Which one among the following is the equivalent weight of sulphuric acid? (Atomic weight: H = 1, S = 32, O = 16)

1. Atomic and Molecular Mass Fundamentals (basic)

At the heart of chemistry lies the ability to quantify matter. Since individual atoms are too small to weigh on a standard scale, scientists use the Atomic Mass, which is a relative scale. The standard unit is the unified atomic mass unit (u). For instance, the atomic mass of Carbon is 12 u, and Hydrogen is 1 u Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.66. When atoms combine to form molecules, we calculate the Molecular Mass by simply adding up the atomic masses of every atom present in the chemical formula. For example, to find the mass of water (H₂O), you would add the masses of two Hydrogen atoms and one Oxygen atom (1+1+16 = 18 u). Understanding these masses is crucial because of the Law of Conservation of Mass, which states that mass is neither created nor destroyed during a chemical reaction. 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. In competitive exams, you will often see this applied to homologous series—groups of compounds like alkanes or alcohols where each successive member differs by a specific unit, such as a –CH₂– group, leading to a consistent increase in molecular mass Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.67. It is also important to distinguish between Mass and Weight. While we often use these terms interchangeably in daily life (e.g., saying a bag "weights" 10 kg), scientifically, mass is the actual amount of matter in an object and remains constant regardless of location. Weight, however, is the force of gravity acting on that mass and can change depending on where you are in the universe Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.75.

Concept	Definition	Unit
Atomic Mass	Mass of a single atom relative to Carbon-12.	u (unified mass unit)
Molecular Mass	Sum of atomic masses of all atoms in a molecule.	u (or g/mol for molar mass)
Mass	The quantity of matter in an object.	kg / g

Sources: Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.66-67; Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.75

2. Chemical Properties of Acids and Bases (basic)

To understand how substances behave in the lab, we must look at their behavior in water. Acids are substances that generate hydrogen ions (H⁺) in an aqueous solution. However, not all acids are created equal. The strength of an acid depends on the degree of ionization; strong acids like Hydrochloric acid (HCl) produce a high concentration of H⁺ ions, while weak acids like Acetic acid (CH₃COOH) produce fewer ions Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26. Similarly, bases generate hydroxide ions (OH⁻). A key distinction to remember is that bases which are soluble in water are called alkalis; they are typically soapy to touch and corrosive Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.24.

When an acid and a base react, they undergo a neutralization reaction. In this process, the H⁺ from the acid and the OH⁻ from the base combine to form water (H₂O), while the remaining ions form a salt. For example, when Ethanoic acid reacts with Sodium Hydroxide (NaOH), it forms Sodium Ethanoate and water Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.74. This fundamental reaction can be summarized as: Acid + Base → Salt + Water.

In quantitative chemistry, we use the concept of basicity for acids and acidity for bases. Basicity refers to the number of replaceable hydrogen ions a single molecule of an acid can donate. For instance, HCl is monobasic (1 H⁺), while Sulphuric acid (H₂SO₄) is dibasic because it contains two replaceable hydrogen atoms. This leads us to the Equivalent Weight, a crucial value for titrations. It is calculated by dividing the Molecular Weight of the substance by its basicity (for acids). For H₂SO₄, the molecular weight is 98 g/mol; since it is dibasic, its equivalent weight is 98 / 2 = 49.

Feature	Strong Acid/Base	Weak Acid/Base
Ionization	Complete dissociation in water.	Partial dissociation in water.
Ion Concentration	High concentration of H⁺ or OH⁻.	Low concentration of H⁺ or OH⁻.
Example	HCl, NaOH	CH₃COOH, NH₄OH

Sources: Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.24; Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26; Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.74

3. Sulphuric Acid: The King of Chemicals (intermediate)

Sulphuric acid (H₂SO₄) is often hailed as the 'King of Chemicals' because its per capita consumption is a primary indicator of a country's industrial strength. To understand why it is so potent, we must look at its chemical personality. It is a strong, mineral acid that acts as a powerful dehydrating agent and an oxidizing agent. When non-metals like sulphur are burned, they produce acidic oxides (like SO₂), which can eventually lead to the formation of sulphuric acid in the atmosphere, a key component of acid rain Environment and Ecology, Majid Hussain, Environmental Degradation and Management, p.8.

