To check whether a chemical equation is balanced, count the atoms of each element on both sides of the equation. A balanced equation has the same number of atoms of every element among the reactants and the products. This requirement follows from the law of conservation of mass, which states that matter is not created or destroyed during an ordinary chemical reaction.
The process is straightforward: identify each element, count its atoms in the reactants, count its atoms in the products, and compare the totals. If every element has the same count on both sides, the equation is balanced. If even one element has a different count, the equation needs to be corrected.
Understand the parts of a chemical equation
A chemical equation represents a chemical reaction using chemical formulas and symbols. The substances present before the reaction are called reactants, and the substances formed are called products. Reactants appear to the left of the arrow, while products appear to the right.
For example, the equation for hydrogen reacting with oxygen to form water can be written as:
H₂ + O₂ → H₂O
Hydrogen and oxygen are the reactants, and water is the product. The arrow means that the reactants undergo a chemical change to produce the product.
The small numbers written below the line in chemical formulas are called subscripts. They indicate how many atoms of an element are present in a molecule or formula unit. In H₂O, the subscript 2 means that each water molecule contains two hydrogen atoms. Oxygen has no written subscript, which means there is one oxygen atom.
Counting these atoms reveals that the equation above is not balanced. The reactant side contains two hydrogen atoms and two oxygen atoms. The product side contains two hydrogen atoms but only one oxygen atom. Oxygen has an unequal count, so the equation must be adjusted.
Count the atoms on both sides
The most reliable way to check an equation is to examine one element at a time. Begin with the reactants and count the atoms represented by every chemical formula. Then repeat the process for the products.
Consider the unbalanced equation for forming water:
H₂ + O₂ → H₂O
On the reactant side, H₂ contains two hydrogen atoms, and O₂ contains two oxygen atoms. The totals are therefore two hydrogen atoms and two oxygen atoms.
On the product side, H₂O contains two hydrogen atoms and one oxygen atom. The totals are two hydrogen atoms and one oxygen atom.
Comparing the two sides shows that hydrogen is balanced, but oxygen is not. The equation cannot be considered balanced until the oxygen counts match.
A simple atom-count table can make this comparison easier, especially when an equation contains several elements or compounds.
| Element | Reactants | Products | Balanced? |
|---|---|---|---|
| Hydrogen (H) | 2 | 2 | Yes |
| Oxygen (O) | 2 | 1 | No |
For more complicated equations, make a separate entry for every element. Do not rely on the appearance of the formulas or on whether the equation seems chemically reasonable. The atom counts provide the decisive test.
Distinguish coefficients from subscripts
One of the most important rules in balancing chemical equations is the difference between a coefficient and a subscript.
A coefficient is a number placed in front of a chemical formula. It tells you how many molecules or formula units are represented. A subscript, by contrast, tells you how many atoms of an element occur within each molecule or formula unit.
For example:
2H₂O
The coefficient 2 means there are two water molecules. Each molecule contains two hydrogen atoms and one oxygen atom. Multiplying the coefficient by the number of atoms in each molecule gives four hydrogen atoms and two oxygen atoms in total.
In general, the total number of atoms of an element in a formula is found by multiplying the coefficient by the number of atoms of that element in one formula unit. If the element appears more than once in a formula, add its contributions together.
This distinction matters because balancing an equation requires changing coefficients, not subscripts. Changing a subscript changes the chemical identity of a substance. For instance, H₂O is water, whereas H₂O₂ is hydrogen peroxide. They are different compounds with different properties.
If an equation is unbalanced, changing H₂O to H₂O₂ would not be a valid way to balance the original water-forming reaction. The correct approach is to adjust the coefficients so that the same substances remain in the equation while their atom totals become equal.
Check a balanced equation step by step
Once you understand how to count atoms, you can verify a balanced equation using a consistent procedure.
Consider the reaction between hydrogen and oxygen:
2H₂ + O₂ → 2H₂O
First, count the hydrogen atoms on the reactant side. The coefficient 2 applies to H₂, which contains two hydrogen atoms per molecule. Therefore, the reactants contain 2 × 2 = 4 hydrogen atoms.
Next, count the oxygen atoms on the reactant side. O₂ has no coefficient written in front of it, so its coefficient is understood to be 1. The reactants contain 1 × 2 = 2 oxygen atoms.
Now count the atoms on the product side. The coefficient 2 applies to H₂O, so there are two water molecules. Each contains two hydrogen atoms and one oxygen atom. The product totals are 2 × 2 = 4 hydrogen atoms and 2 × 1 = 2 oxygen atoms.
The comparison is clear:
| Element | Reactants | Products |
|---|---|---|
| Hydrogen (H) | 4 | 4 |
| Oxygen (O) | 2 | 2 |
Both elements have equal counts on the two sides. The equation is balanced.
Notice that balancing did not require changing the chemical formulas. Only the coefficients changed, preserving the identities of hydrogen gas, oxygen gas, and water.
Account for parentheses and repeated elements
Some chemical formulas contain parentheses, which group atoms together. When counting atoms, multiply the subscripts inside the parentheses by the subscript outside them.
For example, Ca(OH)₂ contains one calcium atom, two oxygen atoms, and two hydrogen atoms. The subscript 2 outside the parentheses applies to both O and H because the entire OH group occurs twice.
