a multiple of the empirical formula.

Empirical vs molecular formula

Empirical shows ratio; molecular shows actual count of atoms.

Mass percent

(mass of element in 1 mol of compound ÷ molar mass of compound) × 100.

Steps to find empirical formula from percentage

1. Assume 100 g total. 2. Convert % to mass (g). 3. Convert each to moles (mass ÷ Ar). 4. Divide by smallest mole value. 5. Multiply to get whole numbers.

Steps to find molecular formula from empirical formula

1. Find empirical formula mass. 2. Divide molar mass ÷ empirical formula mass. 3. Multiply subscripts by that whole number.

Ammonium

NH₄⁺ — polyatomic ion.

Hydroxide

OH⁻ — polyatomic ion.

Nitrate (V)

NO₃⁻ — polyatomic ion.

Nitrate (III) / Nitrite

NO₂⁻ — polyatomic ion.

Hydrogencarbonate (Bicarbonate)

HCO₃⁻ — polyatomic ion.

Carbonate

CO₃²⁻ — polyatomic ion.

Sulfate (VI)

SO₄²⁻ — polyatomic ion.

Sulfite (IV)

SO₃²⁻ — polyatomic ion.

Phosphate (V)

PO₄³⁻ — polyatomic ion.

Phosphite (III)

PO₃³⁻ — polyatomic ion.

Ethanoate (Acetate)

CH₃COO⁻ — polyatomic ion.

Cyanide

CN⁻ — polyatomic ion.

Hydrocarbon reaction

Combustion of hydrocarbons with oxygen produces CO₂ and H₂O.

Moles into grams formula

n = m ÷ M (m = mass in g, M = molar mass).

Ideal gas law

pV = nRT.

Assumptions of the ideal gas law (5)

1. Particles have negligible volume. 2. No intermolecular forces. 3. Collisions are perfectly elastic. 4. Constant random motion. 5. Average kinetic energy ∝ temperature (K).

Combined gas law

(p₁V₁)/T₁ = (p₂V₂)/T₂.

Boyle-Mariotte law (pressure-volume)

At constant temperature, p₁V₁ = p₂V₂ (p ∝ 1/V).

Pressure unit conversion

1 Pa = 1 N m⁻² = 1 J m⁻³.