How to Balance Chemical Equations
To balance a chemical equation, write the correct formula for every reactant and product, then add whole-number coefficients (never change subscripts) until each element has the same atom count on both sides. Balance metals first, then other nonmetals, then hydrogen, then oxygen last, and recheck every element before calling the equation balanced.
Why Chemical Equations Must Be Balanced
Chemical equations must balance because atoms are neither created nor destroyed in an ordinary chemical reaction, only rearranged into new combinations. This principle, the law of conservation of mass, means the same number of atoms of each element that starts on the reactant side has to show up somewhere on the product side. A reaction that appears to gain or lose atoms on paper is not actually possible; it is only an equation written incorrectly.
Balancing keeps a written equation consistent with what really happens in a flask or reactor. Every calculation built on top of an equation, including the mole ratios used to find theoretical yield or to work through stoichiometry problems, depends on the coefficients being correct. An unbalanced equation gives wrong mole ratios, which gives a wrong theoretical yield, which throws off every percent yield calculation that follows.
The Balancing Method: A Step-by-Step Procedure
Balancing by inspection, a systematic trial-and-error approach guided by a set order, is the standard method taught in general chemistry and handles the large majority of equations encountered in an introductory course. Follow the same five steps every time.
- Write the unbalanced skeleton equation using the correct chemical formula for every reactant and product. Formulas are fixed by the identity of the substance and cannot be changed during balancing.
- Count the atoms of each element on the reactant side and the product side separately, and list them side by side so mismatches are obvious.
- Balance one element at a time, usually in this order: metals first, then other nonmetals besides hydrogen and oxygen, then hydrogen, then oxygen last. Adjust only the coefficients placed in front of formulas, never the subscripts inside a formula.
- If balancing one element unbalances another, go back and adjust that element's coefficient again. If a coefficient ends up fractional, multiply every coefficient in the equation by the smallest number that clears the fraction.
- Recount every element, including hydrogen and oxygen, once all coefficients are in place. The equation is balanced only when each element matches on both sides and the coefficients are the smallest possible whole numbers.
Balance-Order Quick Reference
The table below summarizes the recommended balancing order and the reason it works for most equations.
| Order | Element type | Why this order works |
|---|---|---|
| 1 | Metals | Metals usually appear in only one compound per side, so their coefficient is easy to set without disturbing other elements. |
| 2 | Nonmetals other than H and O | Elements such as carbon, nitrogen, sulfur, and the halogens are typically tied to one compound per side and settle quickly once metals are fixed. |
| 3 | Hydrogen | Hydrogen often appears in more than one compound, including acids and water, so it balances more cleanly after simpler elements are locked in. |
| 4 | Oxygen | Oxygen is saved for last because it frequently appears in the most compounds on both sides and shifts with every earlier change. |
Worked Example 1: Simple Synthesis (H2 + O2 -> H2O)
Start with the skeleton equation: H2 + O2 -> H2O. Counting atoms shows the left side has 2 H and 2 O, while the right side has only 2 H and 1 O.
- Left: H = 2, O = 2
- Right: H = 2, O = 1
Oxygen is short by one atom on the right, so place a coefficient of 2 in front of H2O: H2 + O2 -> 2H2O. That fixes oxygen at 2 and 2, but hydrogen is now unbalanced (2 on the left, 4 on the right). Add a coefficient of 2 in front of H2 to restore hydrogen: 2H2 + O2 -> 2H2O.
- Left: H = 4, O = 2
- Right: H = 4, O = 2
Both sides match, so 2H2 + O2 -> 2H2O is the balanced equation.
Worked Example 2: Simple Combustion (CH4 + O2 -> CO2 + H2O)
Skeleton equation: CH4 + O2 -> CO2 + H2O. Carbon is already balanced at 1 and 1. Hydrogen is 4 on the left and only 2 on the right, so place a coefficient of 2 in front of H2O: CH4 + O2 -> CO2 + 2H2O.
- Left: C = 1, H = 4, O = 2
- Right: C = 1, H = 4, O = 4 (2 from CO2 plus 2 from 2H2O)
Oxygen is now 2 on the left and 4 on the right. Since O2 supplies atoms in pairs, place a coefficient of 2 in front of O2 on the left: CH4 + 2O2 -> CO2 + 2H2O.
