According to which one of the following laws it is indicated that when two or more gases react with one another, their volumes bear a simple ratio?

1. Foundations of Chemical Laws: Mass and Definite Proportions (basic)

Welcome to your first step in mastering chemistry! To understand how the universe is built, we start with the Foundational Laws of Chemical Combination. These laws tell us that chemical reactions are not chaotic; they follow strict mathematical rules. The most fundamental of these is the Law of Conservation of Mass, formulated by Antoine Lavoisier. It states that mass can neither be created nor destroyed in a chemical reaction. This means the total mass of the products must exactly equal the total mass of the reactants, because the number of atoms of each element remains the same before and after the process Science, Class X, Chapter 1, p.3. This is the very reason we must always use balanced chemical equations to represent reactions accurately Science, Class X, Chapter 1, p.14.

Building on this, the Law of Definite Proportions (or Constant Proportions) tells us that a pure chemical compound always contains the same elements combined together in the exact same ratio by mass, regardless of its source. For instance, whether you get water from a river or create it in a lab, the ratio of the mass of hydrogen to the mass of oxygen is always 1:8. When we look at reactions specifically involving gases, we encounter Gay-Lussac’s Law of Gaseous Volumes. Formulated in 1808, it states that when gases react at constant temperature and pressure, they do so in volumes that bear a simple whole-number ratio to one another and to the gaseous products formed.

For example, in the formation of water vapor, two volumes of Hydrogen gas react with one volume of Oxygen gas to produce two volumes of water vapor (2H₂ + O₂ → 2H₂O). This yields a simple volumetric ratio of 2:1:2. While the Law of Conservation of Mass focuses on the weight of matter, Gay-Lussac’s law focuses on the space (volume) that gases occupy, providing a crucial bridge to understanding how molecules interact in the gas phase.

Law	Focus	Key Principle
Conservation of Mass	Total Weight	Mass of Reactants = Mass of Products
Definite Proportions	Composition	Fixed mass ratio of elements in a compound
Gay-Lussac’s Law	Gaseous Volume	Simple whole-number ratios for reacting gas volumes

Sources: Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3; Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.14

2. Law of Multiple Proportions (intermediate)

Concept: Law of Multiple Proportions

3. Dalton's Atomic Theory and Matter (basic)

To understand the building blocks of our universe, we must start with John Dalton, who in 1808 provided the first scientific framework for the nature of matter. Before Dalton, the idea of atoms was purely philosophical; he transformed it into a quantitative scientific theory. At its heart, Dalton’s Atomic Theory proposes that all matter is composed of tiny, indivisible particles called atoms, which can neither be created nor destroyed during a chemical reaction.

Dalton’s theory was revolutionary because it explained why chemical reactions follow specific patterns. He noted that atoms of a single element are identical in mass and properties, while atoms of different elements differ. When these atoms combine to form compounds, they do so in simple whole-number ratios. While we now know from modern science that atoms are actually composed of subatomic particles like protons, neutrons, and electrons Physical Geography by PMF IAS, The Universe, p.2, Dalton's focus on ratios remains the cornerstone of stoichiometry.

Building on these ideas of ratios, Joseph Louis Gay-Lussac formulated the Law of Gaseous Volumes in 1808. While Dalton focused on the mass of substances, Gay-Lussac observed that when gases react at a constant temperature and pressure, the volumes of the reacting gases and their products bear a simple whole-number ratio to one another. For example, in the formation of water vapor, two volumes of Hydrogen (H₂) react with one volume of Oxygen (O₂) to produce two volumes of water vapor (H₂O), giving us a clean 2:1:2 ratio.

Law	Primary Focus	Key Scientist
Law of Multiple Proportions	Masses of elements in a compound	John Dalton
Law of Gaseous Volumes	Volume of reacting gases	Gay-Lussac

