Balance equations and use mole ratios
Conserve atoms, distinguish coefficients from subscripts and connect a balanced equation with quantities.
In this guide
A chemical equation keeps track of atoms
In an ordinary chemical reaction, atoms are rearranged into new combinations. A balanced equation represents equal counts of each element on the reactant and product sides. A coefficient multiplies an entire chemical formula. A subscript belongs to the formula itself. Changing a coefficient changes how much of a substance is represented; changing a subscript can change which substance it is. Balancing therefore adjusts coefficients rather than rewriting the identities of the listed reactants and products.
Worked example: count each element
Consider the equation Al + O2 → Al2O3 as a symbolic classroom model. Each product formula unit contains two aluminium atoms and three oxygen atoms. Oxygen appears in pairs on the left and groups of three on the right, so use six oxygen atoms as a common count: 3O2 and 2Al2O3. The two product units contain four aluminium atoms, requiring 4Al. The balanced equation is 4Al + 3O2 → 2Al2O3. Check aluminium: four on each side. Check oxygen: six on each side.
Coefficients also give mole ratios
For the balanced equation 2H2 + O2 → 2H2O, two moles of hydrogen react with one mole of oxygen to form two moles of water under the idealized complete-reaction model. If 3 mol of hydrogen reacts with enough oxygen, it requires 3 × (1/2) = 1.5 mol of oxygen and forms 3 mol of water. These are amount ratios, not equal mass ratios. Equal mole counts of different substances generally have different masses because their molar masses differ.
The smaller reaction capacity limits the result
Now suppose the model starts with 3 mol H2 and 1 mol O2. The hydrogen could form 3 mol H2O, but the oxygen can support only 2 mol H2O. Oxygen is the limiting reactant. One mole of oxygen consumes 2 mol hydrogen, leaving 1 mol hydrogen unreacted and producing 2 mol water in the ideal calculation. Comparing the raw starting numbers, three and one, is not the method; compare how much product each amount can generate using the equation's coefficients.
Keep the calculation's assumptions visible
A balanced equation alone does not guarantee that a reaction proceeds rapidly, completely or under every condition. Introductory quantity problems usually state or assume an ideal complete reaction with the listed products. Real yield may differ. These examples are symbolic quantity exercises, not directions to mix or ignite materials. For an ionic equation, electric charge must also balance as well as the atoms; the simple neutral equations here do not explore that additional step.
- Count a subscript multiplied by its coefficient, such as 2 × 3 oxygen atoms in 2Al2O3.
- Use the lowest whole-number coefficient ratio when requested.
- Convert mass to moles before using a mole ratio, then convert back if the requested answer is a mass.
Try it yourself
Balance N2 + H2 -> NH3. Under a complete-reaction model, start with 2 mol N2 and 9 mol H2. Identify the limiting reactant, the amount of NH3 formed, and the amount of unused reactant remaining. Check each element count and the balanced mole ratios.
Reveal the worked answer
Balance N2 + H2 → NH3. Two nitrogen atoms on the left require 2NH3 on the right, which contains six hydrogen atoms; therefore use 3H2. The result is N2 + 3H2 → 2NH3. With 2 mol N2 and 9 mol H2 under the complete-reaction model, nitrogen limits the reaction: 2 mol N2 needs 6 mol H2 and forms 4 mol NH3. Three moles of H2 remain. Verify that both the amount calculation and each element count respect the balanced ratio.
Balance N2 + H2 → NH3. Two nitrogen atoms on the left require 2NH3 on the right, which contains six hydrogen atoms; therefore use 3H2. The result is N2 + 3H2 → 2NH3. With 2 mol N2 and 9 mol H2 under the complete-reaction model, nitrogen limits the reaction: 2 mol N2 needs 6 mol H2 and forms 4 mol NH3. Three moles of H2 remain. Verify that both the amount calculation and each element count respect the balanced ratio.
Put one idea into practice.
Try a short science session, then use the explanations to choose what to review next.
Start a short sessionSources & further reading
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