Chemical Laws and Mole Concept – NDA Chemistry Notes

When chemists study reactions, they need to answer two types of questions. First: what are the rules that govern how elements combine? Second: how much of each substance is involved?

The chemical laws answer the first question. They describe patterns that scientists noticed when studying chemical reactions over hundreds of years. The mole concept answers the second question. It gives chemists a way to count atoms and molecules, even though atoms are far too small to see or count individually.

NDA tests this chapter through law identification questions (which example proves which law), scientist-law match lists, mole calculation questions, and gas identification from density at STP. The chapter appears regularly, both as direct questions and as part of assertion-reason pairs.

1. The Five Chemical Laws

Law of Conservation of Mass

Proposed by: Antoine Lavoisier (1789)

Statement: Matter can neither be created nor destroyed in a chemical reaction. The total mass of reactants equals the total mass of products.

Simple way to remember it: In any chemical reaction, nothing disappears, and nothing new appears from nowhere. Mass is conserved.

Best example: 12 g of carbon + 32 g of oxygen → 44 g of carbon dioxide. 12 + 32 = 44. Total mass before = total mass after. [NDA 2009-II]

What this law tells us: When you balance a chemical equation, you are applying this law. The number of atoms on both sides must be equal.

The law of conservation of mass states that matter can neither be created nor destroyed. [NDA 2018-II]

Law of Definite Proportions (Law of Constant Composition)

Proposed by: Joseph Proust (1799)

Statement: A pure chemical compound always contains the same elements in the same fixed ratio by mass, regardless of where it comes from or how it was made.

Simple way to remember it: Water is always H₂O. Whether you get water from a river in India or distill it in a laboratory in France, it always contains hydrogen and oxygen in the ratio 1:8 by mass. The composition never changes.

Example: Limestone (calcium carbonate, CaCO₃), no matter where it is found in the world, always contains calcium, carbon, and oxygen in the same fixed proportion by mass. This proves the law of definite proportions. [NDA 2010-II]

Law of Multiple Proportions

Proposed by: John Dalton (1803)

Statement: When two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.

Simple way to remember it: Carbon and oxygen can form two compounds: CO (carbon monoxide) and CO₂ (carbon dioxide). In CO, 12 g of carbon combines with 16 g of oxygen. In CO₂, 12 g of carbon combines with 32 g of oxygen. The ratio of oxygen masses is 16:32 = 1:2. This is a simple whole number ratio.

The fact that samples of limestone from different locations have the same composition validates the law of definite proportion, NOT the law of multiple proportions. [NDA 2015-II]

Law of Combining Volumes (Gay-Lussac’s Law)

Proposed by: Joseph Gay-Lussac (1808)

Statement: When gases react together, and the products are also gases, all volumes are measured at the same temperature and pressure. They combine in simple whole number ratios.

Example: Nitrogen + Hydrogen → Ammonia. N₂ + 3H₂ → 2NH₃. 1 volume of N₂ combines with 3 volumes of H₂ to produce 2 volumes of NH₃. Ratio = 1:3:2. These are simple whole numbers. [NDA 2016-II]

Important: This law applies only to GASES, not to solids or liquids.

100 molecules of nitrogen require 300 molecules of hydrogen to react. Ratio is 1:3. [NDA 2009-I]

Avogadro’s Law (Avogadro’s Hypothesis)

Proposed by: Amedeo Avogadro (1811)

Statement: Equal volumes of all gases, measured at the same temperature and pressure, contain equal numbers of molecules.

Simple way to remember it: If you take 1 litre of hydrogen gas and 1 litre of oxygen gas, both at the same temperature and pressure, both containers have the same number of molecules. It does not matter which gas.

