What is the number of water molecules present in a tiny drop of water (volume 0.0018 ml) at room temperature?

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

Welcome to your first step in mastering chemistry! To understand the world around us, we must look at the particulate nature of matter. Everything you see, from the screen in front of you to the air you breathe, is made up of unimaginably tiny particles called atoms and molecules. You can think of atoms as the fundamental building blocks of the universe. For instance, a piece of pure gold is made up entirely of individual atoms of gold Science, Class VIII (NCERT 2025 ed.), Particulate Nature of Matter, p.115.

However, many atoms are not stable enough to exist on their own in nature. To achieve stability, they group together to form molecules. A molecule is formed when two or more atoms are chemically bonded together. These can be atoms of the same element, like two hydrogen atoms joining to form a hydrogen molecule (H₂), or atoms of different elements, like two hydrogen atoms and one oxygen atom combining to form a water molecule (H₂O) Science, Class VIII (NCERT 2025 ed.), Particulate Nature of Matter, p.115. This bonding often happens because atoms seek a stable electronic configuration, such as an "octet," by sharing electrons Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.60.

To visualize how these bonds work, consider the nitrogen molecule (N₂). Nitrogen atoms share three pairs of electrons to form a triple bond, which provides the stability they need to exist Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.60. Because these particles are so microscopic, even a tiny amount of substance contains a staggering number of them. For example, a single drop of water is not just one "unit" of water, but a collection of billions upon billions of individual H₂O molecules packed closely together.

Particle	Definition	Example
Atom	The smallest unit of an element that maintains its identity.	Iron (Fe), Gold (Au)
Molecule	A group of atoms bonded together, representing the smallest unit of a compound.	Water (H₂O), Carbon Dioxide (CO₂)

Sources: Science, Class VIII (NCERT 2025 ed.), Particulate Nature of Matter, p.115; Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.59-60

2. Physical Properties: Density and Volume (basic)

Welcome to the next step of our journey! To understand how chemicals behave, we must first look at the most fundamental physical properties of matter: Mass, Volume, and Density. Simply put, matter is anything that has mass and occupies space. The amount of space an object takes up is its Volume, while Density describes how tightly packed the matter is within that volume. As we find in Science, Class VIII. NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.140, density is mathematically defined as:

Density = Mass / Volume

Think of density as the "compactness" of a substance. An important rule to remember is that density is an intrinsic property; it does not change based on the shape or size of the object. Whether you have a tiny drop of water or a whole bucket, the density of water at room temperature remains constant at approximately 1 g/mL (or 1 g/cm³). This means 10 mL of water will weigh 10 g, and 100 mL will weigh 100 g Science, Class VIII. NCERT (Revised ed 2025), Chapter 9, p.141. This benchmark makes water the perfect reference point for Relative Density—the comparison of a substance's density to that of water.

Understanding density also helps us predict how substances interact. For instance, why does oil float on water? It is because oil is less dense than water. Conversely, a stone sculpture will sink because its mass-to-volume ratio is higher than that of water Science, Class VIII. NCERT (Revised ed 2025), Chapter 9, p.150. However, density isn't entirely static; it is influenced by temperature. When you heat water, the particles gain energy and move faster, which generally causes them to spread out, thereby slightly decreasing the density Science, Class VIII. NCERT (Revised ed 2025), Chapter 8: Particulate Nature of Matter, p.110.

Property	SI Unit	Common Lab Unit
Mass	Kilogram (kg)	Gram (g)
Volume	Cubic metre (m³)	Millilitre (mL) or cm³
Density	kg/m³	g/mL or g/cm³

Sources: Science, Class VIII. NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.140, 141, 150; Science, Class VIII. NCERT (Revised ed 2025), Chapter 8: Particulate Nature of Matter, p.110

