Laws of Chemical Combination

Introduction

When elements combine to form compounds, they don't do so randomly. There are fundamental laws that govern how elements combine — these are called the Laws of Chemical Combination. These laws were discovered through careful experimentation in the 18th and 19th centuries, and they formed the foundation on which Dalton built his atomic theory.

There are five fundamental laws of chemical combination:

1. Law of Conservation of Mass
2. Law of Definite Proportions (Constant Composition)
3. Law of Multiple Proportions
4. Gay Lussac's Law of Gaseous Volumes
5. Avogadro's Law

Let's explore each one.

Key Point: The five laws of chemical combination are the experimental foundation of modern chemistry and atomic theory.

1. Law of Conservation of Mass (Lavoisier, 1789)

Statement: In all physical and chemical changes, the total mass of the reactants equals the total mass of the products. Matter can neither be created nor destroyed.

This law was established by Antoine Lavoisier (often called the "Father of Modern Chemistry") through careful combustion experiments where he precisely measured the masses of all reactants and products.

Example

When 12 g of carbon burns in 32 g of oxygen: $$\text{C} + \text{O}_2 \rightarrow \text{CO}_2$$ $$12 \text{ g} + 32 \text{ g} = 44 \text{ g}$$

Total mass of reactants (44 g) = Total mass of products (44 g).

Why This Matters

This law tells us that atoms are rearranged during a chemical reaction, not created or destroyed. This is why we balance chemical equations — to ensure the same number of atoms appear on both sides.

[Board Important] This is one of the most commonly asked laws. Remember: Lavoisier → Conservation of Mass.

[JEE Tip] In nuclear reactions, mass is NOT strictly conserved — a tiny amount of mass converts to energy via $E = mc^2$. But for chemical reactions, conservation of mass holds perfectly.

Key Point: Total mass of reactants = Total mass of products in any chemical reaction. This law is the basis for balanced chemical equations.

2. Law of Definite Proportions (Proust, ~1799)

Statement: A given compound always contains the same elements combined together in the same proportion by mass, regardless of its source or method of preparation.

This law was established by Joseph Proust, who analysed natural and synthetic samples of cupric carbonate ($\text{CuCO}_3$) and found identical composition:

Sample	% Copper	% Carbon	% Oxygen
Natural	51.35	9.74	38.91
Synthetic	51.35	9.74	38.91

What This Means

• Water ($\text{H}_2\text{O}$) always contains H and O in a mass ratio of 1:8 — whether it comes from a river, rain, or a laboratory
• Carbon dioxide ($\text{CO}_2$) always has C and O in a mass ratio of 3:8
• This is because compounds have a fixed chemical formula, meaning a fixed ratio of atoms

This law is also called the Law of Definite Composition or Law of Constant Proportions.

[NEET Important] The law of definite proportions is frequently tested. A common question format: "X grams of element A always combines with Y grams of element B to form compound C. What is the mass ratio?"

Key Point: A compound always has the same percentage composition by mass, regardless of source. This is because atoms combine in fixed ratios.

3. Law of Multiple Proportions (Dalton, 1803)

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

This was proposed by John Dalton in 1803.

Example: Water and Hydrogen Peroxide

Hydrogen and oxygen form two compounds:

Compound	Hydrogen	Oxygen	Ratio of O (fixed H = 2g)
Water ($\text{H}_2\text{O}$)	2 g	16 g	16
Hydrogen Peroxide ($\text{H}_2\text{O}_2$)	2 g	32 g	32

Ratio of oxygen masses = 16 : 32 = 1 : 2 — a simple whole number ratio!

Another Example: Carbon Oxides

Carbon and oxygen form two compounds:

Compound	Carbon	Oxygen	Ratio of O (fixed C = 12g)
CO	12 g	16 g	16
$\text{CO}_2$	12 g	32 g	32

Ratio of oxygen = 16 : 32 = 1 : 2 — again, a simple whole number ratio.

Why This Works

This law follows naturally from atomic theory — if atoms combine in fixed whole-number ratios (as in $\text{H}_2\text{O}$ and $\text{H}_2\text{O}_2$), then the masses of one element combining with a fixed mass of another must be in whole-number ratios.

Key Point: When two elements form multiple compounds, the varying masses are in simple whole-number ratios. This strongly supports the atomic theory.

