Which one among the following equations is correctly balanced?

1. Chemical Reactions and the Law of Conservation of Mass (basic)

At its heart, a chemical reaction is a process of transformation where substances, known as reactants, undergo a change to form entirely new substances called products. You can think of this as a cosmic Lego set: we aren't creating new bricks or throwing any away; we are simply pulling them apart and snapping them back together in a different arrangement. As noted in Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.6, atoms of one element do not change into another, nor do they disappear; they simply experience the breaking and making of chemical bonds.

This brings us to the most fundamental rule of chemistry: the Law of Conservation of Mass. First formulated by Antoine Lavoisier, this law states that mass can neither be created nor destroyed in a chemical reaction. In practical terms, this means that if you weigh your reactants before the reaction and your products after, the total mass must remain exactly the same Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3. Because mass is tied to the number of atoms, this law dictates that the number of atoms of each element must be identical on both sides of a chemical equation.

When we write a chemical equation that doesn't yet account for this balance, we call it a skeletal equation. To make it scientifically accurate, we must "balance" it. We do this by adding coefficients (numbers in front of the molecules) to ensure that the tally of atoms on the reactant side (Left Hand Side) matches the tally on the product side (Right Hand Side) Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.5. For example, in the formation of water (H₂ + O₂ → H₂O), we must balance it to 2H₂ + O₂ → 2H₂O so that we have four hydrogen atoms and two oxygen atoms on both sides.

Sources: Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.1; Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3; Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.5; Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.6

2. Symbols, Formulas, and Valency (basic)

In the world of chemistry, we use a specialized shorthand to describe the building blocks of matter. Symbols are one- or two-letter abbreviations for elements (like Al for Aluminium or Na for Sodium), acting as the 'alphabet' of chemistry. When these elements combine, they form Chemical Formulas—the 'words' of the language. As noted in Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3, using these formulae makes representing reactions much more concise and useful than using word equations.

The way these formulas are constructed isn't random; it is governed by Valency. Valency is the 'combining capacity' of an atom—think of it as the number of 'arms' an atom has to hold onto others. For instance, Sodium (Na) has a valency of 1, while Oxygen (O) has a valency of 2. To balance their 'arms,' two Sodium atoms are needed for every one Oxygen atom, giving us Na₂O. This fundamental logic allows us to write the formulae for various salts, such as Potassium sulphate or Magnesium sulphate, by ensuring the positive and negative charges of the ions (based on their valencies) are balanced Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.28.

Finally, these formulas are arranged into Chemical Equations to represent reactions. To be accurate, an equation must be balanced, meaning the number of atoms for each element must be identical on both the Reactant (LHS) and Product (RHS) sides. This satisfies the Law of Conservation of Mass, which states that mass cannot be created or destroyed in a chemical reaction Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3. To make these equations even more informative, we often add symbols for physical states: (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.

Term	Analogy	Example
Symbol	A single letter	H, O, Al
Formula	A complete word	H₂O, Al₂O₃
Valency	Combining capacity	Carbon = 4, Hydrogen = 1

Sources: Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.3; Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.28; Science, Class X (NCERT 2025 ed.), Chemical Reactions and Equations, p.5

3. Properties of Bases: Focus on Sodium Hydroxide (NaOH) (intermediate)

To understand bases, we must look closely at Sodium Hydroxide (NaOH), often called caustic soda. It is a classic example of an alkali—a base that is highly soluble in water. In the laboratory, NaOH is produced through the chlor-alkali process, where electricity is passed through an aqueous solution of sodium chloride (brine). This process is so named because it yields chlorine gas (at the anode) and the alkali, sodium hydroxide (at the cathode) Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.30. As a strong base, NaOH dissociates completely in water to release hydroxide ions (OH⁻), giving it a characteristic soapy feel and the ability to turn red litmus paper blue.

