Which one of the following would have highest number of molecules?

1. Classification of Matter: Atoms and Molecules (basic)

To understand the universe at its most fundamental level, we must look at the particulate nature of matter. Everything we see—from the pen in your hand to the air you breathe—is composed of incredibly tiny particles called atoms and molecules. An atom is the basic building block of an element. For instance, a block of pure gold is made up of gold atoms, and a piece of iron consists of iron atoms. Science, Class VIII, Particulate Nature of Matter, p.115

However, many atoms are chemically "unstable" on their own and cannot exist independently in nature. To achieve stability, these atoms bond with others to form molecules. A molecule is the smallest particle of a substance (element or compound) that can exist independently and retain all the properties of that substance. If atoms of the same element combine, we get a molecule of an element (like O₂ or N₂). If atoms of different elements combine in a fixed ratio, we get a compound (like H₂O). Science, Class VIII, Nature of Matter: Elements, Compounds, and Mixtures, p.123

In the world of chemistry, we often need to count these particles. Since they are too small to count individually, we use the Mole Concept. One mole of any substance contains exactly 6.022 × 10²³ particles (known as Avogadro’s Number). The relationship between mass and the number of particles is governed by the Molar Mass (the mass of one mole of that substance). To find out how many molecules are in a sample, you use a simple logic: the lower the molar mass of a substance, the more molecules you will find in a single gram of it.

Feature	Atoms	Molecules
Definition	The smallest unit of an element.	A group of two or more atoms chemically bonded.
Existence	Most cannot exist independently (except noble gases).	Capable of independent existence.
Composition	Consists of subatomic particles (protons, neutrons, electrons).	Consists of two or more atoms (same or different).

Sources: Science, Class VIII, Particulate Nature of Matter, p.115; Science, Class VIII, Nature of Matter: Elements, Compounds, and Mixtures, p.123; Science, Class X, Carbon and its Compounds, p.60

2. Understanding Atomic and Molecular Mass (basic)

To understand chemistry, we must first learn how to 'weigh' the invisible. Since atoms are incredibly tiny, scientists use a relative scale called the Unified Atomic Mass Unit (u). By international agreement, an atom of Carbon-12 is assigned a mass of exactly 12u. Everything else is measured against this standard. For instance, a Hydrogen atom is approximately 1u, meaning it is 1/12th the mass of a Carbon-12 atom Science, Carbon and its Compounds, p.66. Moving from single atoms to molecules, we calculate the Molecular Mass. This is simply the sum of the atomic masses of all the atoms present in a molecule. For example, to find the mass of water (H₂O), you would add the mass of two Hydrogen atoms (2 × 1u) to the mass of one Oxygen atom (16u), totaling 18u. This precision is vital because, as the Law of Conservation of Mass dictates, mass is neither created nor destroyed during a chemical reaction; the total mass of your reactants must equal the total mass of your products Science, Chemical Reactions and Equations, p.3. In organic chemistry, this concept helps us identify patterns. In a homologous series (a family of compounds like alcohols or alkanes), each member differs from the next by a specific unit, usually a -CH₂- group. By knowing that Carbon is 12u and Hydrogen is 1u, we can calculate that each successive member in such a series increases in molecular mass by exactly 14u Science, Carbon and its Compounds, p.67.

Concept	Definition	Example
Atomic Mass	Mass of a single atom in 'u'.	Carbon (C) = 12u
Molecular Mass	Sum of atomic masses in a molecule.	CO₂ = 12 + (16×2) = 44u

Sources: Science (NCERT 2025 ed.), Carbon and its Compounds, p.66-67; Science (NCERT 2025 ed.), Chemical Reactions and Equations, p.3

3. The Mole Concept and Avogadro’s Constant (intermediate)

In chemistry, we often need to count atoms and molecules, but because they are so incredibly small, counting them one by one is impossible. To solve this, scientists use the Mole—a fundamental unit that acts as a bridge between the microscopic world of atoms and the macroscopic world we can measure in a lab. Think of a 'mole' just like the word 'dozen'; while a dozen means 12 items, a mole represents exactly 6.022 × 10²³ items. This enormous value is known as Avogadro’s Constant (N_A).

The beauty of the mole concept lies in its relationship with mass. The mass of one mole of a substance is called its Molar Mass, and it is numerically equal to the substance's atomic or molecular mass expressed in grams. For instance, the atmosphere around us is composed mostly of Nitrogen (N²) and Oxygen (O²) Physical Geography by PMF IAS, Earth's Atmosphere, p.271. If the molecular mass of O² is 32 units, then its molar mass is 32 grams per mole. This means 32 grams of Oxygen contains exactly one Avogadro's number of molecules.