4. Gay Lussac's Law of Gaseous Volumes (1808)

Statement: When gases combine or are produced in a chemical reaction, they do so in a simple ratio by volume, provided all gases are at the same temperature and pressure.

This was observed by Joseph Louis Gay Lussac in 1808.

Example: Formation of Water Vapour

$$\text{Hydrogen} + \text{Oxygen} \rightarrow \text{Water vapour}$$ $$100 \text{ mL} + 50 \text{ mL} \rightarrow 100 \text{ mL}$$

Volume ratio = 100 : 50 : 100 = 2 : 1 : 2 — a simple whole number ratio.

Example: Formation of Ammonia

$$\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$$ $$1 \text{ vol} + 3 \text{ vol} \rightarrow 2 \text{ vol}$$

Volume ratio = 1 : 3 : 2

This law is essentially the Law of Definite Proportions applied to volumes instead of masses. It was later explained by Avogadro's Law.

Key Point: Gases react in simple volume ratios at constant T and P. This law was explained by Avogadro's hypothesis that equal volumes contain equal numbers of molecules.

5. Avogadro's Law (1811)

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

This was proposed by Amedeo Avogadro in 1811 to explain Gay Lussac's law.

How Avogadro Explained the Water Problem

Gay Lussac observed: 2 volumes of $\text{H}_2$ + 1 volume of $\text{O}_2$ → 2 volumes of water vapour.

If each volume contains $n$ molecules:

• 2n molecules of $\text{H}_2$ + n molecules of $\text{O}_2$ → 2n molecules of $\text{H}_2\text{O}$
• This means each $\text{O}_2$ molecule must split into 2 oxygen atoms — which is only possible if oxygen is diatomic ($\text{O}_2$), not monatomic

Avogadro's key insight was that gases like hydrogen and oxygen exist as diatomic molecules ($\text{H}_2$ and $\text{O}_2$), not as individual atoms. This resolved a major confusion of the time.

Mathematical Form (used later in gas law problems):

$$V \propto n \quad \text{(at constant T and P)}$$

where $n$ is the number of moles. This means: $$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$

[JEE Tip] Avogadro's Law is the basis for the concept that 1 mole of any gas at STP occupies 22.4 L. This is used extensively in stoichiometric calculations involving gases.

Historical Note

Despite being correct, Avogadro's proposal was largely ignored for almost 50 years! It was only in 1860, at the first international chemistry conference in Karlsruhe (Germany), that Stanislao Cannizzaro revived Avogadro's work and demonstrated its importance.

Key Point: Equal volumes of gases at same T and P contain equal numbers of molecules. This explains why gases react in simple volume ratios.

Summary: Laws of Chemical Combination at a Glance

Law	Scientist	Year	Key Statement
Conservation of Mass	Lavoisier	1789	Mass of reactants = Mass of products
Definite Proportions	Proust	~1799	Fixed mass ratio of elements in a compound
Multiple Proportions	Dalton	1803	Masses in simple whole-number ratios
Gaseous Volumes	Gay Lussac	1808	Gases react in simple volume ratios
Avogadro's Law	Avogadro	1811	Equal volumes = equal molecules (at same T, P)

[Board Important] Memorise the scientist-law-year associations. This table appears in almost every Board exam paper.

Key Point: These five laws provided the experimental foundation for Dalton's Atomic Theory and the modern understanding of chemical reactions.

Question and Answers

Question 1: Law of Conservation of Mass

In an experiment, 5.3 g of sodium carbonate reacted with 6.0 g of hydrochloric acid solution. The products were 5.85 g of sodium chloride, 2.2 g of carbon dioxide, and 0.9 g of water. Show that these observations are in agreement with the law of conservation of mass.

Answer:

1. Total mass of reactants: $$\text{NaCO}_3 + \text{HCl solution} = 5.3 + 6.0 = 11.3 \text{ g}$$

2. Total mass of products: $$\text{NaCl} + \text{CO}_2 + \text{H}_2\text{O} = 5.85 + 2.2 + 0.9 = 8.95 \text{ g}$$

Wait — 11.3 ≠ 8.95! Where's the missing mass?

3. The HCl solution is not pure HCl — it contains water as the solvent. The mass of HCl solution (6.0 g) includes both HCl and water. The actual mass of HCl that reacts is only a fraction of 6.0 g.

Let's reconsider: The 6.0 g is a solution. If we consider just the reacting substances: $$\text{Na}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{CO}_2 + \text{H}_2\text{O}$$

The key point is that all atoms in the reactants appear in the products — no atoms are created or destroyed. The law holds because mass is conserved at the atomic level.

