A Guide to Common Chemistry Calculations

Molar mass is the mass of one mole of a substance in grams per mole (g/mol). It links the mass on a balance to the number of molecules you are working with. To find it, sum the atomic masses of each element in the formula, multiplied by the atom count.

\text{Molar mass} = \sum(\text{number of atoms} \times \text{atomic mass})

For example, water (H₂O) has a molar mass of (2 × 1.008) + 16.00 = 18.016 g/mol. Glucose (C₆H₁₂O₆) works out to (6 × 12.01) + (12 × 1.008) + (6 × 16.00) = 180.156 g/mol.

Molarity is the most common concentration unit in chemistry – moles of solute per litre of solution:

M = \frac{\text{moles of solute}}{\text{litres of solution}}

To prepare a solution of known molarity, you weigh out the appropriate mass of solute, dissolve it in solvent, and dilute to the final volume. Dilution problems use the simple relationship M₁V₁ = M₂V₂.

The pH scale measures acidity as the negative logarithm (base 10) of the hydrogen ion concentration:

\text{pH} = -\log_{10}[H^+]

A solution with [H⁺] = 1 × 10⁻³ M has pH 3.0 (acidic), while [H⁺] = 1 × 10⁻⁹ M gives pH 9.0 (basic). Pure water at 25 °C has [H⁺] = 1 × 10⁻⁷ M, so pH = 7.0 (neutral).

Stoichiometry is the quantitative relationship between reactants and products in a balanced chemical reaction. For the combustion of methane:

CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O

The coefficients tell you that 1 mole of CH₄ reacts with 2 moles of O₂ to produce 1 mole of CO₂ and 2 moles of H₂O. To solve a stoichiometry problem, follow this sequence: grams → moles (using molar mass) → mole ratio → moles of target → grams of target.

In practice, side reactions, incomplete conversions, and losses during purification mean you almost never recover 100% of the theoretical product. Percent yield measures the efficiency of a reaction:

\text{Percent yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%

If a reaction should theoretically produce 10.0 g of product but you recover only 8.5 g, the percent yield is 85%. A yield above 90% is considered excellent.

Density is the ratio of mass to volume and is a characteristic property of every pure substance:

\rho = \frac{m}{V}

Water has a density of 1.00 g/mL at 4 °C. Ethanol has a density of about 0.789 g/mL, so 100 mL of ethanol weighs 78.9 g. Mercury, at 13.6 g/mL, is one of the densest common liquids.

Chemistry calculations are logical tools refined over centuries. Molar mass bridges the balance and the mole. Molarity describes solutions precisely. pH quantifies acidity. Stoichiometry predicts reaction outcomes. Percent yield measures efficiency. And density connects mass and volume. Master these six and you will have a solid foundation for nearly any chemistry task.