Theory: Mole Concept — Complete Guide
1. The Mole Concept
One mole of any substance contains exactly 6·022 × 10²³ particles (atoms, molecules, ions, etc.) — this number is Avogadro's constant (Nₐ). One mole of a substance has a mass equal to its molar mass in grams. Moles = mass (g) / molar mass (g/mol). Number of particles = moles × Nₐ. For molecules, multiply by the number of atoms per molecule to get atoms. The mole concept connects the macroscopic world (grams) to the microscopic world (atoms, molecules).
2. Structure of Urea
📌 Formula: NH₂CONH₂ (carbamide)
📌 Molecular formula: CH₄N₂O
📌 Molar mass: C(12) + H₄(4) + N₂(28) + O(16) = 60 g/mol ✓
📌 H atoms per molecule: 2 (in NH₂) + 2 (in NH₂) = 4 H atoms ← KEY STEP
📌 N atoms per molecule: 2, C atoms: 1, O atoms: 1
📌 First organic compound synthesised from inorganic compound (Wöhler, 1828) — disproved vitalism
📌 Main nitrogen-containing component of human urine — body excretes excess nitrogen as urea
3. Mole Calculations — Step-by-Step Method
Standard approach: (1) Write the formula and count atoms of interest. (2) Calculate moles = mass/molar mass. (3) Multiply by the number of atoms per molecule. (4) Multiply by Nₐ to get number of atoms. Formula: Number of atoms = (mass/M) × n × Nₐ, where n = atoms of that type per molecule. For H in urea: = (5·4/60) × 4 × 6·022×10²³ = 0·09 × 4 × 6·022×10²³ = 0·36 × 6·022×10²³ = 2·168×10²³.
4. Common Molar Masses (Memorise for NEET)
📌 H₂O = 18, CO₂ = 44, NH₃ = 17, CH₄ = 16, HCl = 36·5
📌 NaCl = 58·5, CaCO₃ = 100, H₂SO₄ = 98, HNO₃ = 63
📌 Urea (NH₂CONH₂) = 60, Glucose (C₆H₁₂O₆) = 180, Ethanol = 46
📌 Benzene (C₆H₆) = 78, Toluene (C₇H₈) = 92
📌 NaOH = 40, KOH = 56, Ca(OH)₂ = 74, Mg(OH)₂ = 58
📌 Fe = 56, Cu = 63·5, Zn = 65, Ag = 108, Au = 197
5. Percentage Composition from Formula
%X = (mass of X in one mole / molar mass of compound) × 100. For urea: %H = (4 × 1 / 60) × 100 = 6·67%. %N = (2 × 14 / 60) × 100 = 46·67%. %C = (12/60) × 100 = 20%. %O = (16/60) × 100 = 26·67%. Check: 6·67 + 46·67 + 20 + 26·67 = 100·01% ≈ 100% ✓. Urea is the richest solid nitrogen fertiliser (46·67% N by mass) — widely used in agriculture. More nitrogen per kg than any other solid fertiliser.
6. Empirical and Molecular Formulas
Empirical formula: simplest whole-number ratio of atoms (e.g., CH₂O for glucose). Molecular formula: actual number of atoms (e.g., C₆H₁₂O₆ for glucose). Molecular formula = n × Empirical formula, where n = Molar mass / Empirical formula mass. For urea: Molecular formula = CH₄N₂O (both empirical and molecular since no common factor). Steps to find empirical formula from % composition: (1) Divide % by atomic mass → moles ratio. (2) Divide by smallest → simplest ratio. (3) Multiply to get whole numbers. Key: if mole ratio has 0·5, multiply all by 2; if 0·33, multiply by 3.
7. Number of Molecules, Atoms, and Electrons
📌 Molecules in n moles = n × Nₐ
📌 Atoms in n moles of compound XₐYb = n × (a+b) × Nₐ (total atoms)
📌 Atoms of X = n × a × Nₐ
📌 Electrons: each atom of element Z has Z electrons. Electrons in n moles of compound = Σ(nᵢ × Zᵢ) × Nₐ
📌 Example: electrons in 1 mol H₂O = (2×1 + 1×8) × Nₐ = 10 × Nₐ = 10 × 6·022×10²³
📌 For ions: add or subtract electrons for charge
8. Wöhler's Synthesis — Historic Significance
In 1828, Friedrich Wöhler synthesised urea (an organic compound) from ammonium cyanate (an inorganic compound): NH₄OCN → NH₂CONH₂. This was the first synthesis of an organic compound from inorganic material, disproving the "vital force theory" (vitalism) — the belief that organic compounds could only be made by living organisms. This event is considered the birth of modern organic chemistry. Wöhler's synthesis showed that organic and inorganic chemistry are not fundamentally different — the same chemical laws apply to both.
