Which one of the following laws expains the formation of carbon monoxide and carbon dioxide from carbon and oxygen?

1. Law of Conservation of Mass (basic)

Welcome to your first step in mastering the fundamentals of chemistry! To understand how the universe interacts at a molecular level, we must start with the Law of Conservation of Mass. Formulated by Antoine Lavoisier in the late 18th century, this law is the bedrock of all chemical calculations. It states that mass can neither be created nor destroyed in a chemical reaction (Science, Chemical Reactions and Equations, p.3). In simpler terms, if you weigh your starting materials (reactants) and then weigh the resulting substances (products), the total mass will remain identical, provided nothing has escaped.

Why does this happen? At the atomic level, a chemical reaction is essentially a rearrangement of atoms. Think of it like playing with LEGO bricks: you can take apart a castle and build a plane, but the total number of bricks—and thus the total weight—remains exactly the same. Because atoms are not created or destroyed during these transformations, the number of atoms of each element must stay constant before and after the reaction (Science, Chemical Reactions and Equations, p.3). This fundamental truth is the reason why we must always balance chemical equations; an unbalanced equation would imply that atoms vanished or appeared out of thin air, which is physically impossible (Science, Chemical Reactions and Equations, p.14).

Consider the reaction where Magnesium (Mg) burns in Oxygen (O₂) to form Magnesium Oxide (MgO). If you precisely measure the mass of the Magnesium ribbon and the Oxygen it consumes, the mass of the resulting white powder (MgO) will be exactly equal to the sum of the two. If it ever seems like mass is lost—for example, when wood burns to a small pile of ash—it is only because some of the products, like Carbon Dioxide (CO₂) and water vapor (H₂O), have escaped into the atmosphere as gases. If you were to conduct that same burn in a sealed container, the weight would not change by even a fraction of a gram.

Sources: Science, Chemical Reactions and Equations, p.3; Science, Chemical Reactions and Equations, p.14

2. Law of Definite Proportions (Constant Composition) (basic)

The Law of Definite Proportions, also known as the Law of Constant Composition, is a fundamental pillar of chemistry. It states that a given chemical compound always contains its component elements in a fixed ratio by mass, regardless of the source of the compound or how it was prepared. This means that whether you collect a sample of water from a river in India, a glacier in the Arctic, or synthesize it in a high-tech laboratory, the proportion of hydrogen to oxygen by weight will always be the same.

To understand this clearly, consider the difference between a mixture and a compound. While a mixture (like salt and sand) can be blended in any proportion, a compound has a fixed chemical composition Science, Class VIII. NCERT (Revised ed 2025), Nature of Matter: Elements, Compounds, and Mixtures, p.130. For example, in pure water (H₂O), the mass ratio of Hydrogen to Oxygen is always approximately 1:8. If you have 9 grams of water, it will always consist of 1 gram of Hydrogen and 8 grams of Oxygen. If the ratio were different, it simply wouldn't be water!

This law allows scientists to predict exactly how much of an element is needed to react with another. It highlights that substances like A and B, which cannot be broken down further (elements), combine in specific ways to form a product C (a compound) that possesses its own unique and fixed composition Science, Class VIII. NCERT (Revised ed 2025), Nature of Matter: Elements, Compounds, and Mixtures, p.131. This consistency is what makes the study of chemical reactions predictable and precise.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Nature of Matter: Elements, Compounds, and Mixtures, p.130; Science, Class VIII. NCERT (Revised ed 2025), Nature of Matter: Elements, Compounds, and Mixtures, p.131

3. Dalton's Atomic Theory and its Postulates (intermediate)

To understand the building blocks of matter, we must look back to 1808, when John Dalton provided a scientific framework that transformed chemistry from a collection of observations into a structured science. Before Dalton, scientists knew that substances reacted in specific patterns, but they didn't know why. Dalton proposed his Atomic Theory to provide a theoretical justification for the laws of chemical combination we have been discussing, such as the Law of Conservation of Mass and the Law of Definite Proportions.

The core of Dalton's theory rests on several postulates. He argued that all matter is composed of tiny, indivisible particles called atoms. According to Dalton, atoms of a given element are identical in mass and chemical properties, while atoms of different elements differ in these aspects. This explains why a specific compound like water (H₂O) always has the same proportion of elements by mass—because it always contains the same fixed number of hydrogen and oxygen atoms. As we see in Science, Class X, Chapter: Carbon and its Compounds, p.59, the combining capacity of elements is a fundamental concept that stems from these atomic interactions.

One of the most powerful applications of Dalton's theory is explaining the Law of Multiple Proportions. This law states that if two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in a ratio of small whole numbers. For example, carbon and oxygen can form Carbon Monoxide (CO) and Carbon Dioxide (CO₂). In CO, one atom of carbon combines with one atom of oxygen. In CO₂, one atom of carbon combines with two atoms of oxygen. Because atoms are indivisible units, they must combine in these simple whole-number ratios (1:1 or 1:2), never in fractions like 1.5 atoms. This simple logic beautifully explains why the mass of oxygen in CO₂ (32g) is exactly double the mass of oxygen in CO (16g) for the same 12g of carbon.