One of the most fascinating chemical properties of NaOH is its reaction with metals. While many are familiar with acids reacting with metals to produce hydrogen gas, only a few metals react with strong bases. Aluminium (Al) and Zinc (Zn) are notable exceptions. When aluminium reacts with a hot solution of sodium hydroxide and water, it doesn't just sit there; it undergoes a vigorous reaction to produce a complex salt called sodium aluminate (NaAlO₂) and releases hydrogen gas (H₂) Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.19. This reaction is a staple in chemistry because it demonstrates that some metals have "amphoteric" tendencies, reacting with both acids and strong bases.

Beyond metals, NaOH plays a critical role in neutralization reactions. When it meets an acid, it forms a salt and water. For instance, when NaOH reacts with ethanoic acid (acetic acid), it produces a salt known as sodium ethanoate (or sodium acetate) and water Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.74. This ability to neutralize organic and mineral acids makes it indispensable in both industrial manufacturing and laboratory synthesis.

Sources: Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.30; Science, Class X (NCERT 2025 ed.), Acids, Bases and Salts, p.19; Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.74

4. Metals and Their Reactivity with Water and Bases (intermediate)

To understand how metals interact with the world, we must first look at the Reactivity Series. This is a list of metals arranged in descending order of their chemical activity Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.45. While some metals like Sodium (Na) are so reactive they catch fire in cold water, others like Aluminium (Al) or Iron (Fe) are more 'reserved.' When metals react with water, they generally produce a metal oxide and hydrogen gas; however, if the metal oxide is soluble, it dissolves further to form a metal hydroxide.

Interestingly, certain metals possess a 'dual personality' called amphoterism. While most metals only react with acids, metals like Aluminium and Zinc can also react with strong bases such as Sodium Hydroxide (NaOH). When Aluminium reacts with an aqueous solution of Sodium Hydroxide, it doesn't just sit there—it undergoes a vigorous reaction to produce a complex salt called Sodium Aluminate (NaAlO₂) and releases Hydrogen gas (H₂). This is a crucial concept because it shows that some metals can be corroded by alkaline substances, not just acidic ones.

To represent this precisely, we use a balanced chemical equation. Balancing ensures that the law of conservation of mass is respected—meaning every atom that enters the reaction must be accounted for in the products. For the reaction of Aluminium with Sodium Hydroxide and water, the stoichiometry is 2Al + 2NaOH + 2H₂O → 2NaAlO₂ + 3H₂. Notice that for every 2 atoms of Aluminium, we get 3 molecules of Hydrogen gas. This ratio is a fundamental aspect of chemical calculations (stoichiometry) used in industrial extractions and laboratory tests Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.49.

Reactant Type	Metal Behavior	Common Products
Cold Water	Highly reactive (e.g., Na, K)	Metal Hydroxide + H₂ + Heat
Steam	Moderately reactive (e.g., Al, Fe)	Metal Oxide + H₂
Strong Bases	Amphoteric metals (e.g., Al, Zn)	Complex Salt (e.g., Aluminate) + H₂

Sources: Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.45; Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.49

5. Amphoteric Nature of Aluminum (exam-level)

In the study of chemistry, we generally classify metal oxides as basic because they react with acids to form salt and water. For example, Copper(II) oxide (CuO) follows this standard behavior (Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.41). However, Aluminum is a 'chemical chameleon.' It belongs to a unique group of elements whose oxides show amphoteric behavior. An amphoteric substance is one that can react as both an acid and a base. Aluminum oxide (Al₂O₃) and Aluminum metal itself demonstrate this dual nature. When Aluminum reacts with a strong acid like Hydrochloric acid (HCl), it behaves like a typical metal, producing Aluminum Chloride and Hydrogen gas (Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.44). But the real magic happens when it encounters a strong base like Sodium Hydroxide (NaOH). In this environment, Aluminum acts 'acidically' to neutralize the base. When Aluminum metal reacts with aqueous Sodium Hydroxide, it produces a complex salt called Sodium Aluminate (NaAlO₂) and releases Hydrogen gas (H₂). To maintain the law of conservation of mass, the balanced equation requires 2 moles of Aluminum to react with 2 moles of NaOH and 2 moles of water:
2Al + 2NaOH + 2H₂O → 2NaAlO₂ + 3H₂