A defining characteristic of sulphuric acid is its basicity. In chemistry, the basicity of an acid refers to the number of replaceable hydrogen atoms (H⁺ ions) in one molecule of the acid. Since H₂SO₄ can release two hydrogen ions per molecule, it is classified as a dibasic acid. This property is crucial when calculating the Equivalent Weight of the acid, which is defined as the Molecular Weight divided by its Basicity. For sulphuric acid, the molecular weight is calculated as: (2 × 1 for H) + (1 × 32 for S) + (4 × 16 for O) = 98 g/mol. Therefore, its standard equivalent weight is 98 / 2 = 49.

In practical applications, sulphuric acid is indispensable. For instance, its reaction with metal hydrogencarbonates is utilized in soda-acid fire extinguishers. When the acid mixes with sodium hydrogencarbonate (NaHCO₃), it triggers a reaction that releases a rapid discharge of carbon dioxide (CO₂), which effectively smothers flames Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.36. Whether in a lab setting or in the complex chemical cycles of our atmosphere, H₂SO₄ remains a cornerstone of chemical science.

Sources: Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.36; Environment and Ecology, Majid Hussain, Environmental Degradation and Management, p.8

4. Expressing Concentrations: Molarity vs Molality (intermediate)

When we talk about the "strength" of a solution, we are essentially describing how much solute (the substance being dissolved) is present in a specific amount of solvent or solution. As we move from basic chemical reactions to precision measurements, we need precise ways to express these concentrations. The two most common methods are Molarity and Molality. While they sound similar, they serve different purposes based on how physical conditions like temperature affect them.

Molarity (M) is defined as the number of moles of solute per liter of solution. It is the most common unit used in laboratories because measuring liquid volume is convenient. However, there is a catch: volume is sensitive to temperature. As a liquid heats up, it expands, increasing the volume and thereby decreasing the molarity, even though the amount of solute remains the same. In Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26, we see that the strength of acids like HCl depends on their concentration; if we change the temperature, a "one molar" solution might technically fluctuate in concentration.

Molality (m), on the other hand, is the number of moles of solute per kilogram of solvent. This is a mass-based measurement. Since mass does not change with temperature or pressure, molality is the preferred choice for experiments involving temperature changes (like boiling point elevation). This distinction is vital because, as noted in Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141, the mass of a substance is a more stable reference than volume when physical conditions vary.

Feature	Molarity (M)	Molality (m)
Denominator	Volume of Solution (Liters)	Mass of Solvent (Kilograms)
Temp. Effect	Changes with temperature	Independent of temperature
Primary Use	Volumetric analysis, general lab work	Thermodynamic studies

Sources: Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26; Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141

5. Normality and the n-factor Concept (exam-level)

To master chemical stoichiometry, we must move beyond counting molecules (Molarity) and start counting 'reactive power.' This is where Normality (N) comes in. While Molarity tells us how many moles of a substance are in a liter, Normality tells us the concentration of reactive equivalents. The bridge between these two is the n-factor (also known as the valency factor). In simple terms, Normality = Molarity × n-factor. This concept is crucial because, in any chemical reaction, one equivalent of a substance always reacts exactly with one equivalent of another, regardless of the reaction's complexity. For acids, the n-factor is defined as its basicity—the number of replaceable Hydrogen ions (H⁺) per molecule. As we know, the acidic nature of a substance is fundamentally linked to the formation of H⁺ ions in solution Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.33. For instance, Hydrochloric acid (HCl) is monobasic (n-factor = 1), while Sulphuric acid (H₂SO₄) is dibasic (n-factor = 2) because it can donate two protons. Similarly, for bases, the n-factor is the acidity, representing the number of replaceable Hydroxyl (OH⁻) ions. To perform calculations, we use the Equivalent Weight, which is the Molar Mass of the substance divided by its n-factor. Let's take Sulphuric acid (H₂SO₄) as our gold standard: its molecular weight is approximately 98 g/mol (H: 1×2, S: 32, O: 16×4). Since its n-factor is 2, its equivalent weight is 98 / 2 = 49. This means that 49 grams of H₂SO₄ provides one 'unit' of reactive power (1 mole of H⁺ ions).