To calculate the number of molecules in any given sample, we follow a simple two-step logic:

• Step 1: Find the number of moles by dividing the given mass by the molar mass:
  n = Mass (m) / Molar Mass (M)
• Step 2: Multiply the number of moles by Avogadro’s Constant to find the total count of molecules:
  Total Molecules = n × 6.022 × 10²³

This quantitative approach was central to the development of modern chemistry in India, pioneered by figures like Acharya Prafulla Chandra Ray, who is celebrated as the 'Father of Modern Indian Chemistry' for his work in advancing scientific research and establishing the nation's first pharmaceutical company Science Class VII NCERT (Revised ed 2025), Exploring Substances, p.17. Whether you are studying simple gases or complex carbon structures like cyclohexane (C&sup6;H¹²) Science Class X (NCERT 2025 ed.), Carbon and its Compounds, p.65, the mole remains the master key for all chemical calculations.

Sources: Physical Geography by PMF IAS, Earth's Atmosphere, p.271; Science Class VII NCERT (Revised ed 2025), Exploring Substances: Acidic, Basic, and Neutral, p.17; Science Class X (NCERT 2025 ed.), Carbon and its Compounds, p.65

4. Gas Laws and Stoichiometry (intermediate)

To understand how gases behave in our atmosphere, we must look at the relationship between their Pressure (P), Volume (V), and Temperature (T). A practical way to visualize this is a vehicle tire: when a car travels, friction increases the air temperature inside the tube. Because the volume of the tube is relatively constant, this rise in temperature leads to a direct increase in pressure, which can lead to a burst if the pressure threshold is crossed Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.296. In an ideal gas, we also find that the speed of sound is directly proportional to the square root of temperature, regardless of the gas density or pressure Physical Geography by PMF IAS, Earths Atmosphere, p.274.

While physical properties like pressure tell us how a gas acts, Stoichiometry tells us how much of it is actually there. In chemistry, we count particles using the Mole. One mole of any substance contains exactly 6.022 × 10²³ molecules (Avogadro's Number). This is a critical concept when measuring atmospheric constituents, such as Ozone. For instance, the Dobson Unit measures the total abundance of ozone in a column of air by calculating the number of molecules present if they were compressed at Standard Temperature and Pressure (STP) Environment, Shankar IAS Academy, Ozone Depletion, p.267.

The link between mass and the number of molecules is the Molar Mass (the mass of one mole of a substance). To find the number of molecules in a sample, we use the formula:
Number of Molecules = (Given Mass / Molar Mass) × Avogadro's Number.

Because the denominator is Molar Mass, there is an inverse relationship: for a fixed mass of gas, the substance with the smallest molar mass will contain the highest number of molecules. For example, Hydrogen (H₂) is much lighter than Carbon Dioxide (CO₂). Consequently, 1 gram of Hydrogen contains significantly more molecules than 1 gram of Carbon Dioxide, even though the CO₂ molecule is much larger and has a higher Global Warming Potential Environment, Shankar IAS Academy, Climate Change, p.260.

Sources: Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.296; Physical Geography by PMF IAS, Earths Atmosphere, p.274; Environment, Shankar IAS Academy, Ozone Depletion, p.267; Environment, Shankar IAS Academy, Climate Change, p.260

5. Diatomic Molecules and Gas Properties (intermediate)

In nature, atoms of most elements are like social beings—they rarely prefer to exist alone. Instead, they combine to form stable particles called molecules. When two atoms of the same element bond together, we call the resulting structure a diatomic molecule. For example, hydrogen (H₂) and oxygen (O₂) exist naturally in this paired form because the individual atoms are too reactive to stay solitary Science, Class VIII. NCERT(Revised ed 2025), Nature of Matter: Elements, Compounds, and Mixtures, p.123.

The strength and nature of these bonds depend on the element's valency. To achieve a stable "octet" or noble gas configuration, atoms share electrons. In a nitrogen molecule (N₂), each nitrogen atom shares three electrons, creating a powerful triple bond Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.60. Understanding these molecular structures is vital because the molar mass of a gas is simply the sum of the masses of the atoms within its molecule. For instance, since H₂ is made of two hydrogen atoms (each weighing ~1 unit), its molar mass is approximately 2 g/mol, making it one of the lightest molecules known.