If a coefficient appears in front of this formula, it multiplies every atom in the formula. For example, 3Ca(OH)₂ represents three formula units, containing three calcium atoms, six oxygen atoms, and six hydrogen atoms.
Compounds may also contain the same element in multiple parts of a formula. In such cases, count every occurrence and add the totals. For example, in Al₂(SO₄)₃, there are two aluminum atoms, three sulfur atoms, and twelve oxygen atoms. The subscript 3 outside the parentheses multiplies both the sulfur and oxygen counts inside the sulfate group.
These rules help prevent common counting errors in equations involving hydroxides, sulfates, nitrates, and other compounds with grouped atoms.
Remember that coefficients multiply entire formulas
A coefficient applies to the complete chemical formula that follows it, not just to the first element.
For example, 2CO₂ represents two carbon dioxide molecules. Each molecule contains one carbon atom and two oxygen atoms, so the total is two carbon atoms and four oxygen atoms.
Similarly, 3NH₃ represents three ammonia molecules, containing three nitrogen atoms and nine hydrogen atoms altogether.
A useful check is to read each term as a complete unit. Identify the number of atoms in one molecule or formula unit, then multiply that number by the coefficient. If parentheses are present, account for their subscripts before applying the coefficient.
This approach is especially useful when checking equations with several reactants or products, where overlooking a coefficient can make an otherwise correct equation appear unbalanced.
Recognize common signs of an unbalanced equation
Several mistakes can lead to an incorrect atom count.
One common error is counting only the visible element symbols and ignoring subscripts. In CO₂, for example, there is one carbon atom but two oxygen atoms, not one of each.
Another mistake is overlooking coefficients. In 4Fe, there are four iron atoms, even though the formula contains no subscript. A missing subscript does not mean that the coefficient should be ignored; the coefficient determines the total number of atoms represented.
Parentheses can also cause errors. In Mg(OH)₂, the oxygen and hydrogen counts are both two, not one, because the OH group occurs twice.
Finally, an equation may appear balanced if you inspect only one element. For example, an equation can have equal hydrogen counts but unequal oxygen counts. Every element must be checked independently.
The presence of the same number of different molecules on each side is not required. A reaction may begin with two molecules and produce three, or it may involve many reactant particles and fewer product particles. What must remain equal is the number of atoms of each element, not the number of molecules.
Check equations involving ions and electrical charge
For reactions involving ions, counting atoms alone may not be sufficient. A balanced ionic equation must also conserve electrical charge.
An ion is an atom or group of atoms that carries a net electrical charge because it has gained or lost electrons. For example, Na⁺ has a positive charge, while Cl⁻ has a negative charge.
Consider the net ionic equation for forming a silver chloride precipitate:
Ag⁺ + Cl⁻ → AgCl
The reactant side contains one silver atom and one chlorine atom, matching the product side. The total charge on the left is +1 + (−1) = 0. The product, AgCl, is electrically neutral, so its total charge is also zero. Both atoms and charge are balanced.
In other ionic reactions, the number of atoms may match while the total charge does not. In that case, the equation is not fully balanced. Check the number of each type of atom and add the signed charges on both sides to confirm that they are equal.
For redox reactions, which involve the transfer of electrons, charge conservation is particularly important. Depending on the method used, electrons may appear explicitly in intermediate half-reactions. When those half-reactions are combined, the electrons must cancel appropriately.
Understand what a balanced equation tells you
A balanced chemical equation expresses the conservation of atoms during a reaction. Chemical reactions rearrange atoms into new combinations; they do not ordinarily create or destroy the nuclei of those atoms.
For example, when hydrogen reacts with oxygen to form water, hydrogen and oxygen atoms become part of water molecules. The atoms are reorganized, but the total number of hydrogen atoms and oxygen atoms remains unchanged.
The coefficients in a balanced equation also communicate the relative amounts of reactants and products involved in the reaction. In 2H₂ + O₂ → 2H₂O, the coefficients indicate a ratio of two hydrogen molecules to one oxygen molecule to two water molecules.
These ratios are important in stoichiometry, the study of quantitative relationships in chemical reactions. They allow chemists to calculate how much product can form from given amounts of reactants, provided the reaction proceeds according to the equation and the relevant conditions are accounted for.
However, a balanced equation does not by itself show how quickly a reaction occurs, whether it proceeds completely, or what conditions are required. It establishes the correct accounting of atoms and, for ionic equations, electrical charge. Other chemical principles are needed to explain reaction rates, equilibrium, and energy changes.
Use a final checklist to verify the equation
Before deciding that an equation is balanced, make one final pass through the formulas and coefficients.
- Identify every element present in the equation.
- Count each element’s atoms on the reactant side.
- Count the same element’s atoms on the product side.
- Multiply atom counts by coefficients and account for subscripts and parentheses.
- Confirm that the totals match for every element.
- For ionic equations, verify that the total electrical charge is also equal on both sides.
- Make sure the chemical formulas have not been altered merely to force the counts to match.
If every element has the same number of atoms on both sides and any required charge balance is satisfied, the equation is balanced. The key is to treat each formula systematically and verify the totals rather than relying on visual inspection or intuition.