Equal volumes of gases contain equal numbers of molecules. [NDA 2023-I, NDA 2017-II]

Important: Avogadro’s law applies only to GASES. It does NOT apply to solids, liquids, or mixtures of different states. [NDA 2010-II]

Avogadro’s law was proposed by Avogadro, not Charles, Boyle, or Gay-Lussac. [NDA 2023-I]

Law	Proposed by	Key Statement
Law of Conservation of Mass	Antoine Lavoisier	Total mass before = total mass after a reaction
Law of Definite Proportions	Joseph Proust	Fixed composition in every pure compound
Law of Multiple Proportions	John Dalton	Masses combine in simple whole number ratios
Law of Combining Volumes	Joseph Gay-Lussac	Gas volumes combine in simple whole number ratios
Avogadro’s Law	Amedeo Avogadro	Equal volumes of gases have equal number of molecules

NDA asks match-list questions pairing each scientist with their law. Memorise the table above.

2. The Mole Concept

Atoms are unimaginably small. A single atom of hydrogen has a mass of about 1.67 × 10⁻²⁴ grams. We cannot count atoms one by one.

Chemists solved this problem by inventing the mole, a counting unit for atoms and molecules, just like “dozen” means 12 and “gross” means 144.

One mole = 6.022 × 10²³ particles (atoms, molecules, or ions)

This number is called Avogadro’s number, symbolised as Nₐ.

Avogadro’s number = 6.022 × 10²³

The weight of one hydrogen atom = 1/(6.023 × 10²³) grams = 1.66 × 10⁻²⁴ grams. [NDA 2007-I]

3. Molar Mass

Molar mass is the mass of one mole of a substance. Its unit is grams per mole (g/mol).

The molar mass of an element in grams = its atomic mass in atomic mass units (u).

Examples:

• Hydrogen (H): atomic mass = 1 u → molar mass = 1 g/mol
• Oxygen (O): atomic mass = 16 u → molar mass = 16 g/mol
• Carbon (C): atomic mass = 12 u → molar mass = 12 g/mol
• Nitrogen (N): atomic mass = 14 u → molar mass = 14 g/mol

For a molecule, add up the atomic masses of all atoms in the formula.

Examples of molecular mass:

• H₂O: 2(1) + 16 = 18 g/mol
• CO₂: 12 + 2(16) = 44 g/mol
• N₂: 2(14) = 28 g/mol
• NH₃: 14 + 3(1) = 17 g/mol
• NaOH: 23 + 16 + 1 = 40 g/mol
• Na₂CO₃: 2(23) + 12 + 3(16) = 106 g/mol
• Al(OH)₃: 27 + 3(16+1) = 78 g/mol
• CuSO₄·5H₂O: 64 + 32 + 4(16) + 5(18) = 250 g/mol

Mass of 0.5 mole of N₂: Molar mass of N₂ = 28 g/mol. Mass = 0.5 × 28 = 14 g [NDA 2024-II]

4. Gram Atoms and Gram Molecules

Gram atom: The mass of one mole of atoms of an element in grams. Equal to the atomic mass expressed in grams.

• 1 gram atom of oxygen = 16 g (contains 6.022 × 10²³ oxygen atoms)

Gram molecule: The mass of one mole of molecules of a substance in grams. Equal to the molecular mass expressed in grams.

• 1 gram molecule of water = 18 g (contains 6.022 × 10²³ water molecules)

Gram atoms of hydrogen in CuSO₄·5H₂O: CuSO₄·5H₂O has 10 hydrogen atoms per formula unit (5 water molecules × 2 H each = 10 H). 0.04 mole of CuSO₄·5H₂O contains: 0.04 × 10 = 0.4 gram atoms of hydrogen. [NDA 2006-I]

Water molecules in a tiny drop of water (0.0018 mL): 0.0018 mL of water = 0.0018 g (density of water = 1 g/mL). Moles of water = 0.0018/18 = 0.0001 = 10⁻⁴ mol. Number of molecules = 10⁻⁴ × 6.023 × 10²³ = 6.023 × 10¹⁹ [NDA 2008-II]

Hydrogen atoms in one mole of Al (OH)₃: Al (OH)₃ has 3 OH groups → 3 hydrogen atoms per formula unit. 1 mole of Al(OH)₃ contains 3 moles of hydrogen atoms. [NDA 2016-II]

5. Identifying a Gas at STP

At STP (Standard Temperature and Pressure, 0°C and 1 atm):

• 1 mole of any gas occupies 22.4 litres
• This is called the molar volume of a gas

If 1 litre of a gas at STP weighs 1.25 g, what gas is it?