Sources: Science, Class X, Carbon and its Compounds, p.59

4. Gay-Lussac’s Law of Gaseous Volumes (intermediate)

In our journey through chemical principles, we now move from the masses of substances to the behavior of gases. Gay-Lussac’s Law of Gaseous Volumes 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 all gases are measured at the same temperature and pressure. For instance, if 100 mL of Hydrogen reacts with 50 mL of Oxygen, it produces exactly 100 mL of Water Vapor. The ratio of their volumes (100:50:100) simplifies to 2:1:2, a perfect set of small whole numbers.

It is critical to remember that this law specifically applies to volumes, not masses. While the Law of Definite Proportions focuses on the fixed mass ratio of elements (like the 1:8 mass ratio of Hydrogen to Oxygen in water), Gay-Lussac’s Law highlights the mathematical elegance of gas volumes. This predictability occurs because gases consist of particles moving freely with negligible interparticle attractions, meaning they don't have a fixed shape or volume of their own but expand to fill their containers Science, Class VIII NCERT, Particulate Nature of Matter, p.106. In our atmosphere, where gases like Nitrogen (78%) and Oxygen (21%) exist in fixed proportions Physical Geography by PMF IAS, Earths Atmosphere, p.271, these volumetric relationships are the foundation of atmospheric chemistry.

The condition of constant temperature and pressure is the secret ingredient for this law to work. As you might know from geography, when an air parcel rises, the ambient pressure falls and the gas volume increases, causing the temperature to drop Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.297. Because volume is so sensitive to these external factors, we can only observe the simple whole-number ratios of Gay-Lussac’s Law when we keep the environment stable. This law was a massive breakthrough because it eventually led scientists like Avogadro to realize that equal volumes of gases must contain an equal number of molecules, connecting the macro world of liters and milliliters to the micro world of atoms.

Sources: Science, Class VIII NCERT, Particulate Nature of Matter, p.106; Physical Geography by PMF IAS, Earths Atmosphere, p.271; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.297

5. Avogadro’s Law and the Mole Concept (intermediate)

Imagine you are trying to count the grains of sand on a beach. In chemistry, we deal with atoms so small that even a tiny droplet of water contains trillions. To handle this, we use the Mole—the fundamental unit for the 'amount of substance.' Just as a 'dozen' always means 12, a mole always means 6.022 × 10²³ particles (known as Avogadro’s number). This number is the bridge between the microscopic world of atoms and the macroscopic world of grams. The beauty of the mole is its consistency: the mass of one mole of an element in grams is numerically equal to its atomic mass. For example, since the atomic mass of Carbon is 12 u, one mole of Carbon weighs exactly 12 grams Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.66. Building on this, Avogadro’s Law provides a vital rule for gases: Equal volumes of all gases, at the same temperature and pressure, contain an equal number of molecules. This is profound because it tells us that gas behavior is determined by the number of particles, not their size or identity. Whether you have a liter of light Hydrogen (H₂) or a liter of heavier Nitrogen (N₂), they contain the same number of molecules if the conditions are identical Physical Geography by PMF IAS, Earths Atmosphere, p.271. This explains why, when we decompose water using electricity, we see exactly twice the volume of Hydrogen gas compared to Oxygen gas—because the water molecule (H₂O) contains twice as many Hydrogen atoms as Oxygen atoms Science, Class VIII . NCERT(Revised ed 2025), Nature of Matter, p.122. To master numerical problems, remember the Molar Volume: at Standard Temperature and Pressure (STP), one mole of any ideal gas occupies 22.4 liters. This allows chemists to 'count' atoms simply by measuring the volume of a gas. This principle is essential for maintaining the Law of Conservation of Mass in chemical reactions, ensuring that the number of atoms remains balanced before and after a reaction Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3.

Concept	Definition	Physical Context
Mole	6.022 × 10²³ particles	Relates mass (grams) to count (atoms).
Avogadro’s Law	Equal Volume = Equal Molecules	Relates volume (liters) to count (moles).

Sources: Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.66; Physical Geography by PMF IAS, Earths Atmosphere, p.271; Science, Class VIII . NCERT(Revised ed 2025), Nature of Matter, p.122; Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3

