Mole Concept

Syllabus Unit: Physical Chemistry

Why it matters

Chapter overview

The mole is the chemist's bridge between the invisible world of atoms and the measurable world of grams and litres. This topic builds the full toolkit — atomic and molecular mass, Avogadro's number, molar volume, percentage composition, empirical/molecular formulas, and stoichiometric calculations with limiting reagents — that underlies nearly every numerical problem JEE sets across physical, organic and inorganic chemistry.

Chemistry Syllabus Structure Physical Chemistry ~33% weightage

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Isotope MassMass of one specific isotope, e.g. ³⁵Cl = 34.97 u

Average Atomic MassAbundance-weighted mean, e.g. Cl = 35.45 u

Molecular MassSum over a molecular formula, e.g. H2O = 18 u

Formula MassSum per formula unit for ionic solids, e.g. NaCl = 58.5 u

1Atomic & Molecular Mass

Every mass calculation in chemistry rests on one fixed reference point: 1/12th the mass of a carbon-12 atom.

Learning Objectives

Define the atomic mass unit (u) as 1/12th the mass of a C-12 atom and state its value in kg.
Calculate the weighted average atomic mass of an element from its isotopic abundances.
Compute molecular mass by summing atomic masses over a molecular formula.
Distinguish molecular mass (discrete molecules) from formula mass (ionic lattices like NaCl).

Key Terms

Atomic Mass Unit (u)1/12th the mass of one C-12 atom; equals 1.66054 × 10⁻²⁷ kg, fixed by the 1961 IUPAC C-12 standard.

Average Atomic MassThe isotope-abundance-weighted mean atomic mass of an element, e.g. chlorine's 35.45 u.

Molecular MassSum of the atomic masses of all atoms in a molecule's formula, e.g. H2O = 18 u.

Formula MassSum of atomic masses per formula unit for compounds with no discrete molecule, e.g. NaCl = 58.5 u.

Atomic masses need a fixed reference point since atoms are far too light to weigh directly. Chemistry settled on the **carbon-12 standard** in 1961: one atomic mass unit (u) is defined as exactly 1/12th the mass of a single C-12 atom.

The atomic mass unit

1 u = 1.66054 × 10⁻²⁷ kg, which is also equal to 1/NA grams — this is the exact link between the atomic mass scale and the mole, since a C-12 atom's mass in u (12) equals its molar mass in grams (12 g/mol).

Average atomic mass: weighting by isotopic abundance

Chlorine occurs as two isotopes: ³⁵Cl (75.77% abundance, mass 34.97 u) and ³⁷Cl (24.23% abundance, mass 36.97 u).
Average atomic mass = (0.7577 × 34.97) + (0.2423 × 36.97) ≈ 35.45 u — the value printed on the periodic table.
This is a weighted average, not a simple average of the two isotope masses.

Exam TipJEE frequently gives isotopic masses and % abundances and asks for the average atomic mass — always weight by fractional abundance, never take a plain arithmetic mean.

Molecular mass vs. formula mass

H2O = 2(1) + 16 = 18 u; CO2 = 12 + 2(16) = 44 u; these are true molecular masses since discrete molecules exist.
NaCl = 23 + 35.5 = 58.5 u is technically a formula mass, since NaCl exists as an extended ionic lattice with no single discrete molecule.

M(H2SO4) = 2(1) + 32 + 4(16) = 2 + 32 + 64 = 98 u

Common MistakeDo not confuse mass number (a whole number = protons + neutrons of one specific isotope) with atomic mass (a decimal, the abundance-weighted average across all isotopes) — a frequent JEE distractor pair.