There is a crucial inverse relationship between the mass of an individual molecule and the number of molecules present in a specific weight of gas. Imagine you have 1 kilogram of marbles and 1 kilogram of bowling balls. You would obviously have many more marbles than bowling balls because each marble is lighter. Similarly, if you have equal masses of different gases, the gas with the lowest molar mass will contain the highest number of molecules. This is because fewer "heavy" molecules are needed to reach the target weight, whereas many more "light" molecules (like H₂) are required to make up the same mass.

Gas Molecule	Type of Bonding	Approx. Molar Mass
Hydrogen (H₂)	Single Bond	2 g/mol
Oxygen (O₂)	Double Bond	32 g/mol
Nitrogen (N₂)	Triple Bond	28 g/mol
Carbon Dioxide (CO₂)	Double Bonds (C=O)	44 g/mol

Sources: Science, Class VIII. NCERT(Revised ed 2025), Nature of Matter: Elements, Compounds, and Mixtures, p.123; Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.60

6. Comparative Analysis: Mass vs. Number of Molecules (exam-level)

To understand the relationship between mass and the number of molecules, we must look past the physical weight and focus on the Mole Concept. In chemistry, mass measures the 'heaviness' of a sample, but it doesn't tell us the count of individual particles. To bridge this gap, we use the formula: Number of Molecules = (Given Mass / Molar Mass) × Avogadro's Number. Because Avogadro's number (approximately 6.022 × 10²³) is a constant, the number of molecules is directly proportional to the number of moles. If you have more moles, you have more molecules.

The 'trap' many students fall into is assuming that a larger mass automatically means more molecules. In reality, the molar mass (the weight of one mole of that substance) acts as a denominator. For instance, as discussed in Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.66, molecular masses are calculated by summing the atomic masses of the constituent atoms (like Carbon = 12 u and Hydrogen = 1 u). Because the molar mass of Hydrogen (H₂) is very low (~2 g/mol) compared to Carbon Dioxide (CO₂) (~44 g/mol), even a tiny mass of Hydrogen can contain significantly more molecules than a larger mass of a 'heavy' compound.

Think of it this way: if you have 1 kg of feathers and 1 kg of bricks, you will have thousands of feathers but only a few bricks. Similarly, in chemistry, the lighter the molecule, the more molecules you get per gram. To compare different samples, you should always calculate the number of moles (Mass / Molar Mass) first. The sample with the highest mole count will always contain the highest number of molecules.

Substance	Formula	Approx. Molar Mass (g/mol)	Mole Logic
Hydrogen	H₂	2	Very light; high molecule count per gram.
Ammonia	NH₃	17	Medium; see Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.60 for structure.
Oxygen	O₂	32	Heavy; fewer molecules per gram.
Carbon Dioxide	CO₂	44	Very heavy; lowest molecule count for the same mass.

Sources: Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.60; Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.66

7. Solving the Original PYQ (exam-level)

To solve this question effectively, you must synthesize the Mole Concept and Avogadro’s Number that we just covered in our learning path. In the UPSC preliminary exam, these questions aren't just about calculation; they are about understanding the inverse relationship between molar mass and the number of particles. Remember the core building block: the number of molecules is directly proportional to the number of moles. Since Number of Moles = Given Mass / Molar Mass, the substance with the smallest molar mass will often yield the highest molecular count, even if its total weight seems small.

Let’s walk through the coaching logic to arrive at One gram of hydrogen. For Hydrogen (H2), the molar mass is only 2 g/mol, so 1 gram gives you 0.5 moles. Compare this to Carbon Dioxide (CO2); even though you have 10 grams, its heavy molar mass of 44 g/mol reduces its mole count to a mere 0.227. Similarly, 10 grams of Oxygen (O2) results in 0.312 moles, and 5 grams of Ammonia (NH3) results in 0.294 moles. As established in NCERT Class 9 Science, because hydrogen has the highest number of moles here, it must contain the highest number of molecules when multiplied by Avogadro's constant.

The common trap UPSC sets here is the illusion of mass. A student might instinctively choose 10 grams of CO2 because it is the "heaviest" sample provided. However, in the atomic world, "heavy" molecules like CO2 contain fewer individuals per gram than "light" molecules like H2. Do not let the 10-gram figure distract you from the molecular weight. Always convert to moles first to find the true quantity of particles; this systematic approach ensures you avoid the intuitive errors that the examiners anticipate.