Mole, formula, and concentration

Matter in one page

Element: one kind of atom. Compound: elements locked in a fixed mass ratio. Mixture: variable composition; homogeneous if uniform (sugar solution), heterogeneous if not (sand + water).

Laws you lean on in Class 11 stoichiometry: conservation of mass; constant composition; multiple proportions; Gay-Lussac for gas volumes; Avogadro (equal volumes of gases at same T, P → equal number of molecules).

The mole

1 mole = amount that contains as many entities as atoms in 12 g of ¹²C. That number is N_A ≈ 6.022 × 10²³.

Molar mass (g mol^-1) is the mass of one mole. For a gas at STP, many school numericals still use 22.4 L mol^-1 — check what your paper assumes.

Quick conversions: moles = mass / molar mass. Number of particles = moles × N_A. For solutions, moles = molarity × volume(L).

Empirical vs molecular formula

Empirical: simplest whole-number atom ratio (glucose → CH₂O).

Molecular: actual counts in one molecule (glucose → C₆H₁₂O₆).

Molecular formula = n × empirical formula. n = molecular mass / empirical formula mass.

Concentration terms that show up in labs

Molarity (M) = moles of solute / litres of solution. Volume changes with temperature → M changes with T.

Molality (m) = moles of solute / kg of solvent. Mass of solvent does not care about temperature the same way → m is T-independent.

Mole fraction of A = moles A / total moles. Mole fractions of all components sum to 1.

% w/w = (mass solute / mass solution) × 100. % v/v uses volumes.

Normality uses equivalents. For most Class 11 mole problems, stick to moles unless the question forces N. You will meet normality again in Class 12 redox titrations.

Limiting reagent

Convert everything to moles. Compare with the stoichiometric ratio. The reactant that runs out first is limiting. Product amount follows from that reactant.

Example skeleton: N₂ + 3H₂ → 2NH₃. If you have 1 mol N₂ and only 2 mol H₂, H₂ limits (needs 3 mol H₂ per mol N₂).

Significant figures (quick)

Non-zero digits count. Zeros between digits count. Leading zeros after a decimal do not. Trailing zeros after a decimal do.

In addition/subtraction, match the fewest decimal places. In multiplication/division, match the fewest significant figures.

Exact counted numbers (2 eggs, 12 atoms in a definition) do not limit sig figs the way measured values do.