Writing and Balancing Chemical Equations

What a Chemical Equation Tells You

A chemical equation uses formulas and symbols to describe a reaction. Reactants (starting materials) sit on the left, products (substances formed) sit on the right, and an arrow (->) means yields. For example, 2H2 + O2 -> 2H2O reads: two molecules of hydrogen react with one molecule of oxygen to yield two molecules of water.

Writing and balancing equations is an explicitly tested skill on the New York State Regents chemistry exam. On the legacy Physical Setting/Chemistry format, Part B-2 and Part C constructed-response questions routinely instruct you to balance the equation using the smallest whole-number coefficients. The new Physical Science: Chemistry exam embeds the same skill inside its question clusters.

The Law of Conservation of Mass

Balancing exists because of the law of conservation of mass: in a chemical reaction, matter is neither created nor destroyed, so the total mass of the reactants equals the total mass of the products. Atoms are only rearranged into new combinations. Therefore the number of atoms of each element must be identical on both sides of the equation.

• Antoine Lavoisier established conservation of mass through careful measurement in sealed systems.
• In a closed system, mass before reaction = mass after reaction.
• If an equation has unequal atom counts, it is not yet balanced and violates this law.

Coefficients Versus Subscripts (The Golden Rule)

This distinction is the single most important balancing rule, and a guaranteed trap.

• A coefficient is the large number written in front of a formula. It multiplies the entire formula and may be changed freely while balancing.
• A subscript is the small number written inside or after an atom in a formula. It defines the substance and must never be changed to balance.

Changing H2O to H2O2 to gain an oxygen does not balance the equation -- it changes water into hydrogen peroxide, a different compound. You may only place coefficients in front.

A Step-by-Step Balancing Procedure

1. Write the correct, unbalanced formulas for all reactants and products. Get the formulas right first.
2. Count the atoms of each element on both sides.
3. Add coefficients to balance one element at a time. Save hydrogen and oxygen for last when possible.
4. Treat polyatomic ions (such as SO4) as a single unit if they appear unchanged on both sides.
5. Recount every element to confirm the totals match.
6. Reduce coefficients to the smallest whole-number ratio.

Worked Example

Balance: __ CH4 + __ O2 -> __ CO2 + __ H2O.

Start with carbon: 1 C on each side, balanced. Hydrogen: CH4 has 4 H, so put a 2 in front of H2O to get 4 H. Now oxygen: the right side has 2 (from CO2) + 2 (from 2 H2O) = 4 O, so put a 2 in front of O2. Final: CH4 + 2O2 -> CO2 + 2H2O. Check: C 1=1, H 4=4, O 4=4. Balanced.

Diatomic Elements

Seven elements exist as two-atom molecules when uncombined: H2, N2, O2, F2, Cl2, Br2, I2. A useful memory aid is Have No Fear Of Ice Cold Beer (H, N, F, O, I, Cl, Br). On the exam, free hydrogen gas is H2, not H. Writing a diatomic element as a single atom is a frequent formula error that makes balancing impossible.

Coefficients Are Mole Ratios

Once balanced, the coefficients reveal the mole ratio of every species. In 2H2 + O2 -> 2H2O, the ratio is 2 mol H2 : 1 mol O2 : 2 mol H2O. This ratio is the foundation of all stoichiometry, covered in the next section. The coefficients also represent ratios of molecules, but they do not represent ratios of masses or volumes of liquids and solids.

Common Mistakes and Exam Traps

• Changing a subscript instead of a coefficient -- the cardinal sin of balancing.
• Forgetting that a coefficient multiplies every atom in its formula.
• Leaving fractional coefficients; the Regents requires smallest whole numbers, so double them if needed.
• Writing a free diatomic element as a single atom.
• Miscounting atoms inside parentheses with both a subscript and a coefficient (multiply them together).

Recognizing Reaction Types

The Regents often pairs balancing with identifying the type of reaction, which can help you predict products. The four classic types are worth recognizing.

• Synthesis (combination): two or more reactants combine into one product, for example 2H2 + O2 -> 2H2O.
• Decomposition: one reactant breaks into two or more products, for example 2H2O -> 2H2 + O2.
• Single replacement: one element displaces another in a compound, for example Zn + 2HCl -> ZnCl2 + H2.
• Double replacement: ions in two compounds swap partners, for example AgNO3 + NaCl -> AgCl + NaNO3.

Classifying the reaction does not change how you balance it, but it confirms your formulas make chemical sense before you start counting atoms.

A Worked Single-Replacement Balance

Balance: __ Fe + __ Cl2 -> __ FeCl3. Iron starts as 1 on each side. Chlorine appears as Cl2 (diatomic, 2 atoms) on the left and 3 atoms in FeCl3 on the right. The least common multiple of 2 and 3 is 6, so place 3 in front of Cl2 (3 x 2 = 6 Cl) and 2 in front of FeCl3 (2 x 3 = 6 Cl). That makes iron 2 on the right, so place 2 in front of Fe. Final: 2Fe + 3Cl2 -> 2FeCl3. Check: Fe 2=2, Cl 6=6. Using the least common multiple for a stubborn element is the standard Regents technique.