3. Laws of Chemical Combination (intermediate)

In our journey through chemistry, we find that nature follows a strict set of 'accounting rules' whenever substances react. These are known as the Laws of Chemical Combination. 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. In practical terms, this means the total mass of your reactants must exactly equal the total mass of your products Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3. This law is the reason why we must always balance chemical equations—to ensure the number of atoms of each element remains the same before and after the reaction. Moving a step deeper, we encounter the Law of Definite Proportions (or Constant Proportions), proposed by Joseph Proust. This law tells us that a given chemical compound always contains its component elements in a fixed ratio by mass, regardless of its source. For example, in pure water (H₂O), the ratio of the mass of hydrogen to the mass of oxygen is always 1:8. Whether you take a drop of water from the Ganges or synthesize it in a lab, this ratio never changes. This consistency allows us to use physical constants, like the fact that 1 mL of water has a mass of approximately 1 g at room temperature, to perform precise chemical calculations Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141. Finally, the Law of Multiple Proportions explains what happens when two elements form more than one compound. For instance, Carbon and Oxygen can form Carbon Monoxide (CO) or Carbon Dioxide (CO₂). This law states that the masses of oxygen that combine with a fixed mass of carbon will be in a ratio of small whole numbers (in this case, 1:2). These laws collectively provided the experimental foundation for Dalton’s Atomic Theory, proving that matter is composed of discrete, indivisible units called atoms.

Law	Core Principle	Significance
Conservation of Mass	Total mass remains constant.	Basis for balancing chemical equations.
Definite Proportions	Elements combine in fixed mass ratios.	Determines the chemical formula of a substance.
Multiple Proportions	Different compounds of the same elements have simple mass ratios.	Supports the existence of atoms.

Sources: Science, class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3; Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141

4. Solutions and Concentration Terms (intermediate)

At its heart, a solution is a uniform or homogeneous mixture of two or more substances. We identify the components based on their quantity: the substance present in the larger amount is the solvent (the medium), while the substance in the smaller amount is the solute (the substance being dissolved) Science, Class VIII . NCERT(Revised ed 2025), Chapter 9, p.135. For instance, in our atmosphere, Nitrogen acts as the solvent because it makes up about 78% of the air, while Oxygen and Carbon Dioxide are solutes Science, Class VIII . NCERT(Revised ed 2025), Chapter 9, p.149. A solution reaches its saturated state when it has dissolved the maximum possible amount of solute at a specific temperature; any further solute added will simply settle at the bottom Science, Class VIII . NCERT(Revised ed 2025), Chapter 9, p.137.

To transition from observing a solution to measuring it precisely, we use concentration terms. This requires us to understand the relationship between mass, volume, and density. Density is defined as mass per unit volume (Density = Mass/Volume). For water at room temperature, the density is approximately 1 g/mL, meaning 1 mL of water weighs almost exactly 1 g Science, Class VIII . NCERT(Revised ed 2025), Chapter 9, p.141. This simple ratio is a powerful tool in chemistry: if you know the volume of a liquid, you can immediately find its mass, which is the first step toward calculating the number of particles (moles or molecules) present in that sample.

When we deal with microscopic quantities—like a tiny 0.0018 mL drop of water—we follow a logical chain: Volume → Mass → Moles → Molecules. First, using the density of water (1 g/mL), we find the mass of the drop is 0.0018 g. Next, we divide this mass by the molar mass of water (H₂O), which is 18 g/mol, to find the number of moles (0.0018 / 18 = 10⁻⁴ moles). Finally, to find the actual number of water molecules, we multiply the moles by Avogadro’s number (6.023 × 10²³). Even in such a microscopic drop, there are roughly 6.023 × 10¹⁹ molecules, illustrating just how incredibly small and numerous atoms are.

Term	Definition	Context/Formula
Solubility	Max solute that dissolves in a fixed solvent amount.	Increases with temperature for most solids.
Molar Mass	The mass of one mole of a substance.	H₂O = 18 g/mol; CO₂ = 44 g/mol.
Density	How much mass is packed into a specific volume.	Mass / Volume (e.g., 1 g/mL for water).

