Which calculator for which situation
- Mass and amount of substance. Molar mass adds the atomic masses in a formula; moles to grams converts in both directions — the bridge between the balance and the reaction.
- Solutions. Molarity computes concentration in mol/L; dilution applies
C₁V₁ = C₂V₂to prepare a solution from a more concentrated one. - Acidity. pH converts between ion concentration and the 0 to 14 scale.
The mole is the central idea
Chemical reactions happen in ratios of particles, but laboratories and factories work with balances. The mole bridges the two: a fixed quantity of 6.022 × 10²³ entities, with molar mass as the factor that converts one into the other.
That is why the mass ratio is almost never the equation's ratio. Sodium bicarbonate and acetic acid react 1 mole to 1 mole, but by mass that is 35 g of bicarbonate to 25 g of acid — because the molecules weigh differently. Measuring "equal amounts" is the error that leaves reagent unreacted.
pH: a logarithmic scale that deceives
Each pH unit represents a factor of ten in hydrogen ion concentration. Lemon juice (pH 2) is not "a bit" more acidic than coffee (pH 5): it is a thousand times more acidic.
The practical consequence is strong: raising pH by one point requires diluting tenfold. Going from pH 3 to pH 7 would demand a 10,000-fold dilution — and even then it would not work cleanly, because of buffering. It is the same reason diet does not change blood pH: the body holds the 7.35 to 7.45 range through buffer systems and renal and respiratory regulation.
Frequent calculation errors
- Ignoring the subscript outside a parenthesis. Ca(OH)₂ contains two oxygens and two hydrogens — the subscript multiplies everything inside.
- Forgetting water of crystallisation. CuSO₄·5H₂O has a far larger molar mass than the anhydrous salt; the difference is five waters, 90 g/mol. Weighing the hydrate using the anhydrous mass gets the concentration wrong by more than a third.
- Confusing empirical with molecular formula. Glucose's empirical formula is CH₂O (30.03 g/mol); the molecular one is C₆H₁₂O₆ (180.16 g/mol) — a factor of six apart.
- Mixing volume units. Molarity is moles per litre. Preparing in millilitres and forgetting to convert is wrong by a factor of a thousand.
Frequently asked questions
Why are atomic masses not whole numbers? Because the periodic table lists the weighted average of natural isotopes. Chlorine reads 35.45 because nature mixes chlorine-35 and chlorine-37 in roughly 76% and 24% proportions.
When diluting, do I add solvent or top up to volume? You top up to the final volume. C₁V₁ = C₂V₂ solves for the total volume of the diluted solution, not the amount of solvent added — the difference shows up when the dilution is small.
Are molarity and molality the same? No. Molarity is moles per litre of solution; molality is moles per kilogram of solvent. Molality does not vary with temperature, which is why it appears in colligative properties.