What if I get a fractional coefficient?

Fractional coefficients are mathematically valid but usually cleared by convention in standard equations. Multiply every coefficient in the entire equation by the denominator of the fraction to yield whole numbers.

How do I handle polyatomic ions that break apart?

If a polyatomic ion does not appear intact on the product side, you cannot balance it as a single unit. You must count and balance its constituent atoms individually.

Does the order in which I balance elements matter?

While the final balanced equation will be the same, balancing pure elements (like $O_2$ or $Fe$) last prevents you from unbalancing other elements when you adjust them.

How to balance a chemical equation

Balancing a chemical equation ensures that the number of atoms for each element is equal on both the reactant and product sides, satisfying the law of conservation of mass. This method applies to any closed-system chemical reaction where the identities and formulas of all reactants and products are known.

The setup

Write the unbalanced skeletal equation. Place the chemical formulas of the reactants on the left and the products on the right, separated by a reaction arrow ( $\rightarrow$ ). Do not alter the chemical formulas or their subscripts.

The steps

Count the number of atoms of each element on both sides of the equation.
Adjust the stoichiometric coefficients (the numbers placed in front of formulas) to balance the elements one at a time. Start with the most complex molecule or elements that appear in only one reactant and one product.
Balance polyatomic ions as single units if they remain unchanged during the reaction.
Balance diatomic elements (like $O_2$ or $H_2$ ) last.
If a fractional coefficient is required to balance an element, multiply the entire equation by the denominator to clear the fraction.

Checking the result

Tally the final atom counts for each element on the left and right sides. Both sets of totals must match exactly. Ensure that the coefficients are in the lowest possible ratio of whole numbers. If all coefficients are divisible by a common integer, divide them to simplify.

Common errors

The most frequent error is changing the subscripts within a chemical formula to balance the atoms (e.g., changing $H_2O$ to $H_2O_2$ ). This changes the chemical identity of the substance. Only coefficients may be modified.

Worked example

Balance the following chemical equation for the combustion of ethane: $C_2H_6 + O_2 \rightarrow CO_2 + H_2O$

Initial count: Left (C=2, H=6, O=2); Right (C=1, H=2, O=3).
Balance Carbon: Place a coefficient of 2 before $CO_2$ . $C_2H_6 + O_2 \rightarrow 2CO_2 + H_2O$
Balance Hydrogen: Place a coefficient of 3 before $H_2O$ . $C_2H_6 + O_2 \rightarrow 2CO_2 + 3H_2O$
Count Oxygen: Right side now has $(2 imes 2) + (3 imes 1) = 7$ oxygen atoms.
Balance Oxygen: Place a coefficient of $\frac{7}{2}$ before $O_2$ . $C_2H_6 + \frac{7}{2}O_2 \rightarrow 2CO_2 + 3H_2O$
Clear fraction: Multiply the entire equation by 2. $2C_2H_6 + 7O_2 \rightarrow 4CO_2 + 6H_2O$
Final check: Left (C=4, H=12, O=14); Right (C=4, H=12, O=14). The equation is balanced.

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References: OpenStax Chemistry 2e, Chapter 4: Stoichiometry of Chemical Reactions · Zumdahl Chemistry 10th Edition, Chapter 3: Stoichiometry