Mole Concept: Formulas, Numericals & the Complete Mole Map
From Avogadro’s number to gas volumes — NCERT-aligned theory, the traps NTA actually sets, an interactive mole-map converter, and JEE/NEET numericals solved the way toppers write them.
What is Mole Concept? — Complete Theory
Chemistry happens at a scale where counting is impossible and weighing particles individually is absurd. The mole (symbol: mol) is the SI’s answer — the base unit for amount of substance. One mole of any substance contains exactly 6.02214076 × 10²³ elementary entities — atoms, molecules, ions, electrons, whatever you are counting. Think of it as a chemist’s dozen: the way “a dozen” always means 12, a mole always means 6.022 × 10²³ of anything.
Where does that strange number come from? It is chosen so that the invisible atomic scale and the laboratory scale agree perfectly: the molar mass of a substance in g/mol is numerically equal to its atomic or molecular mass in u. One ¹²C atom has a mass of exactly 12 u; one mole of ¹²C atoms has a mass of exactly 12 g. That single bridge sentence is the heart of the entire mole concept — learn it as an idea, not as a formula.
The molar mass (M) is the mass of one mole of a substance, in g mol⁻¹, built straight from the formula: M(H2O) = 2(1.008) + 16.00 ≈ 18 g mol⁻¹, M(CO2) = 44 g mol⁻¹. For ionic compounds like NaCl there are no molecules — we count formula units and use formula mass (58.5 u for NaCl, hence 58.5 g mol⁻¹).
Every mole problem is one of three conversions — and all of them pass through n, the number of moles:
n = m / M
From particlesn = N / NA
From gas volume, STPn = V / 22.4
| Substance | Molar mass | 1 mol contains | Nature | Vol. of 1 mol at STP |
|---|---|---|---|---|
| Carbon-12 (¹²C) | 12 g | 6.022 × 10²³ atoms | Solid | — |
| Water (H2O) | 18 g | 6.022 × 10²³ molecules | Liquid | — |
| Oxygen gas (O2) | 32 g | 6.022 × 10²³ molecules | Gas | 22.4 L |
| Carbon dioxide (CO2) | 44 g | 6.022 × 10²³ molecules | Gas | 22.4 L |
| Sodium chloride (NaCl) | 58.5 g | 6.022 × 10²³ formula units | Solid | — |
| Term | Meaning | Unit |
|---|---|---|
| Atomic mass | Mass of one atom relative to ¹²C | u |
| Molecular mass | Sum of atomic masses in one molecule | u |
| Formula mass | Sum for ionic compounds (NaCl) | u |
| Molar mass | Mass of one mole of entities | g mol⁻¹ |
| Gram atomic mass | Atomic mass expressed in grams = mass of 1 mol atoms | g |
The percentage composition of a compound is each element’s share of the molar mass: % element = (number of atoms × atomic mass ÷ molar mass) × 100. Water: %H = (2 × 1)/18 × 100 = 11.11%, %O = 88.89%. Run the logic backwards and percentage data gives you the empirical formula (simplest whole-number ratio), which you scale to the molecular formula using n = molar mass ÷ empirical-formula mass.
Why do chemists obsess over moles? Because a balanced equation is a mole recipe: C + O2 → CO2 reads “1 mol C reacts with 1 mol O2 to give 1 mol CO2” — never grams directly. Convert what’s given into moles, use the coefficient ratio, convert back: that is the entire game of stoichiometry (Section 1.10).
Visualising the Mole Map
One hub, three roads. Whatever you’re given and whatever is asked, the journey always changes trains at n.
Mole Map Converter
M values follow NCERT exam convention (H₂O = 18, CO₂ = 44 …). Particle input accepts e-notation (6.022e23). Molar volume: 22.4 L/mol at 1 atm · 22.7 L/mol at 1 bar.
Solved Examples (Step-by-Step)
Given → formula → substitute → verify. Write these same steps on your rough sheet — that is what earns full method marks.
