Theoretical Yield Calculator
Enter the limiting-reagent moles, the stoichiometric ratio (product coefficient / limiting-reagent coefficient) and the product molar mass; the tool instantly computes the product moles and theoretical mass.
Input Data
Results
At a glance:Theoretical yield is a core concept in stoichiometry: the maximum amount of product obtainable, assuming the reaction goes to 100% completion with no loss or side reactions, from the given reactants. It is the theoretical benchmark for evaluating a reaction's efficiency: in practice, due to incomplete reaction, side reactions, and product loss (filtration, transfer, purification), the actual yield is almost always less than the theoretical yield; their ratio is the percent yield = (actual / theoretical) × 100%. Calculating theoretical yield has two key steps. First, find the limiting reagent: when several reactants coexist, one is consumed first and sets the product upper bound — the limiting reagent; the rest are in excess. Second, use the stoichiometric ratio (mole ratio) from the balanced equation to convert limiting-reagent moles to product moles: product moles = limiting-reagent moles × (product coefficient / limiting-reagent coefficient). Then multiply by the product molar mass to get the theoretical mass: theoretical mass = product moles × product molar mass. Using this tool's ammonia example: N₂ + 3H₂ → 2NH₃. If N₂ is the limiting reagent with 1 mol, the NH₃:N₂ coefficient ratio is 2:1, so the stoichiometric ratio = 2/1 = 2, product NH₃ moles = 1 × 2 = 2 mol; NH₃ molar mass 17 g/mol, so theoretical yield = 2 × 17 = 34 g. This calculator splits the flow into three inputs: limiting-reagent moles, stoichiometric ratio (you read from the equation: product coefficient ÷ limiting-reagent coefficient), and product molar mass — directly giving product moles and theoretical mass. Notes: first, balance the equation first so the coefficients are correct. Second, determine the limiting reagent — common method: divide each reactant's moles by its coefficient; the smallest quotient is the limiting reagent. Third, the stoichiometric ratio is the product : limiting-reagent coefficient ratio, not a mass ratio. Fourth, theoretical yield is an upper bound, so actual yield ≤ theoretical, hence percent yield ≤ 100% (if > 100% it means impure product, moisture, or weighing error). Fifth, all inputs are non-negative.
Formula
Product moles = limiting-reagent moles × (product coefficient / reagent coefficient).
Theoretical mass = product moles × product molar mass.
Percent yield = (actual / theoretical) × 100%.
Limiting reagent: smallest (moles ÷ coefficient) among reactants.
$$m_{\text{theoretical}} = n_{\text{limiting}} \times \dfrac{\nu_{\text{product}}}{\nu_{\text{reagent}}} \times M_{\text{product}}$$How to Use
- Balance the equation, find the limiting reagent and enter its moles.
- Enter the stoichiometric ratio (product coefficient ÷ limiting-reagent coefficient).
- Enter the product molar mass; the right panel instantly shows product moles and theoretical mass.
Theoretical yield examples (limiting reagent 1 mol)
| Reaction | Ratio (product/reagent) | Product Molar Mass | Theoretical Yield |
|---|---|---|---|
| N₂+3H₂→2NH₃ (for N₂) | 2 | 17 (NH₃) | 34 g |
| 2H₂+O₂→2H₂O (for O₂) | 2 | 18 (H₂O) | 36 g |
| CaCO₃→CaO+CO₂ (for CaCO₃) | 1 | 44 (CO₂) | 44 g |
| 2Na+Cl₂→2NaCl (for Cl₂) | 2 | 58.5 (NaCl) | 117 g |
Ratio is the balanced-equation product coefficient ÷ limiting-reagent coefficient; actual yield must be ≤ theoretical.
Case Studies
Theoretical yield of ammonia synthesis
N₂ + 3H₂ → 2NH₃, N₂ is limiting with 1 mol.
NH₃:N₂ ratio = 2/1 = 2, product = 1 × 2 = 2 mol.
NH₃ molar mass 17 g/mol, theoretical yield = 2 × 17 = 34 g.
Percent yield from theoretical yield
Theoretical yield 34 g, experiment actually got 27.2 g NH₃.
Percent yield = (27.2 / 34) × 100% = 80%.
Below 100% reflects incomplete reaction or loss.
FAQ
What is the limiting reagent?
When more than one reactant is present, the one consumed first is the limiting reagent, which sets the product upper bound. To identify it, divide each reactant's moles by its coefficient; the smallest quotient is the limiting reagent.
How do I fill the stoichiometric ratio?
Balance the equation, read the target product and limiting-reagent coefficients, then ratio = product coefficient ÷ limiting-reagent coefficient. E.g. for N₂+3H₂→2NH₃ relative to N₂ it is 2/1 = 2.
What differs theoretical from actual yield?
Theoretical yield assumes 100% completion and no loss — the maximum possible. Actual yield is what the experiment truly gives, usually smaller (incomplete reaction, side reactions, transfer loss). Their ratio is the percent yield.
Why is percent yield usually below 100%?
Because real reactions rarely go fully to completion, plus side reactions and losses during filtration/purification. If you compute above 100%, it usually means impurity, moisture or weighing error.
Must the equation be balanced first?
Yes. The stoichiometric ratio comes from balanced coefficients; an unbalanced equation gives wrong coefficients and a wrong theoretical yield. Always balance first.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.