Stoichiometry Calculator

Using coefficients to scale molar amounts

Start with a balanced chemical equation and identify the coefficients of the known and target substances. These coefficients represent the mole ratio in which the substances react. The known amount is the number of moles you measure or calculate for the first substance. The target amount is the unknown number of moles of a different substance in the same reaction. The calculator multiplies the known moles by the ratio of target coefficient to known coefficient.

Both coefficients must be positive numbers. The known amount may be zero, representing a scenario where you have no starting material, but the coefficients themselves must be strictly greater than zero because they are multiplicative factors. Once you enter the known moles and both coefficients, the result appears instantly as the calculated mole amount of the target substance. This output is valid only if the reaction proceeds completely, meaning the substance you started with is the limiting reactant and none is left over.

Decomposition of hydrogen peroxide with coefficients 2 to 1

Hydrogen peroxide decomposes into water and oxygen gas. The balanced coefficients are 2, 2, and 1 for H₂O₂, H₂O, and O₂ respectively. If you start with 2.0 moles of H₂O₂, you must find how many moles of O₂ form. From the equation, two H₂O₂ molecules produce exactly one O₂ molecule. The mole ratio is 1 O₂ for every 2 H₂O₂, or expressed as a fraction, 1 ÷ 2 = 0.5.

Multiplying 2.0 mol by 0.5 gives 1.0 mol of oxygen gas. This stoichiometric relationship holds regardless of the actual masses involved: 2.0 moles of H₂O₂ will always produce exactly 1.0 moles of O₂ when the reaction goes to completion. The same coefficient ratio applies to any starting amount, such as 5.0 mol H₂O₂ producing 2.5 mol O₂, or 0.10 mol H₂O₂ producing 0.05 mol O₂.

Finding limiting reactants and products in synthesis

In laboratory reactions, you often have measured quantities of multiple starting materials and need to predict the amount of product that can form. Using stoichiometry, calculate the theoretical yield from each reactant separately, assuming each is the only limiting factor. For example, in the reaction N₂ + 3H₂ → 2NH₃, if you have 1.0 mol N₂ and 2.0 mol H₂, the nitrogen would produce 2.0 mol ammonia (1.0 × 2 ÷ 1), while the hydrogen would produce only 1.33 mol ammonia (2.0 × 2 ÷ 3). Hydrogen is the limiting reactant because it produces the smaller amount of ammonia.

In practice, the amount of product you actually obtain is determined by whichever reactant runs out first. Understanding this stoichiometric constraint helps you optimize reactions, plan reagent purchase quantities, and diagnose when reactions don't achieve theoretical predictions. If your experimental yield falls far below the theoretical value calculated using stoichiometry, factors like incomplete reactions, side reactions, or lost product during workup may be responsible.

Common reaction stoichiometries and their coefficient ratios

• Combustion: C + O₂ → CO₂ has a 1:1 coefficient ratio for reactant to product, so 1 mol of carbon always produces 1 mol of CO₂.
• Acid-base titration: HCl + NaOH → NaCl + H₂O has 1:1 stoichiometry, so 50 mL of 1.0 M HCl requires exactly 50 mL of 1.0 M NaOH to neutralize.
• Redox reactions can have larger ratios: 2Fe + 3Cl₂ → 2FeCl₃ shows that 2 moles of iron react with 3 moles of chlorine, a 3:2 ratio of coefficients.
• Precipitation: 3CaCl₂ + 2Na₃PO₄ → Ca₃(PO₄)₂ + 6NaCl involves a 3:1 coefficient ratio from reactant to product, so 3 mol CaCl₂ yields 1 mol of the precipitate.
• Gas-phase synthesis: N₂ + 3H₂ → 2NH₃ shows a 1:3:2 ratio, meaning from 1 mol N₂ you get 2 mol NH₃ if hydrogen is not limiting.

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