Mass → moles → molecules
How many moles of water and how many molecules of water are present in 36 g of pure water? (M = 18 g mol⁻¹, NA = 6.022 × 10²³ mol⁻¹)
- Givenm = 36 g, M(H2O) = 18 g mol⁻¹. Find n and N.
- Formula
n = m / M - Substitute
n = 36 ÷ 18 = 2 mol - Convert
N = n × NA = 2 × 6.022 × 10²³ = 1.2044 × 10²⁴
n = 2 mol · N = 1.204 × 10²⁴ molecules
Atoms, not molecules — count twice
The total number of atoms present in 4.25 g of NH3 is approximately: (a) 1.5 × 10²³ (b) 2.5 × 10²³ (c) 6.022 × 10²³ (d) 4 × 6.022 × 10²³
- Givenm = 4.25 g, M(NH3) = 17 g mol⁻¹ — NH3 has 4 atoms per molecule.
- Moles
n = 4.25 ÷ 17 = 0.25 mol→ molecules = 0.25 × NA - Atomicity
atoms = 4 × 0.25 × NA = 1.0 × NA— multiply by 4 — this is the step the marks are on.
Option (c) — 6.022 × 10²³ atoms
From percentage data to empirical formula
An oxide of iron contains 69.9% Fe and 30.1% oxygen by mass. Determine its empirical formula. (Fe = 56, O = 16)
- AssumeTake exactly 100 g of oxide: Fe = 69.9 g, O = 30.1 g.
- Moles
n(Fe) = 69.9 ÷ 56 = 1.248·n(O) = 30.1 ÷ 16 = 1.881 - RatioDivide by the smaller: Fe = 1.000, O = 1.507 ≈ 1.5
- Whole no.× 2 → Fe : O = 2 : 3
- VerifyM(Fe2O3) = 160 → %Fe = 112/160 × 100 = 70% ≈ 69.9% ✓
Empirical formula: Fe₂O₃
Key Formulas & Takeaways
Eight lines that solve this chapter
NA = 6.02214076 × 10²³ mol⁻¹ (exact, SI 2019) · 1 u = 1.6605 × 10⁻²⁴ g · Molar volume = 22.4 L mol⁻¹ (1 atm) | 22.7 L mol⁻¹ (1 bar) · STP = 273.15 K
- A mole is a count, not a weight — 6.022 × 10²³ of anything. The gram-value arrives only through molar mass.
- Every road passes through n — mass ↔ n ↔ particles / gas volume. Two formulas do 90% of the numericals.
- Molar volume is a gas-only, STP-only shortcut — 22.4 L at 1 atm, 22.7 L at 1 bar. Liquids and solids: no entry.
- Atoms vs molecules is where marks die — multiply by atomicity before you box the answer.
FAQs
What is a mole in chemistry?
One mole is the amount of substance that contains exactly 6.02214076 × 10²³ elementary entities — atoms, molecules, ions or electrons. It is the SI base unit of amount of substance (symbol: mol) and works like a chemist’s dozen.
How do you calculate the number of moles from mass?
Divide the given mass by the molar mass: n = m ÷ M. For example, 36 g of water (M = 18 g/mol) contains 36 ÷ 18 = 2 moles of water molecules.
Why is 22.4 L called the molar volume of a gas?
At STP (273.15 K, 1 atm) one mole of any ideal gas occupies 22.4 L. The latest NCERT defines STP at 1 bar, where the molar volume is 22.7 L — so always check which standard pressure a question assumes.
How many particles are there in one mole?
Exactly 6.02214076 × 10²³ particles — Avogadro’s constant. So 0.5 mol of O₂ contains 3.011 × 10²³ O₂ molecules, which is 6.022 × 10²³ oxygen atoms.
Practice Questions
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QCC Notes — Class 11 Chemistry
Strictly NCERT-aligned notes for JEE Main & NEET, prepared by QCC Notes (Padho Likho JEE). Content follows the latest NCERT edition and current NTA exam pattern.