6. Law of Multiple Proportions (exam-level)

In our journey through chemical principles, we have seen how elements combine to form compounds. However, nature is often versatile—the same two elements can combine in different ways to form entirely different substances. For example, when coal burns, it typically forms Carbon Dioxide (CO₂) Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.7, but in restricted oxygen, it might form Carbon Monoxide (CO). The Law of Multiple Proportions, proposed by John Dalton, governs these variations. It states that if 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 a ratio of small whole numbers. To understand this from first principles, let’s look at the math behind Carbon and Oxygen. In Carbon Monoxide (CO), 12g of Carbon combines with 16g of Oxygen. In Carbon Dioxide (CO₂), 12g of Carbon combines with 32g of Oxygen. If we keep the mass of Carbon fixed at 12g, the ratio of the masses of Oxygen that combine with it is 16:32, which simplifies beautifully to 1:2. This simple whole-number ratio is not a coincidence; it reflects the fact that atoms combine as discrete units. You cannot have half an atom of oxygen joining a carbon atom; you either have one, two, or more. Students often confuse this with the Law of Definite Proportions. The key difference lies in the scope: the Law of Definite Proportions deals with the fixed ratio within a single compound (like how water is always H₂O), while the Law of Multiple Proportions compares the relationship between different compounds formed by the same pair of elements. We see these chemical relationships play out in complex environmental processes, such as Ocean Acidification, where the specific behavior of CO₂ molecules interacting with water changes the sea's chemistry Environment, Shankar IAS Academy (ed 10th), Ocean Acidification, p.264.

Comparison: Definite vs. Multiple Proportions

Feature	Law of Definite Proportions	Law of Multiple Proportions
Focus	A single specific compound.	Two or more different compounds.
Core Concept	The ratio of elements in H₂O is always the same.	Comparing the ratio of Oxygen in CO vs. Oxygen in CO₂.

Sources: Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.7; Environment, Shankar IAS Academy (ed 10th), Ocean Acidification, p.264

7. Law of Reciprocal Proportions (exam-level)

The Law of Reciprocal Proportions (also known as the Law of Equivalent Proportions) is one of the foundational laws of chemical combination. While other laws focus on how two elements interact, this law explores the relationship between three different elements. It states that if two elements (let's call them A and B) combine separately with a fixed mass of a third element (C), then the ratio of the masses in which they do so will be either the same or a simple multiple of the ratio in which A and B combine with each other. Think of it as a "triangular relationship." In chemistry, this law was instrumental in establishing the concept of equivalent weights before the full structure of the atom was understood. While the Law of Definite Proportions ensures a fixed ratio within a single compound, and the Law of Multiple Proportions looks at two compounds made of the same two elements, the Law of Reciprocal Proportions acts as a bridge connecting different chemical systems through a common third element. To see this in action, consider the elements Carbon (C), Hydrogen (H), and Oxygen (O):

• C and O combine to form CO₂: Here, 12g of Carbon combines with 32g of Oxygen.
• H and O combine to form H₂O: Here, 2g of Hydrogen combines with 16g of Oxygen.

If we fix the mass of the "third party" (Oxygen) at 32g, we find that 12g of Carbon and 4g of Hydrogen (since 2g H needs 16g O, then 4g H needs 32g O) relate to this fixed mass. The ratio of C to H is 12:4 or 3:1. Now, if Carbon and Hydrogen combine directly to form Methane (CH₄), the ratio of C to H is 12:4, which is exactly 3:1. This perfect match illustrates the law!

Relationship	Elements Involved	Mass Ratio
Compound 1 (with Oxygen)	C : O (in CO₂)	12 : 32
Compound 2 (with Oxygen)	H : O (in H₂O)	4 : 32 (scaled)
Direct Compound	C : H (in CH₄)	12 : 4 (or 3:1)

Unlike the Law of Variable Proportions found in economics, which describes changing output as one factor of production is increased Microeconomics (NCERT class XII 2025 ed.), Production and Costs, p.41, this chemical law describes a fixed, predictable mathematical symmetry in the physical world.

Sources: Microeconomics (NCERT class XII 2025 ed.), Production and Costs, p.41

8. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental laws of chemical combination, this question serves as the perfect test of your ability to distinguish between them in a practical scenario. You've learned that chemistry isn't just about reactions, but about the precise mathematical relationships between atoms. This specific problem asks you to look at a pair of compounds—carbon monoxide (CO) and carbon dioxide (CO2)—and identify which rule governs their relationship. This is a classic application of the building blocks where we transition from looking at a single substance to comparing how the same two elements can combine in different ways.

To arrive at the correct answer, think like a chemist analyzing masses. In CO, 12g of carbon reacts with 16g of oxygen. In CO2, that same 12g of carbon reacts with 32g of oxygen. If we keep the mass of carbon fixed at 12g, the masses of oxygen that combine with it (16g and 32g) stand in a simple 1:2 ratio. This exact phenomenon—where the masses of one element combining with a fixed mass of another are in a ratio of small whole numbers—is the definition of the Law of multiple proportions. This law, famously proposed by John Dalton, is what allows for the existence of different oxides of the same element, and it is the key to solving this PYQ.

UPSC often uses the other laws as distractors to test your conceptual clarity. The Law of definite proportions is the most common trap; remember that it only describes a single compound (e.g., any sample of CO2 always has the same ratio), whereas this question asks about the relationship between two different compounds. The Law of conservation of mass simply states that mass is neither created nor destroyed, which is too general for this specific chemical relationship. Finally, the Law of reciprocal proportions involves three different elements reacting in a cycle, which does not apply to this two-element system. By identifying that we are comparing two distinct compounds made of the same elements, you can confidently select (B) Law of multiple proportions.

Sources: