The Mole Concept and Stoichiometry

The mass number of an isotope is an integer counting protons and neutrons. Its relative isotopic mass is a measured mass ratio and need not equal that integer exactly. For example, use the isotopic masses supplied in a question rather than silently replacing them with mass numbers.

A relative mass is dimensionless. A molar mass, M, is mass per mole and has a unit such as g mol^-1. Their numerical values agree when M is expressed in g mol^-1: CO₂ has M_r = 44.0 and M = 44.0 g mol^-1. For NaCl, say relative formula mass rather than relative molecular mass.

One mole contains exactly 6.02214076 × 10²³ specified elementary entities. This fixes the Avogadro constant N_A = 6.02214076 × 10²³ mol^-1. Use N = nN_A and n = m/M. The amount n is measured in mol, not in grams.

For isotopes, A_r = Σ(isotopic mass × fractional abundance). Percent abundances must first be divided by 100; relative peak intensities can instead be divided by their total. A weighted mean must lie between the masses used and closer to the more abundant isotope.

An empirical formula gives the simplest whole-number ratio of atoms of each element. A molecular formula gives the actual numbers in a molecule. Benzene has empirical formula CH and molecular formula C₆H₆. An ionic formula such as MgCl₂ describes a formula-unit ratio, not a molecule.

For complete combustion of a compound containing C and H, every mole of CO₂ contains one mole of original carbon atoms, while every mole of H₂O contains two moles of original hydrogen atoms. Thus n(C) = n(CO₂) and n(H) = 2n(H₂O). Oxygen in the products comes from both the compound and the oxygen supply, so product oxygen cannot directly give the original oxygen content.

This deduction assumes complete combustion and quantitative product collection. A water absorber can also collect moisture from the incoming gas unless the gas is dried. Incomplete combustion, escaping CO₂ or a compound containing an unaccounted element makes the simple mass balance unreliable. State the assumptions when evaluating experimental data.

A balanced equation conserves each element and total charge. For an ionic equation, remove unchanged spectator ions, then check atoms and charge again. For example, CO₃^2-(aq) + 2H⁺(aq) → CO₂(g) + H₂O(l) has zero net charge on both sides. Replacing CO₃ with CO₂ to balance oxygen would change the reacting species and is invalid.

If the isolated dry product is less than this maximum, percentage yield = actual yield / theoretical yield × 100%. Impure or wet product can give an apparent yield above 100%; this is evidence about the measurement, not extra creation of matter. Distinguish product yield from the percentage purity of a starting sample.

For gases behaving ideally, V is proportional to n at fixed temperature and pressure. The balanced coefficients therefore also give gas-volume ratios under those conditions. If conditions differ, use pV = nRT first. Do not insert a memorised molar gas volume when the stated temperature and pressure require a different value.

Complete combustion of a hydrocarbon obeys C_xH_y + (x + y/4)O₂ → xCO₂ + (y/2)H₂O. The carbon dioxide amount gives x; oxygen consumption then gives y. For an oxygen-containing fuel C_xH_yO_z, the oxygen coefficient becomes x + y/4 - z/2.

c = n/V, with V in dm³ when c is in mol dm^-3. Divide cm³ by 1000 before using n = cV. Dilution changes concentration and volume but preserves solute amount, provided no solute is lost or reacts: c₁V₁ = c₂V₂.

An aliquot is a measured fraction of a well-mixed solution. If 25.00 cm³ is taken from 250.0 cm³, the whole flask contains ten times the aliquot amount. Do not multiply the aliquot concentration by ten to obtain the flask concentration: they are the same solution.

Report a final result to the significant figures justified by the measurements or requested by the question. Stoichiometric coefficients and exact unit conversions do not limit significant figures. A burette titre is the difference of two readings; its uncertainty depends on both readings.

For an unknown reaction, calculate the amounts actually consumed, divide by their smallest common amount, then infer coefficients. A balanced atom-and-charge check is still necessary. An observed amount ratio can be distorted by excess unreacted reagent, side reactions or incomplete collection; it is not automatically the stoichiometric ratio.

Formula from mass: divide by atomic molar masses. Combustion: n(C) = n(CO₂), n(H) = 2n(H₂O). A gas-volume ratio equals a mole ratio only at matching temperature and pressure. An aliquot changes amount, not the concentration of the solution it came from.