Sources: Science, class X (NCERT 2025 ed.), Acids, Bases and Salts, p.33

6. Basicity of Acids and Replaceable Hydrogen (intermediate)

When we talk about the basicity of an acid, it can feel a bit counterintuitive at first—why use the word "basicity" for an acid? In chemistry, the basicity of an acid refers to the number of replaceable hydrogen ions (H⁺) that a single molecule of that acid can donate to a base during a reaction. This is a fundamental concept because the strength and reactivity of an acid depend significantly on how many H⁺ ions it releases in an aqueous solution Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26.

It is crucial to distinguish between the total number of hydrogen atoms in a molecule and the replaceable ones. For example, in Acetic Acid (CH₃COOH), there are four hydrogen atoms in total, but only one (the one attached to the oxygen) is ionizable. Therefore, Acetic Acid is a monobasic acid. In contrast, Sulphuric Acid (H₂SO₄) is a dibasic acid because it can release two H⁺ ions. The ability of these acids to form different families of salts depends on these ions; for instance, Sulphuric Acid can form both normal salts (like Na₂SO₄) and acid salts (like NaHSO₄) Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.29.

This lead us to the concept of Equivalent Weight. While the Molecular Weight is the mass of one mole of the entire molecule, the Equivalent Weight is the mass that provides exactly one mole of H⁺ ions. You calculate it using this simple relationship:

Equivalent Weight = Molecular Weight / Basicity

For example, let's look at H₂SO₄. Its molecular weight is approximately 98 g/mol (H=1×2, S=32, O=16×4). Since its basicity is 2, its equivalent weight is 98 / 2 = 49. This value is essential in laboratory titrations and when determining the normality of a solution.

Type of Acid	Basicity	Example	Equivalent Weight Formula
Monobasic	1	HCl, HNO₃	M / 1
Dibasic	2	H₂SO₄, H₂C₂O₄	M / 2
Tribasic	3	H₃PO₄	M / 3

Sources: Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26; Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.29

7. The Formula for Equivalent Weight (exam-level)

To understand Equivalent Weight, we must look beyond the total mass of a molecule and focus on its reactive capacity. While Molecular Weight tells us the mass of one mole of a substance, Equivalent Weight tells us how much of that substance is required to provide or react with one mole of a specific reactive unit (like H⁺ ions in acids or OH⁻ ions in bases). As noted in Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26, the strength and behavior of acids depend on the number of H⁺ ions they produce. The general formula is:

Equivalent Weight = Molecular Weight / n-factor

The 'n-factor' represents the valency factor. For an acid, this factor is its basicity—the number of replaceable hydrogen ions (H⁺) per molecule. For a base, it is the acidity—the number of replaceable hydroxyl ions (OH⁻).

Let us apply this to Sulphuric Acid (H₂SO₄). First, we calculate its Molecular Weight by summing the atomic masses: (2 × 1.008 for H) + (1 × 32.06 for S) + (4 × 16.00 for O), which approximately equals 98 g/mol. Since H₂SO₄ is a dibasic acid (it can release two H⁺ ions), its n-factor is 2. Applying our formula: 98 / 2 = 49. This means 49 grams of H₂SO₄ is 'equivalent' to one mole of reactive hydrogen ions in a standard neutralization reaction, as described in the context of acid-base interactions in Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.34.

Sources: Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.26; Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.34

8. Solving the Original PYQ (exam-level)

To solve this question, you must synthesize two core concepts we recently covered: molecular weight and basicity. As detailed in NCERT Class XI Chemistry, the equivalent weight of an acid is its reactive capacity, calculated by dividing the total molecular mass by the number of replaceable hydrogen ions. First, calculate the molecular weight of H2SO4 using the provided atomic weights: (2 × 1) + 32 + (4 × 16) = 98 g/mol. Next, identify the basicity; since sulphuric acid is dibasic (releasing two H+ ions), you must divide that mass by 2. This logical progression leads you straight to the correct answer (D) 49.

UPSC frequently uses distractor options to test your attention to detail. Option (A) 98 is a classic trap; it is the molecular weight, and many candidates mistakenly stop there without applying the final step of the formula. Options (B) and (C) are designed to catch students who make arithmetic errors during the summation of atomic weights. In the exam, always distinguish between the structural mass and the functional equivalent to avoid these common pitfalls. The equivalent weight is essentially the 'effective' weight in a chemical reaction, and for H2SO4, that weight is halved because of its dual hydrogen contribution.