Reaction Environment	Nature of Aluminum	Key Product
With Acids (e.g., HCl)	Basic	Aluminum Chloride (AlCl₃)
With Bases (e.g., NaOH)	Acidic	Sodium Aluminate (NaAlO₂)

Sources: Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.41; Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.44

6. Principles of Balancing Chemical Equations (exam-level)

At the heart of every chemical reaction lies the Law of Conservation of Mass, which dictates that matter can neither be created nor destroyed in a chemical reaction. Consequently, the total mass of the reactants must equal the total mass of the products. For us as students, this means the number of atoms of each element must remain identical on both sides of the equation. This process of equalization is known as balancing. As outlined in Science, Class X (NCERT), Chemical Reactions and Equations, p.4, we typically use the hit-and-trial method, where we apply the smallest whole number coefficients to the formulas until the atom counts match.

To balance effectively, always start with the most complex molecule or the element present in the maximum number of atoms. It is a cardinal rule that you must never alter the subscripts in a chemical formula; doing so would change the identity of the substance itself (for example, changing H₂O to H₂O₂ to balance oxygen turns water into hydrogen peroxide). Instead, we place coefficients in front of the formulas. For instance, when balancing the reaction between iron and steam to form iron oxide (Fe₃O₄) and hydrogen, we start by balancing the four oxygen atoms in Fe₃O₄ by placing a '4' before H₂O, then proceed to balance the iron and hydrogen atoms sequentially Science, Class X (NCERT), Chemical Reactions and Equations, p.4.

To provide a complete picture, a balanced equation should also reflect the physical states of the participants. We use notations like (s) for solids, (l) for liquids, (g) for gases, and (aq) for aqueous solutions (substances dissolved in water). These notations make the chemical equation a much more informative tool for researchers and students alike Science, Class X (NCERT), Chemical Reactions and Equations, p.5.

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

7. Solving the Original PYQ (exam-level)

Now that you have mastered the Law of Conservation of Mass and the fundamentals of stoichiometry, this question serves as a perfect application of those building blocks. The core principle here is that in any chemical reaction, atoms are neither created nor destroyed; they are simply rearranged. When tackling a reaction involving a metal like Aluminium and a base like Sodium Hydroxide, you must ensure that the count for every single element—Sodium (Na), Aluminium (Al), Oxygen (O), and Hydrogen (H)—remains identical on both sides of the arrow. As explained in NCERT Class 10 Science, the reaction between amphoteric metals and bases is a frequent focus in competitive exams because it requires careful tracking of hydrogen atoms from multiple sources.

To arrive at the correct answer, let us use a systematic atom-counting strategy on Option (B). On the reactant side, we have 2 NaOH, 2 Al, and 2 H2O. This totals 2 Na, 2 Al, 4 Oxygen (2 from the hydroxide and 2 from the water), and 6 Hydrogen (2 from the hydroxide and 4 from the water). Moving to the product side, we see 2 NaAlO2 and 3 H2. This yields 2 Na, 2 Al, 4 Oxygen, and 6 Hydrogen. Because the atomic ledger is perfectly balanced for every element, (B) 2 NaOH + 2 Al + 2 H2O -> 3 H2 + 2 NaAlO2 is the only scientifically valid representation.

UPSC often includes "near-miss" distractors to punish superficial scanning. In Option (A), the hydrogen count is imbalanced (3 vs 4), while in Options (C) and (D), the stoichiometry of water or hydrogen gas is modified, leading to an oxygen-hydrogen mismatch. A common trap is to assume that because the metal atoms (Na and Al) are balanced, the whole equation is correct. Always remember to verify Oxygen and Hydrogen last, as these are where most balancing errors are hidden in complex aqueous reactions.