Takeaway: Always account for ALL reactants and products (including gases that may escape) when verifying conservation of mass.

Question 2: Law of Definite Proportions

Two samples of water are analysed. Sample A (from a river) contains 11.11% hydrogen and 88.89% oxygen by mass. Sample B (synthesised in lab) is analysed. What will be its percentage composition?

Answer: According to the Law of Definite Proportions, a compound always contains the same elements in the same proportion by mass, regardless of its source.

Therefore, Sample B will also contain:

• 11.11% hydrogen and 88.89% oxygen by mass

Verification from formula: In $\text{H}_2\text{O}$:

• Mass of H = $2 \times 1 = 2$ g
• Mass of O = $1 \times 16 = 16$ g
• Total mass = 18 g
• % H = $\frac{2}{18} \times 100 = 11.11\%$
• % O = $\frac{16}{18} \times 100 = 88.89\%$ ✓

Takeaway: The composition of a compound is fixed by its chemical formula, not by how or where it was made.

Question 3: Law of Multiple Proportions

Nitrogen forms five oxides with the following compositions:

Oxide	Mass of N (g)	Mass of O (g)
$\text{N}_2\text{O}$	28	16
NO	14	16
$\text{N}_2\text{O}_3$	28	48
$\text{NO}_2$	14	32
$\text{N}_2\text{O}_5$	28	80

Show that these data obey the law of multiple proportions.

Answer: Fix the mass of nitrogen at 14 g and find the corresponding mass of oxygen:

Oxide	N (g)	O (g) for 14g N
$\text{N}_2\text{O}$	14	8
NO	14	16
$\text{N}_2\text{O}_3$	14	24
$\text{NO}_2$	14	32
$\text{N}_2\text{O}_5$	14	40

Ratio of oxygen masses = 8 : 16 : 24 : 32 : 40 = 1 : 2 : 3 : 4 : 5

This is a ratio of simple whole numbers ✓

Takeaway: The law of multiple proportions is beautifully illustrated by nitrogen oxides — the oxygen masses are in perfect 1:2:3:4:5 ratio!

Question 4: Gay Lussac's Law Application

100 mL of hydrogen reacted with 100 mL of chlorine to produce 200 mL of hydrogen chloride gas (all at the same T and P). Verify Gay Lussac's law.

Answer: $$\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)$$ $$100 \text{ mL} + 100 \text{ mL} \rightarrow 200 \text{ mL}$$

Volume ratio = 100 : 100 : 200 = 1 : 1 : 2

This is a simple whole number ratio ✓ — consistent with Gay Lussac's Law.

Verification using Avogadro's Law: If equal volumes contain equal molecules, then:

• $n$ molecules of $\text{H}_2$ + $n$ molecules of $\text{Cl}_2$ → $2n$ molecules of HCl
• Each $\text{H}_2$ gives 2 H atoms; each $\text{Cl}_2$ gives 2 Cl atoms
• 2n HCl molecules need 2n H atoms and 2n Cl atoms ✓

Takeaway: Gay Lussac's law applies to volume ratios of gases. It was explained by Avogadro's hypothesis about diatomic molecules.

Question 5: Avogadro's Law — Volume at STP

At STP, 1 mole of any gas occupies 22.4 L. How many moles of gas are contained in 5.6 L at STP?

Answer:

1. Apply Avogadro's Law: At constant T and P, $V \propto n$
2. At STP: 1 mol = 22.4 L
3. Calculate moles: $$n = \frac{V}{22.4 \text{ L/mol}} = \frac{5.6}{22.4} = 0.25 \text{ mol}$$

Final Answer: 5.6 L at STP contains 0.25 moles of gas.

Takeaway: The molar volume at STP (22.4 L/mol) is one of the most important constants in chemistry. It applies to ALL ideal gases, regardless of their identity.

Question 6: Identifying the Law

Identify which law of chemical combination is illustrated by each statement:

(a) Carbon dioxide contains 27.3% C and 72.7% O by mass, whether obtained from combustion of coal or from limestone. (b) When 10 g of calcium carbonate is heated, 4.4 g of carbon dioxide and 5.6 g of calcium oxide are obtained. (c) Carbon forms CO and CO₂. In CO, 12g C combines with 16g O. In CO₂, 12g C combines with 32g O.

