How to Balance Each of the Following Equations Step by Step

To balance each of the following equations, apply the law of conservation of mass: the number of atoms of every element must be identical on both sides of the arrow. You do this by adjusting coefficients — the numbers placed in front of formulas — never by changing subscripts, because altering subscripts changes the substance itself. The standard method is to list each element, count its atoms on both sides, and add coefficients until the counts match, then reduce to the simplest whole-number ratio. A balanced equation confirms that matter is neither created nor destroyed in a chemical reaction, a principle taught in introductory chemistry courses such as Khan Academy.

The Balancing Method

Reactants rearrange into products, but no atoms appear or disappear. Coefficients (whole numbers in front of a formula) multiply every atom in that formula, while subscripts (small numbers inside a formula) are fixed parts of the substance’s identity.

Follow this sequence for any equation:

1. Write the unbalanced equation with correct formulas for every reactant and product.
2. Inventory the atoms by listing each element and counting how many appear on each side.
3. Balance one element at a time, usually starting with the element that appears in only one place on each side.
4. Use coefficients to adjust counts, then recount after each change.
5. Balance hydrogen and oxygen last, since they often appear in multiple compounds.
6. Check every element and reduce all coefficients to the smallest whole-number ratio.

A simple tally table helps track large molecules accurately: one row per element, one column per side of the arrow. Update the counts every time you change a coefficient.

A Worked Example

Balancing is best learned by doing. Consider the combustion of methane:

Unbalanced: CH₄ + O₂ → CO₂ + H₂O

• Left: 1 C, 4 H, 2 O. Right: 1 C, 2 H, 3 O.
• Carbon already matches. Balance hydrogen with a 2 before H₂O.
• Now the right side has 1 C, 4 H, 4 O.
• Balance oxygen with a 2 before O₂.
• Final: CH₄ + 2O₂ → CO₂ + 2H₂O. Check: 1 C, 4 H, 4 O on each side. Balanced.

The recurring theme: balance the awkward element first, then clean up the rest.

Equations With Polyatomic Ions

A polyatomic ion is a charged group of atoms that stays together as a unit in a reaction, such as sulfate (SO₄²⁻), nitrate (NO₃⁻), or phosphate (PO₄³⁻). When the same polyatomic ion appears on both sides unchanged, treat it as a single particle rather than counting its individual atoms separately. This simplifies the tally and reduces errors.

Consider: AgNO₃ + CaCl₂ → AgCl + Ca(NO₃)₂

• Treat NO₃ as one unit. Left: 1 Ag, 1 NO₃, 1 Ca, 2 Cl. Right: 1 Ag, 1 Cl, 1 Ca, 2 NO₃.
• Balance nitrate with a 2 before AgNO₃.
• Now Ag is uneven. Place a 2 before AgCl.
• Chloride is already satisfied by the 2 Cl from CaCl₂ and 2AgCl.
• Final: 2AgNO₃ + CaCl₂ → 2AgCl + Ca(NO₃)₂. Nitrate stays intact throughout, so it is counted as one unit and never split.

The American Chemical Society notes that recognizing these stable groups is a central skill in writing correct chemical equations. If an ion does break apart or change identity, you can no longer treat it as a unit and must count its atoms individually.

Common Mistakes to Avoid

Most balancing errors fall into a few recognizable patterns.

• Changing subscripts instead of coefficients. Turning H₂O into H₂O₂ to fix an oxygen count changes water into hydrogen peroxide — a different compound entirely.
• Forgetting that coefficients multiply whole formulas. A 2 in front of H₂O means 4 H and 2 O, not 2 H and 2 O.
• Balancing one element at a time without recounting. Every coefficient change affects multiple elements.
• Leaving fractions in the final answer. Fractions can be useful intermediate steps, but multiply through to reach whole numbers, then reduce to the smallest ratio.
• Claiming balance without a final check. Recount every element on both sides.

A reliable verification habit is to rebuild the tally table from scratch after finishing, ignoring your earlier work. If every element matches and the coefficients share no common factor, the equation is correctly balanced. Practicing this discipline, as reinforced by resources like Khan Academy, builds the speed and accuracy needed for more advanced stoichiometry.

Reading Coefficients and Subscripts Correctly

A subscript is written to the lower right of a symbol and is part of the substance’s identity — it tells you how many atoms of that element are bonded in one unit of the compound. A coefficient is written to the left of the whole formula and tells you how many of those units participate in the reaction. In 3Ca(NO₃)₂, the coefficient is 3, and it multiplies everything inside the parentheses: 3 calcium atoms, 6 nitrogen atoms, and 18 oxygen atoms.

Remember that an element written alone, like Fe or O₂, is never given a subscript of 1 in writing but always counts as 1 unit. Oxygen and a handful of other elements exist as diatomic molecules — H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂ — so you must balance them as pairs, not as lone atoms. This single rule resolves many stubborn equations that refuse to close out.

Equations With Odd and Even Counts

A frequent obstacle is an element whose atom count is odd on one side and even on the other. An odd number can never equal an even number by multiplying with whole numbers alone, so you must first make both sides even — often by doubling a molecule that contains the odd element.

Take the combustion of ethane: C₂H₆ + O₂ → CO₂ + H₂O.

• Balance carbon: 2 carbons on the left need 2CO₂ on the right.
• Balance hydrogen: 6 hydrogens on the left need 3H₂O on the right.
• Now count oxygen on the right: 2CO₂ gives 4 O, and 3H₂O gives 3 O, for a total of 7 — an odd number.
• Oxygen on the left comes only in pairs, so 7 cannot be matched directly.
• Final: 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O. Check: 4 C, 12 H, 14 O on each side. Balanced.

You may place a fractional coefficient temporarily to balance an odd count, then multiply the entire equation by the denominator to restore whole numbers. For ethane, writing 7/2 before O₂ balances the oxygen immediately; multiplying everything by 2 produces the same final equation. Fractions are a legitimate intermediate tool, never a final answer.

A Checklist for Any Equation

When an equation resists balancing, working through a fixed checklist prevents wasted effort.

• Confirm every formula is chemically correct before touching coefficients.
• Write the full atomic tally for both sides.
• Balance metals and complex ions first, nonmetals next, hydrogen and oxygen last.
• Clear any fractions by multiplying through, then reduce to the lowest whole-number ratio.
• Recount every element independently as a final confirmation.

With practice, this checklist becomes automatic, and you can move directly from a written equation to its balanced form with confidence.

Key Takeaways

• Matter is conserved, so every element must have equal atom counts on both sides of the arrow.
• Adjust coefficients only; never change subscripts, which would alter the substance.
• Balance one element at a time, saving hydrogen and oxygen for last, and recount after every change.
• Treat polyatomic ions that stay intact as single units to simplify the count.
• Reduce final coefficients to the smallest whole-number ratio and always verify with a fresh tally.