- Left: C = 1, H = 4, O = 4
- Right: C = 1, H = 4, O = 4
All three elements match, so CH4 + 2O2 -> CO2 + 2H2O is balanced.
Worked Example 3: Metal-Acid Reaction (Al + HCl -> AlCl3 + H2)
Skeleton equation: Al + HCl -> AlCl3 + H2. Aluminum is a metal, so balance it first; it is already 1 and 1. Chlorine is 1 on the left and 3 on the right, so place a coefficient of 3 in front of HCl: Al + 3HCl -> AlCl3 + H2.
- Left: Al = 1, H = 3, Cl = 3
- Right: Al = 1, Cl = 3, H = 2
Chlorine now matches, but hydrogen is 3 on the left and 2 on the right, an odd-versus-even mismatch. Scale the whole equation to a common multiple of 6 hydrogen atoms by doubling the aluminum and HCl coefficients and tripling the H2 coefficient: 2Al + 6HCl -> 2AlCl3 + 3H2.
- Left: Al = 2, H = 6, Cl = 6
- Right: Al = 2, Cl = 6, H = 6
Every element matches, so 2Al + 6HCl -> 2AlCl3 + 3H2 is balanced. This equation is also useful for practicing mole ratio and limiting reactant problems, since aluminum and hydrochloric acid rarely start out in the exact 2-to-6 ratio the coefficients show.
Worked Example 4: Precipitation Reaction (Pb(NO3)2 + KI -> PbI2 + KNO3)
Skeleton equation: Pb(NO3)2 + KI -> PbI2 + KNO3. Treat the nitrate ion, NO3, as a single unit because it appears intact on both sides. Lead is already balanced at 1 and 1. Iodine is 1 on the left and 2 on the right, so place a coefficient of 2 in front of KI: Pb(NO3)2 + 2KI -> PbI2 + KNO3.
- Left: Pb = 1, NO3 = 2, K = 2, I = 2
- Right (before fixing K and NO3): Pb = 1, I = 2, K = 1, NO3 = 1
Potassium and nitrate are still off, 2 on the left and only 1 on the right, so place a coefficient of 2 in front of KNO3: Pb(NO3)2 + 2KI -> PbI2 + 2KNO3.
- Left: Pb = 1, NO3 = 2, K = 2, I = 2
- Right: Pb = 1, I = 2, K = 2, NO3 = 2
Every ion and atom matches, so Pb(NO3)2 + 2KI -> PbI2 + 2KNO3 is balanced.
Worked Example 5: Complex Combustion Needing a Fraction Cleared (C3H8 + O2 -> CO2 + H2O)
Skeleton equation: C3H8 + O2 -> CO2 + H2O. Balance carbon first by placing a coefficient of 3 in front of CO2: C3H8 + O2 -> 3CO2 + H2O. Balance hydrogen next by placing a coefficient of 4 in front of H2O: C3H8 + O2 -> 3CO2 + 4H2O.
- Left: C = 3, H = 8, O = 2
- Right: C = 3, H = 8, O = 10 (6 from 3CO2 plus 4 from 4H2O)
The right side now needs 10 oxygen atoms, and each O2 molecule supplies 2, so O2 needs a coefficient of 5: C3H8 + 5O2 -> 3CO2 + 4H2O. Some textbooks reach this same answer by first writing a fractional coefficient, such as O2 at 5, expressed as a non-whole intermediate value, then clearing it by multiplying every coefficient in the equation by 2 if the first pass over carbon and hydrogen had left an odd oxygen total. Either path lands on the same whole-number result.
- Left: C = 3, H = 8, O = 10
- Right: C = 3, H = 8, O = 10
All elements match, so C3H8 + 5O2 -> 3CO2 + 4H2O is the fully balanced equation.
Common Mistakes When Balancing Equations
Most balancing errors come from one of a small handful of habits, all avoidable by following the same procedure every time.
- Changing a subscript instead of adding a coefficient. Changing H2O to H2O2 does not represent more water molecules; it changes the substance into hydrogen peroxide, a different compound entirely. Only the whole number placed in front of a formula may change.
- Forgetting to recount after each adjustment. Fixing one element commonly unbalances another, especially oxygen and hydrogen, since both tend to appear in the most compounds. Recount every element, not only the one just adjusted.
- Leaving a fractional coefficient in the final answer. A value such as 1/2 or 5/2 is an acceptable intermediate step but not an acceptable final answer. Multiply every coefficient in the equation by the smallest number that clears all fractions.
