chemistry

Balancing Chemical Equations

Balancing a chemical equation means making sure the same number of atoms of each element appears on both sides of the equation. This follows the law of conservation of mass, because atoms are rearranged during a chemical reaction but are not created or destroyed.

Visual note, a 2:56 episode with transcript, a mind map, 12 flashcards and a 5 question quiz.

Balancing Chemical Equations at a glance

Visual note summarising balancing chemical equations

Listen: Balancing Chemical Equations

Two hosts talking it through, 2:56. The full transcript is below, so you can read along or skip the audio.

Transcript

AnnaWhy do chemical equations have to be balanced?

MarcoBecause atoms are conserved. During a reaction, atoms are rearranged into new substances, but they are not created or destroyed. So the number of atoms of every element must be the same among the reactants on the left and the products on the right. An unbalanced equation gives the wrong quantities.

AnnaWhat exactly can we change when balancing?

MarcoWe change coefficients, which are numbers placed before formulas. A coefficient multiplies every atom in the formula. Three H two O means three water molecules, so it contains six hydrogen atoms and three oxygen atoms. We should not change subscripts, the small numbers inside formulas. Changing a subscript changes the substance itself.

AnnaWhat method would you use for a new equation?

MarcoFirst, write the correct formulas for every reactant and product. Then count each element on both sides. A tally or table can help. Next, add coefficients one element at a time. It is useful to begin with an element appearing in only one formula on each side. Usually, leave hydrogen and oxygen until later when they occur in several substances. After every change, recount all the atoms.

AnnaCan we test that with the formation of water?

MarcoYes. Start with H two plus O two produces H two O. There are two oxygen atoms on the left and one on the right, so put a two before H two O. Now there are four hydrogen atoms on the right, so put a two before H two. The result is two H two plus O two produces two H two O. Both sides have four hydrogen atoms and two oxygen atoms.

AnnaDoes the same reasoning work for magnesium and oxygen?

MarcoIt does. Magnesium plus O two produces MgO. Put a two before MgO to match the two oxygen atoms. That gives two magnesium atoms on the right, so put a two before magnesium. The balanced equation is two Mg plus O two produces two MgO.

AnnaWhat changes when we balance combustion?

MarcoComplete combustion of a hydrocarbon produces carbon dioxide and water. For propane, start with C three H eight plus O two produces carbon dioxide plus water. Balance carbon with three carbon dioxides, then hydrogen with four waters. That creates ten oxygen atoms on the right, so use five O two. The final equation is C three H eight plus five O two produces three carbon dioxides plus four waters.

AnnaWhat mistakes should we watch for?

MarcoNever change a subscript, such as turning water into H two O two. Also remember that a coefficient affects the whole formula, including atoms inside brackets. In calcium hydroxide, the two applies to both oxygen and hydrogen. Finally, recount every element, balance oxygen last in combustion, and reduce the coefficients to the smallest whole-number ratio. If a fraction appears, multiply every coefficient to obtain whole numbers.

The notes

Why chemical equations must balance

A chemical equation represents a reaction between reactants and products. The reactants are written on the left, and the products are written on the right. Each chemical formula shows which elements are present and how many atoms of each element are in one particle or formula unit.

In a chemical reaction, atoms are rearranged into new substances. The total number of atoms of every element must therefore be the same before and after the reaction. An unbalanced equation does not correctly represent the quantities involved in the reaction.

Coefficients and subscripts

A coefficient is a number placed in front of a chemical formula. It multiplies every atom in that formula. For example, 3H2O represents three water molecules, containing six hydrogen atoms and three oxygen atoms in total.

A subscript is the small number within a formula, such as the 2 in H2O. Subscripts are part of the chemical formula and must not be changed when balancing an equation. Changing a subscript changes the substance itself. Only coefficients should normally be changed.

A reliable step by step method

First, write the correct formulas for all the reactants and products. Then count the atoms of each element on both sides. It can help to make a tally or a table. Do not count the coefficient until after multiplying it by every subscript in the formula.

Next, add coefficients to balance one element at a time. Begin with an element that appears in only one formula on each side. Leave hydrogen and oxygen until later when they occur in several substances, especially in combustion reactions. After each change, recount all atoms.

When all elements balance, reduce the coefficients to the smallest possible whole number ratio. Finally, check that the formulas have not been changed and that the total number of atoms of every element is equal on both sides.

Worked examples from simple reactions

Consider the formation of water: H2 + O2 → H2O. There are two oxygen atoms on the left but only one on the right, so place a 2 before H2O: H2 + O2 → 2H2O. There are now four hydrogen atoms on the right, so place a 2 before H2: 2H2 + O2 → 2H2O. The equation is balanced, with four hydrogen atoms and two oxygen atoms on each side.

For magnesium reacting with oxygen, start with Mg + O2 → MgO. Oxygen occurs as O2 on the left, so place a 2 before MgO: Mg + O2 → 2MgO. This gives two magnesium atoms on the right, so place a 2 before Mg: 2Mg + O2 → 2MgO.

For calcium hydroxide reacting with hydrochloric acid, use Ca(OH)2 + HCl → CaCl2 + H2O. Calcium and chlorine can be balanced by placing a 2 before HCl: Ca(OH)2 + 2HCl → CaCl2 + H2O. There are then four hydrogen atoms on the left, so place a 2 before H2O: Ca(OH)2 + 2HCl → CaCl2 + 2H2O. Oxygen is also balanced, so the equation is complete.

Combustion equations

Complete combustion of a hydrocarbon produces carbon dioxide and water. For example, balance propane burning in oxygen: C3H8 + O2 → CO2 + H2O. Balance carbon first by placing a 3 before CO2, then hydrogen by placing a 4 before H2O: C3H8 + O2 → 3CO2 + 4H2O.

There are now ten oxygen atoms on the right, six in carbon dioxide and four in water. Place a 5 before O2: C3H8 + 5O2 → 3CO2 + 4H2O. Carbon, hydrogen and oxygen are now balanced.

For methane, CH4 + O2 → CO2 + H2O becomes CH4 + 2O2 → CO2 + 2H2O. If balancing produces a fraction such as 5/2O2, multiply every coefficient by 2 to obtain whole numbers.

Common mistakes and final checks

A frequent mistake is changing a subscript to make the numbers match. For example, changing H2O into H2O2 does not balance water, because it changes water into hydrogen peroxide. Another mistake is changing only one part of a compound containing brackets. In Ca(OH)2, the subscript 2 applies to both O and H, so the formula contains two oxygen atoms and two hydrogen atoms.

Students also often forget that a coefficient multiplies the entire formula, or stop after balancing one element without checking the others. In combustion equations, oxygen should usually be balanced last. Before accepting an answer, count every element on both sides, check that all coefficients are whole numbers, and simplify them to the smallest ratio if possible.

What to remember

Chemical equations balance because atoms are conserved during a reaction.
Change coefficients when balancing, not subscripts within chemical formulas.
A coefficient multiplies every atom in the formula that follows it.
Count each element on both sides and recount after every change.
In many reactions, balance elements appearing in fewer compounds before hydrogen and oxygen.
For complete hydrocarbon combustion, the products are carbon dioxide and water.
Use the smallest whole number coefficients in the final equation.