Frequently Asked Questions
1. How many H atoms are in urea and why? ⌄
Urea formula: NH₂-CO-NH₂. Two NH₂ groups, each contributing 2 H atoms. Total H = 2 + 2 = 4 H atoms per molecule. Molecular formula: CH₄N₂O (C=1, H=4, N=2, O=1). Molar mass = 12 + 4 + 28 + 16 = 60 g/mol. This is the critical step — many students mistakenly count only 2 H atoms (one per N). Always write out the full structural formula: H₂N-C(=O)-NH₂ and count all H atoms carefully.
2. Why is the answer 2·168×10²³ and not 1·084×10²³? ⌄
1·084×10²³ = 0·18 × 6·022×10²³ = 2 × 0·09 × Nₐ — this would be the answer if urea had only 2 H atoms per molecule (one NH₂). The correct answer (2·168×10²³) counts all 4 H atoms (two NH₂ groups). The distractor 1·084×10²³ is designed to trap students who forget the second NH₂ group. Similarly, 2·168×10²² would be wrong by a factor of 10 (arithmetic error).
3. What is the mole concept in simple terms? ⌄
A mole is a counting unit for atoms/molecules — just like a "dozen" means 12, a "mole" means 6·022×10²³. Why this specific number? It's defined so that: 1 mol of carbon-12 atoms = exactly 12 grams. So 1 mol of any element X = atomic mass of X in grams. Example: 1 mol H₂O = 18 g (2×1 + 16). In 18 g of water: 6·022×10²³ molecules, 2×6·022×10²³ H atoms, 6·022×10²³ O atoms. The mole bridges the gap between lab-scale masses and atomic-scale counting.
4. How do you find moles from number of particles? ⌄
Moles = Number of particles / Nₐ. Example: if you have 3·011×10²³ molecules of CO₂, moles = 3·011×10²³ / 6·022×10²³ = 0·5 mol. Mass = 0·5 × 44 = 22 g. This is the reverse calculation of moles → particles. Always identify WHAT you're counting: molecules? atoms? ions? And then multiply/divide accordingly. Number of atoms always requires knowing how many atoms per formula unit.
5. What is Avogadro's number and how was it determined? ⌄
Nₐ = 6·022 × 10²³ mol⁻¹. Determined experimentally by several methods: X-ray diffraction of crystals (counting unit cells), Millikan oil drop experiment (charge per electron × number), counting alpha particles from radioactive decay, light scattering (Perrin's experiments on Brownian motion). The 2019 SI redefinition fixed Nₐ = 6·02214076 × 10²³ mol⁻¹ exactly. Named after Amedeo Avogadro (1776–1856) who proposed that equal volumes of gases at same T,P contain equal numbers of molecules — though he never calculated this number.
6. What is the %N in urea and why is urea important as a fertiliser? ⌄
%N in urea = (2×14/60) × 100 = 46·67%. This is the highest nitrogen content of any solid nitrogen fertiliser. Compare: ammonium nitrate (NH₄NO₃) = 35% N, ammonium sulphate ((NH₄)₂SO₄) = 21·2% N. Higher %N means less mass needed per hectare → lower transport costs. Urea is applied directly to soil (or as foliar spray). In soil, urease enzyme converts urea: CO(NH₂)₂ + H₂O → CO₂ + 2NH₃. NH₃ then converts to NO₃⁻ (nitrification) — the form used by plants. Global urea production ~180 million tonnes/year.
7. How many total atoms are in 5·4g of urea? ⌄
Urea CH₄N₂O: 1+4+2+1 = 8 atoms per molecule. Moles of urea = 5·4/60 = 0·09 mol. Total atoms = 0·09 × 8 × 6·022×10²³ = 0·72 × 6·022×10²³ = 4·336×10²³ atoms total. Breakdown: H = 4 × 0·09 × Nₐ = 2·168×10²³, C = 0·09 × Nₐ = 5·42×10²², N = 2 × 0·09 × Nₐ = 1·084×10²³, O = 0·09 × Nₐ = 5·42×10²². NEET often asks for specific atoms — always identify which atom and count carefully from the formula.
8. What is the significance of Wöhler's urea synthesis in chemistry? ⌄
Wöhler (1828): NH₄OCN → NH₂CONH₂. Before this: "vitalism" — belief that organic compounds could only be made by living things, through a mysterious "vital force." This prevented chemists from attempting to synthesise organic compounds in the lab. Wöhler's synthesis showed: (1) Organic compounds obey the same chemical laws as inorganic compounds. (2) No special "vital force" is needed. (3) Same atoms (C, H, N, O) can be rearranged to make organic molecules. This opened the entire field of organic synthesis — everything from aspirin to nylon to pharmaceuticals became possible.