- Stopping before oxygen and hydrogen are checked. These two elements are the easiest to overlook because they are counted last and appear in the widest range of compounds.
After Balancing: What the Coefficients Are Used For
A balanced equation is the starting point, not the end point, of most reaction calculations. The whole-number coefficients become the mole ratios used to convert between reactants and products in stoichiometry problems, to identify the limiting reactant when reagents are not supplied in the exact ratio shown, and to calculate theoretical yield, the maximum mass a reaction can produce. See mole ratio for how those coefficients convert directly into a conversion factor between any two species in the equation, and see the percent yield calculator for how theoretical yield compares against what is actually recovered from a reaction.
Frequently asked questions
Why do chemical equations need to be balanced?
Chemical equations must balance because atoms are neither created nor destroyed in a reaction, only rearranged, a rule called the law of conservation of mass. An equation showing more atoms of an element leaving than entering, or the reverse, does not represent an event that can actually happen. Balancing the coefficients keeps the written equation consistent with the real, measurable amounts of each substance involved in the reaction.
What is the law of conservation of mass?
The law of conservation of mass states that matter is neither created nor destroyed during a chemical reaction, only rearranged into new substances. The total mass of the reactants entering a reaction equals the total mass of the products leaving it. This is the reason a chemical equation has to show the same number of atoms of each element on both the reactant side and the product side.
Can you change a subscript to balance an equation?
No, changing a subscript is never allowed when balancing an equation. A subscript identifies the actual formula of a substance, so changing H2O to H2O2 does not represent more water, it represents hydrogen peroxide, a completely different compound. Balancing only ever adds or adjusts whole-number coefficients placed in front of a formula; the formulas themselves stay fixed throughout the entire process.
What order should you balance elements in?
The most reliable order is metals first, then nonmetals other than hydrogen and oxygen, then hydrogen, then oxygen last. Metals and simple nonmetals usually appear in only one compound per side, so their coefficients settle quickly. Hydrogen and oxygen tend to show up in more compounds, including water, so leaving them for last avoids redoing earlier work when their counts shift.
What if you end up with a fractional coefficient?
A fractional coefficient, such as 1/2 O2, is a normal intermediate result but never the final answer. Multiply every coefficient in the entire equation by the smallest whole number that clears the fraction, typically 2. An equation balanced with a 5/2 in front of oxygen, for example, becomes whole numbers throughout once every coefficient in the equation is doubled at once.
How do you balance equations with polyatomic ions?
Treat a polyatomic ion, such as nitrate (NO3) or sulfate (SO4), as one single unit rather than counting its individual atoms, as long as the entire ion appears unchanged on both sides of the equation. This shortcut works because the ion travels through the reaction intact. If a polyatomic ion breaks apart during the reaction, its atoms need to be counted individually instead.
Is there a fastest method for balancing equations?
Balancing by inspection, following the metals-then-nonmetals-then-hydrogen-then-oxygen order, is the fastest reliable method for equations found in an introductory chemistry course. Algebraic methods that assign a variable to every coefficient and solve a system of equations exist for unusually complex reactions, but they take longer to set up than inspection does for the great majority of synthesis, combustion, and displacement reactions.
What happens if an equation is left unbalanced?
An unbalanced equation gives incorrect mole ratios between reactants and products, which throws off every calculation built on it. Using it for <a href="/mole-ratio/">mole ratio</a> conversions or to calculate <a href="/theoretical/">theoretical yield</a> produces a wrong answer even when every other number in the problem is correct, since the coefficients themselves are the source of the ratio being used.
How do you check your work after balancing?
Recount the atoms of every element on both sides of the finished equation, not only the elements adjusted most recently, since fixing one element commonly shifts another. Pay particular attention to hydrogen and oxygen, which appear in the most compounds and are the easiest to miss. The equation is confirmed balanced only when each element's count matches exactly and all coefficients are whole numbers.
Do coefficients need to be whole numbers?
Yes, a correctly balanced chemical equation is always written with the smallest possible set of whole-number coefficients. Fractional coefficients can appear as a temporary step while working through the balancing procedure, but the final equation must be cleared of fractions by multiplying every term through by a common factor. A ratio such as 1 to 1/2 to 1 is rewritten as 2 to 1 to 2 before the equation is considered finished.