Chemistry » Chemical Reactions and Stoichiometry » Writing and Balancing Chemical Equations

Balancing Chemical Equations

Balancing Equations

The chemical equation described in the previous lesson is balanced, meaning that equal numbers of atoms for each element involved in the reaction are represented on the reactant and product sides. This is a requirement the equation must satisfy to be consistent with the law of conservation of matter. It may be confirmed by simply summing the numbers of atoms on either side of the arrow and comparing these sums to ensure they are equal.

Note that the number of atoms for a given element is calculated by multiplying the coefficient of any formula containing that element by the element’s subscript in the formula. If an element appears in more than one formula on a given side of the equation, the number of atoms represented in each must be computed and then added together.

For example, both product species in the example reaction, CO2 and H2O, contain the element oxygen, and so the number of oxygen atoms on the product side of the equation is:

$$\left ( 1\mathrm{\;CO_2} \text{ molecule} × \cfrac{2\text{ O atoms}}{\mathrm{CO_2}\text{ molecule}} \right )$$$$+ \left ( 2\mathrm{\;H_2O} \text{ molecule} × \cfrac{1\text{ O atom}}{\mathrm{H_2O}\text{ molecule}} \right )$$

$$= 4\text{ O atoms}$$

The equation for the reaction between methane and oxygen to yield carbon dioxide and water is confirmed to be balanced per this approach, as shown here:

$$\mathrm{CH_4} + \mathrm{2O_2} \rightarrow \mathrm{CO_2} + \mathrm{2H_2O}$$

Balanced?

C1 × 1 = 11 × 1 = 11 = 1, yes
H4 × 1 = 42 × 2 = 44 = 4, yes
O2 × 2 = 4(1 × 2) + (2 × 1) = 44 = 4, yes

A balanced chemical equation often may be derived from a qualitative description of some chemical reaction by a fairly simple approach known as balancing by inspection. Consider as an example the decomposition of water to yield molecular hydrogen and oxygen. This process is represented qualitatively by an unbalanced chemical equation:

$$\mathrm{H_2O} \rightarrow \mathrm{H_2} + \mathrm{O_2} \text{ (unbalanced)}$$

Comparing the number of H and O atoms on either side of this equation confirms its imbalance:

Balanced?

H1 × 2 = 21 × 2 = 22 = 2, yes
O1 × 1 = 11 × 2 = 21 ≠ 2, no

The numbers of H atoms on the reactant and product sides of the equation are equal, but the numbers of O atoms are not. To achieve balance, the coefficients of the equation may be changed as needed. Keep in mind, of course, that the formula subscripts define, in part, the identity of the substance, and so these cannot be changed without altering the qualitative meaning of the equation.

For example, changing the reactant formula from H2O to H2O2 would yield balance in the number of atoms, but doing so also changes the reactant’s identity (it’s now hydrogen peroxide and not water). The O atom balance may be achieved by changing the coefficient for H2O to 2.

$$\mathbf{2}\mathrm{H_2O} \rightarrow \mathrm{H_2} + \mathrm{O_2} \text{ (unbalanced)}$$

Balanced?

H2 × 2 = 41 × 2 = 24 ≠ 2, no
O2 × 1 = 21 × 2 = 22 = 2, yes

The H atom balance was upset by this change, but it is easily reestablished by changing the coefficient for the H2 product to 2.

$$\mathrm{2H_2O} \rightarrow \mathbf{2}\mathrm{H_2} + \mathrm{O_2} \text{ (balanced)}$$

Balanced?

H2 × 2 = 42 × 2 = 44 = 4, yes
O2 × 1 = 21 × 2 = 22 = 2, yes

These coefficients yield equal numbers of both H and O atoms on the reactant and product sides, and the balanced equation is, therefore:

$$\mathrm{2H_2O} \rightarrow \mathrm{2H_2} + \mathrm{O_2}$$