Sources: Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.2

4. Connected Concept: Avogadro's Law and Gaseous Behavior (intermediate)

In our journey through chemical principles, we now encounter the fascinating way gases interact. While solids and liquids are often measured by mass, gases are uniquely defined by their volume. In 1808, Joseph Louis Gay-Lussac formulated the Law of Combining Volumes (also known as Gay-Lussac's Law of Gaseous Volumes). He discovered that when gases react together to form other gases, and all volumes are measured at the same temperature and pressure, the ratios of the volumes of the reacting gases and their products can be expressed in simple whole numbers. For instance, in the synthesis of water, 2 volumes of Hydrogen react with 1 volume of Oxygen to produce 2 volumes of Water Vapor, yielding a neat 2:1:2 ratio. This principle is elegantly demonstrated in laboratory experiments, such as the electrolysis of water, where the volume of gas collected in one test tube is exactly double that of the other Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.9.
How do we explain these clean, integer-based ratios? This is where Amedeo Avogadro stepped in 1811 with his revolutionary hypothesis. Avogadro's Law states that equal volumes of all gases, under the same conditions of temperature and pressure, contain an equal number of molecules. This was the 'missing link.' It meant that Gay-Lussac’s volume ratios were actually reflecting the molecular ratios of the reaction. Because gas particles move freely in all directions and have negligible interparticle attraction, they don't have a fixed shape or volume; they simply expand to fill their container Science, Class VIII, NCERT (Revised ed 2025), Particulate Nature of Matter, p.106. Thus, at a specific temperature and pressure, the volume is purely a function of the number of particles present, regardless of whether the gas is light like Hydrogen or heavier like Oxygen or Nitrogen Physical Geography by PMF IAS, Earths Atmosphere, p.271.
It is vital to distinguish this from the Law of Multiple Proportions. While that law deals with the masses of elements forming different compounds, Gay-Lussac’s and Avogadro’s laws focus strictly on the volumetric behavior of substances in the gaseous state. Understanding this allows us to predict how much gas is needed for a reaction without weighing it—we simply measure its volume.

Law	Focus	Key Principle
Gay-Lussac's Law	Gaseous Volume	Gases react in simple whole-number volume ratios.
Avogadro's Law	Molecular Count	Equal volume = Equal number of molecules (at constant T & P).

Sources: Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.9; Science, Class VIII, NCERT (Revised ed 2025), Particulate Nature of Matter, p.106; Physical Geography by PMF IAS, Earths Atmosphere, p.271

5. Connected Concept: Stoichiometry and Balanced Equations (intermediate)

In our journey through chemistry, we must eventually move from what happens to how much happens. This is where Stoichiometry comes in—it is the "recipe book" of chemistry. Stoichiometry deals with the quantitative relationship between reactants and products in a chemical reaction. At its heart lies the Law of Conservation of Mass: because matter cannot be created or destroyed, the total mass of reactants must equal the total mass of products. To respect this law, we use Balanced Equations, where the number of atoms of each element on the left side (reactants) equals the number on the right side (products).

To balance an equation, we use the hit-and-trial method, adjusting the coefficients (the numbers in front of chemical formulas) until the atoms align. For example, when balancing the reaction between Iron and Steam, we ensure the number of Hydrogen atoms is consistent by making the molecules of hydrogen four on the right-hand side to match the four water molecules on the left Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.4. To make these equations truly useful for scientists, we also include Physical States using symbols like (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous solutions Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.5.

A fascinating extension of stoichiometry occurs when we deal specifically with gases. In 1808, Joseph Louis Gay-Lussac observed that when gases react at a constant temperature and pressure, they do so in simple whole-number ratios by volume. This is known as the Law of Combining Volumes (or Gay-Lussac's Law of Gaseous Volumes). For instance, in the synthesis of water vapor, exactly 2 volumes of Hydrogen react with 1 volume of Oxygen to produce 2 volumes of Water vapor (a 2:1:2 ratio). This is revolutionary because it tells us that for gases, the coefficients in a balanced equation don't just represent molecules—they represent volumes!

Sources: Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.4; Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.5

6. Law of Combining Volumes (Gay-Lussac's Law) (exam-level)

The Law of Combining Volumes, formulated by the French chemist Joseph Louis Gay-Lussac in 1808, is a cornerstone of gas stoichiometry. It states that when gases react together, they do so in volumes which bear a simple whole-number ratio to one another and to the volume of the products (if they are also gases), provided that all gases are measured at the same temperature and pressure. This was a revolutionary observation because it shifted the focus from the mass of reactants to their physical volume, hinting at a deeper relationship between the number of molecules and the space they occupy.

To visualize this, consider the synthesis of water vapor. When 2 volumes of Hydrogen gas (H₂) react with 1 volume of Oxygen gas (O₂), they produce exactly 2 volumes of water vapor (H₂O). The volumetric ratio is a clean 2:1:2. This simplicity is striking because it mirrors the coefficients in a balanced chemical equation. It is important to distinguish this from the Law of Definite Proportions, which deals with mass; while mass ratios can often involve complex decimals, volumetric ratios for gases are always simple integers. For instance, while Hydrogen and Oxygen make up the bulk of our atmospheric gases or participate in reactions to form steam Science, class X (NCERT 2025 ed.), Metals and Non-metals, p.43, their volumetric interaction remains consistent under uniform conditions.