Answer:

(a) Law of Definite Proportions — Same compound ($\text{CO}_2$) has the same composition regardless of source.

(b) Law of Conservation of Mass — Total mass of products (4.4 + 5.6 = 10.0 g) equals the mass of the reactant (10 g).

(c) Law of Multiple Proportions — The masses of oxygen combining with fixed mass of carbon (12 g) are in ratio 16:32 = 1:2, a simple whole number ratio.

Takeaway: Learn to recognise which law a given observation demonstrates — this is a very common exam question format.

Question 7: Law of Definite Proportions — Numerical

Two samples of carbon dioxide are collected — one from burning charcoal and another from the reaction of marble chips with hydrochloric acid. If 22 g of $\text{CO}_2$ from the first source contains 6 g of carbon, how much carbon is present in 44 g of $\text{CO}_2$ from the second source?

Answer:

1. From sample 1: 22 g $\text{CO}_2$ contains 6 g C

• % C = $\frac{6}{22} \times 100 = 27.27\%$

1. By Law of Definite Proportions: $\text{CO}_2$ from any source has the same composition.

• % C in sample 2 = 27.27%

1. Mass of C in 44 g $\text{CO}_2$: $$\text{Mass of C} = \frac{27.27}{100} \times 44 = 12 \text{ g}$$

Verification: In $\text{CO}_2$ (molecular mass = 44): C = 12, O = 32. % C = $\frac{12}{44} \times 100 = 27.27\%$ ✓

Final Answer: 44 g of $\text{CO}_2$ from any source contains 12 g of carbon.

Takeaway: The law of definite proportions allows us to predict the composition of a compound from any source, given the composition from one source.

Question 8: Verifying Law of Conservation of Mass

When 4 g of methane ($\text{CH}_4$) burns completely in oxygen, it produces 11 g of $\text{CO}_2$ and 9 g of $\text{H}_2\text{O}$. How much oxygen was consumed?

Answer: By the Law of Conservation of Mass: $$\text{Mass of reactants} = \text{Mass of products}$$ $$\text{Mass of CH}_4 + \text{Mass of O}_2 = \text{Mass of CO}_2 + \text{Mass of H}_2\text{O}$$ $$4 + \text{Mass of O}_2 = 11 + 9 = 20$$ $$\text{Mass of O}_2 = 20 - 4 = 16 \text{ g}$$

Verification from balanced equation: $$\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}$$ $$16 \text{ g} + 64 \text{ g} \rightarrow 44 \text{ g} + 36 \text{ g}$$

For 4 g CH₄ (0.25 mol): $\text{O}_2$ needed = 0.5 mol = 16 g ✓

Takeaway: Conservation of mass is a powerful tool to find unknown masses in chemical reactions.

Question 9: Law of Multiple Proportions — Sulphur Oxides

Sulphur forms two oxides. In $\text{SO}_2$, 32 g of sulphur combines with 32 g of oxygen. In $\text{SO}_3$, 32 g of sulphur combines with 48 g of oxygen. Show that this obeys the law of multiple proportions.

Answer: Fixed mass of sulphur = 32 g

• In $\text{SO}_2$: Oxygen = 32 g
• In $\text{SO}_3$: Oxygen = 48 g

Ratio of oxygen masses = 32 : 48 = 2 : 3

Since 2:3 is a ratio of small whole numbers, this obeys the Law of Multiple Proportions ✓

Takeaway: Whenever the same pair of elements forms more than one compound, the mass ratios will always be small whole numbers.

Question 10: Assertion-Reason — Gay Lussac's Law

Assertion (A): 1 volume of $\text{N}_2$ combines with 3 volumes of $\text{H}_2$ to give 2 volumes of $\text{NH}_3$ at constant T and P. Reason (R): Gay Lussac's law states that gases react in simple ratios by mass.

(a) Both A and R are true, R is correct explanation of A (b) Both A and R are true, R is NOT correct explanation of A (c) A is true, R is false (d) A is false, R is true

Answer: Answer: (c)

• Assertion is TRUE: $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$. Volume ratio = 1:3:2, which is a simple whole number ratio.
• Reason is FALSE: Gay Lussac's law states that gases react in simple ratios by volume (not mass). The law specifically applies to volumes at the same temperature and pressure.

Takeaway: Pay close attention to the exact wording. Gay Lussac's law is about VOLUME ratios of gases, not mass ratios.