Writing balanced equations

A chemical formula identifies a substance and shows the relative numbers of its atoms. For example, $\mathrm{H_2O}$ contains hydrogen and oxygen in a 2:1 ratio, while $\mathrm{CO_2}$ contains carbon and oxygen in a 1:2 ratio. If no small number is shown, the number is understood to be one.

Some useful names and formulae are:

Some systematic names provide clues: the prefix di- in carbon dioxide indicates two oxygen atoms. However, a familiar name such as water does not reveal its formula, so the formula must be known. A formula describes composition; it is not an account of how the substance was made.

From a word equation to a symbol equation

A word equation names the substances taking part:

Reactants are written to the left of the arrow and products to the right. The arrow means “changes into” or “produces”; it is not an equals sign. Replacing each name with its correct formula gives:

This correctly identifies the substances, but it is not yet balanced. There are two oxygen atoms on the left and only one on the right.

Why equations must balance

During a chemical reaction, atoms are rearranged into new combinations. They are not created or destroyed. Consequently, every atom present among the reactants must also be present among the products. This is the particle-level explanation of the conservation of mass: the total mass of the products equals the total mass of the reactants for the complete reaction system.

To balance the magnesium equation, place numbers called coefficients in front of formulae:

The left side now contains two Mg atoms and two O atoms. The right side also contains two Mg atoms and two O atoms. The equation therefore represents both the reaction and conservation of mass.

A coefficient multiplies the entire formula. Thus $\mathrm{2MgO}$ means two lots of $\mathrm{MgO}$, giving two Mg atoms and two O atoms altogether.

Coefficients and subscripts do different jobs

A subscript is part of a substance's formula. The 2 in $\mathrm{O_2}$ says that each oxygen particle shown contains two oxygen atoms. Changing it would change the substance being represented.

A coefficient tells us how many lots of a substance take part. In $\mathrm{2H_2O}$, the coefficient 2 multiplies the whole $\mathrm{H_2O}$ formula:

• hydrogen atoms: $2 \times 2 = 4$
• oxygen atoms: $2 \times 1 = 2$

You must therefore balance an equation by changing coefficients, never by altering correct subscripts. For example, changing $\mathrm{H_2O}$ into $\mathrm{H_2O_2}$ would replace water with hydrogen peroxide rather than balance the equation.

A reliable balancing method

Begin with the word equation so that you know the reactants and products. Then:

1. Write the correct formula for every substance.
2. Count the atoms of each element on both sides.
3. Add a coefficient in front of a formula to correct an unequal count.
4. Recount all elements because one coefficient may affect several atom totals.
5. Continue until every element has equal totals on both sides.
6. Reduce the coefficients to the smallest whole-number ratio if possible.

Consider the combustion of methane:

Carbon is already balanced. Four H atoms on the left require two lots of water on the right. The products then contain four O atoms altogether, so two lots of $\mathrm{O_2}$ are needed:

A final count gives one C, four H and four O atoms on each side. The equation is balanced. Its coefficients also show the reacting ratio: one lot of methane reacts with two lots of oxygen to produce one lot of carbon dioxide and two lots of water.