This law is particularly relevant when discussing the composition of our atmosphere. Our atmosphere is a stable mixture where gases like Nitrogen (N₂) and Oxygen (O₂) exist in fixed proportions—roughly 78% and 21% respectively Physical Geography by PMF IAS, Earths Atmosphere, p.271. In the homosphere, which extends up to 80 km, this blend is nearly uniform Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.7. Gay-Lussac’s Law explains how these gases would interact if they were to react chemically: they wouldn't combine in random, messy fractions, but in predictable, discrete volumes. This principle eventually led to Avogadro’s Hypothesis, which clarified that equal volumes of gases contain equal numbers of molecules.

Sources: Science, class X (NCERT 2025 ed.), Metals and Non-metals, p.43; Physical Geography by PMF IAS, Earths Atmosphere, p.271; Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.7

7. Distinguishing Distractors: Law of Mass Action and Reciprocal Proportions (exam-level)

In our journey through chemical principles, it is easy to get tangled in terms that sound similar but govern entirely different aspects of matter. The Law of Combining Volumes (formulated by Gay-Lussac in 1808) is a cornerstone of gas chemistry. It states that when gases react at constant temperature and pressure, the volumes of the reactants and products bear a simple whole-number ratio to one another. For instance, in the reaction H₂ + Cl₂ → 2HCl, one volume of hydrogen reacts with one volume of chlorine to produce two volumes of hydrogen chloride, yielding a 1:1:2 ratio. This principle is distinct from the Law of Conservation of Mass, which mandates that the total mass remains constant because the number of atoms of each element does not change during a reaction Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3.

The two biggest 'distractors' in this topic are the Law of Reciprocal Proportions and the Law of Mass Action. While the Law of Reciprocal Proportions deals with the mass ratios of three different elements reacting with one another, the Law of Mass Action shifts the focus from 'how much' to 'how fast.' The Law of Mass Action states that the rate of a chemical reaction is proportional to the product of the active masses (concentrations) of the reactants. Interestingly, while the term 'mass action' in chemistry relates to the speed of a reaction, in Indian history, it refers to the collective strength and direct political involvement of the people to achieve Swaraj Modern India, Bipin Chandra, History class XII (NCERT 1982 ed.), Nationalist Movement 1905—1918, p.240. Thinking of it as the 'strength' or 'activity' of the reactants can help you remember that it governs reaction rates, not simple volumetric ratios.

To keep these straight, remember that Gay-Lussac’s Law is the only one specifically focused on the volumes of gases. When you see balanced equations like 2H₂(g) + O₂(g) → 2H₂O(g), the coefficients (2, 1, 2) directly represent these volume ratios Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.15.

Law	Focus Property	Key Insight
Combining Volumes	Gas Volume	Reacting gases follow simple integer volume ratios.
Mass Action	Reaction Rate	The speed of a reaction depends on reactant concentrations.
Reciprocal Proportions	Elemental Mass	Mass ratios of elements combining with a third fixed mass.

Sources: Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3; Modern India, Bipin Chandra, History class XII (NCERT 1982 ed.), Nationalist Movement 1905—1918, p.240; Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.15

8. Solving the Original PYQ (exam-level)

Now that you have mastered the foundational laws of chemical combinations, this question serves as a perfect test of your ability to distinguish between mass-based and volume-based relationships. The building blocks you just learned regarding stoichiometry come together here: while most early chemical laws focus on weights, this specific principle shifts the focus to the physical behavior of gases. As a coach, I want you to zoom in on the phrase "volumes bear a simple ratio." This is the definitive hallmark of the Law of combining volumes (also known as Gay-Lussac’s Law). It indicates that when gases react at a constant temperature and pressure, the ratios of their reacting volumes can be expressed in simple whole numbers, such as the 2:1:2 ratio seen in the synthesis of water vapor from hydrogen and oxygen, as noted in NCERT Class 11 Chemistry.

To navigate this question like a pro, you must learn to spot the common traps UPSC uses by mixing up similar-sounding laws. The Law of multiple proportions and the Law of reciprocal proportions are classic distractors; however, both of these laws deal strictly with the mass of elements, not their gaseous volumes. Similarly, the Law of mass action is a concept you will use when studying reaction rates and equilibrium, making it irrelevant to the physical proportions of the reactants. By identifying that the question specifically targets volumetric behavior rather than mass or speed, you can confidently eliminate the traps and select the Law of combining volumes.