Sources: Science ,Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.135; Science ,Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.149; Science ,Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.137; Science ,Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141

5. The Mole Concept and Avogadro's Constant (exam-level)

In the world of chemistry, atoms and molecules are so incredibly small that counting them individually is impossible. To bridge the gap between the microscopic world of atoms and the macroscopic world we can measure in a lab, scientists use the Mole Concept. Much like we use the word 'dozen' to represent 12 items, chemists use the Mole as a standard unit to represent a specific, enormous quantity of particles. One mole of any substance contains exactly 6.022 × 10²³ representative particles (atoms, molecules, or ions). This number is known as Avogadro’s Constant (Nₐ). To master this concept for the exam, you must understand the relationship between mass, moles, and number of particles. The mass of one mole of a substance is called its Molar Mass (expressed in g/mol), which is numerically equal to its atomic or molecular mass. For example, the molecular mass of water (H₂O) is 18 units, so its molar mass is 18 g/mol. This allows us to perform precise calculations. As noted by the pioneering work of Indian chemist Acharya Prafulla Chandra Ray, who is celebrated as the 'Father of Modern Indian Chemistry', systematic research into substances requires this level of quantitative precision Science-Class VII, Exploring Substances, p.17. Let’s apply this to a real-world scenario: a tiny drop of water measuring 0.0018 mL. To find out how many molecules are inside, we follow these steps:

• Convert Volume to Mass: Using the standard density of water (approximately 1 g/mL), a 0.0018 mL drop has a mass of 0.0018 g Science, Class VIII, Chapter 9, p.141.
• Calculate Moles: Divide the given mass by the molar mass (18 g/mol). 0.0018 g ÷ 18 g/mol = 0.0001 moles (or 10⁻⁴ mol).
• Find Number of Molecules: Multiply the moles by Avogadro’s Constant. 10⁻⁴ × 6.022 × 10²³ = 6.022 × 10¹⁹ molecules.

Even a drop so small it barely wets your finger contains more molecules than there are grains of sand on all the world's beaches!

Sources: Science-Class VII, Exploring Substances: Acidic, Basic, and Neutral, p.17; Science, Class VIII, Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141

6. Molar Mass and Stoichiometric Calculations (exam-level)

To master chemistry at an exam level, we must bridge the gap between what we can see (bulk volume and mass) and what we cannot see (individual atoms and molecules). This bridge is built using two critical tools: Density and Molar Mass. Density acts as the first translator, allowing us to convert a liquid's volume into mass. For example, because the density of water is approximately 1 g/mL at room temperature, a volume of 10 mL is equivalent to a mass of 10 g Science, Class VIII. NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141.

Once we have the mass, we use the Molar Mass to find the number of moles. The molar mass is the sum of the atomic masses of all atoms in a molecule, expressed in grams per mole (g/mol). For water (H₂O), we sum the masses of two Hydrogen atoms (1 u each) and one Oxygen atom (16 u), resulting in a molar mass of 18 g/mol Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.66. The number of moles is calculated using this fundamental relationship:

The final step in stoichiometry is counting the actual particles. By multiplying the number of moles by Avogadro’s Number (6.022 × 10²³), we find the total number of molecules. Consider a tiny drop of water measuring 0.0018 mL. Its mass is 0.0018 g. Dividing this by the molar mass (18 g/mol) gives us 0.0001 (or 10⁻⁴) moles. When we multiply these moles by Avogadro's constant, we discover that even this microscopic drop contains a staggering 6.022 × 10¹⁹ molecules.

Sources: Science, Class VIII. NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141; Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.66

7. Solving the Original PYQ (exam-level)

This question is a perfect application of the Mole Concept Bridge you have just mastered. It tests your ability to link a physical measurement (volume) to a microscopic quantity (number of molecules) using three fundamental pillars: the density of water, molar mass, and Avogadro’s number. As discussed in Science, Class VIII, NCERT (Revised ed 2025), the journey from a visible drop to invisible molecules requires a step-by-step conversion of units.

To arrive at the solution, think like a chemist: First, use the density of water (1 g/mL) to convert the 0.0018 mL volume into a mass of 0.0018 g. Second, find the number of moles by dividing this mass by the molar mass of water (18 g/mol), which gives you 0.0001 (or 10⁻⁴) moles. Finally, multiply these moles by Avogadro’s constant (6.023 x 10²³ molecules/mol). By mathematically shifting the exponent four places to the left, you reach the correct answer: (C) 6.023 x 10¹⁹.

UPSC often uses specific "traps" in the options to catch students who rush. Option (D) is a conceptual trap—it is the value of Avogadro's number itself, which would only be true if you had a full mole (18g) of water. Options (A) and (B) are calculation decoys designed to mislead those who make errors in decimal placement or scientific notation during the division process. Precision in power-of-ten calculations is just as important as knowing the formula itself.