Mass of 22.4 litres = 22.4 × 1.25 = 28 g/mol

Molecular mass = 28 g/mol → This is CO (carbon monoxide, 12+16=28) or N₂ (14+14=28). [NDA 2006-I]

Oxide of nitrogen with molecular weight 30: NO has molecular weight = 14 + 16 = 30. Number of electrons in NO = 7 (in N) + 8 (in O) = 15 electrons. [NDA 2006-I]

6. Equivalent Weight

Equivalent weight is the mass of a substance that reacts with or displaces 1 gram of hydrogen, 8 grams of oxygen, or 35.5 grams of chlorine.

For acids: Equivalent weight = Molecular weight / Basicity (number of replaceable H⁺ ions). For bases: Equivalent weight = Molecular weight / Acidity (number of replaceable OH⁻ ions).

NaOH (equivalent weight equals molecular weight): NaOH has molecular weight = 40 g/mol. NaOH has 1 replaceable OH⁻ (acidity = 1). Equivalent weight = 40/1 = 40 g/mol = molecular weight. So for NaOH, equivalent weight = molecular weight. [NDA 2008-I]

H₂SO₄ (equivalent weight): H₂SO₄ has molecular weight = 98 g/mol. H₂SO₄ has 2 replaceable H⁺ (basicity = 2). Equivalent weight = 98/2 = 49 g/mol [NDA 2012-II]

Iron has variable equivalent weight: Iron shows two valencies: Fe²⁺ (valency 2) and Fe³⁺ (valency 3). Because valency changes, equivalent weight also changes. Fe²⁺: equivalent weight = 56/2 = 28. Fe³⁺: equivalent weight = 56/3 = 18.67. This is why iron shows VARIABLE equivalent mass. [NDA 2007-I]

NaOH (the only option where equivalent weight = molecular weight): Among H₂SO₄, KMnO₄, H₂C₂O₄, and NaOH, only NaOH has equivalent weight equal to molecular weight (because acidity = 1). [NDA 2008-I]

7. Atomic Mass Unit

Atomic masses are measured in atomic mass units (u). One atomic mass unit is defined as 1/12th the mass of one carbon-12 atom.

The standard used for expressing atomic weights is Carbon-12 (¹²C₆). [NDA 2007-I]

This replaced older standards (hydrogen = 1 and oxygen = 16 were used earlier).

8. Different Number of Molecules: Mole Calculation

Which of the following has a DIFFERENT number of molecules at the same temperature and pressure? (a) 3 g of H₂ (b) 48 g of O₂ (c) 42 g of N₂

Calculate moles:

• 3 g of H₂: molar mass = 2, moles = 3/2 = 1.5 mol
• 48 g of O₂: molar mass = 32, moles = 48/32 = 1.5 mol
• 42 g of N₂: molar mass = 28, moles = 42/28 = 1.5 mol

All three have 1.5 moles, equal number of molecules. The odd one out would be any option with a different mole count. [NDA 2016-II]

9. Molecular Formula from Valency

When two elements combine, use the cross-multiplication rule to find the formula.

Valency of A becomes subscript of B. Valency of B becomes subscript of A.

Ammonium carbonate: Ammonium ion NH₄⁺ has valency +1. Carbonate ion CO₃²⁻ has valency −2. Cross multiply: (NH₄)₂CO₃ [NDA 2022-I]

10. Chronological Order of Laws

The five laws were proposed in this order:

1. Lavoisier: Conservation of mass (1789)
2. Proust: Definite proportions (1799)
3. Dalton: Multiple proportions (1803)
4. Gay-Lussac: Combining volumes (1808)

Avogadro: Equal volumes of gases (1811)

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