Theoretical yield formula
Theoretical yield is the maximum amount of product a reaction can make from its limiting reactant.
theoretical yield (g) = moles of limiting reactant × (product coefficient ÷ reactant coefficient) × product molar mass
Percent yield = actual yield ÷ theoretical yield × 100
How to calculate theoretical yield
- Write and balance the chemical equation.
- Convert the mass of each reactant to moles.
- Find the limiting reactant: the reactant that makes the least product.
- Multiply its moles by the coefficient ratio to get moles of product.
- Multiply the moles of product by its molar mass to get grams.
Theoretical yield problems
This calculator takes one known reactant. With two known reactants, find the limiting reactant first, as in problem 3.
Problem 1
2 H2 + O2 → 2 H2O. What is the theoretical yield of water from 4.00 g of H2 with excess O2?
- Moles of H2 = 4.00 g ÷ 2.016 g/mol = 1.984 mol.
- The ratio is 2 mol H2O : 2 mol H2, so 1.984 mol H2O forms.
- Mass of H2O = 1.984 mol × 18.015 g/mol = 35.7 g.
Answer: 35.7 g H2O
Problem 2
CaCO3 → CaO + CO2. What mass of CaO forms when 25.0 g of CaCO3 decomposes?
- Moles of CaCO3 = 25.0 g ÷ 100.086 g/mol = 0.2498 mol.
- The ratio is 1 : 1, so 0.2498 mol CaO forms.
- Mass of CaO = 0.2498 mol × 56.077 g/mol = 14.0 g.
Answer: 14.0 g CaO
Problem 3
2 Al + 3 Cl2 → 2 AlCl3. Find the theoretical yield of AlCl3 from 10.0 g of Al and 20.0 g of Cl2.
- Al = 10.0 ÷ 26.982 = 0.3706 mol. Cl2 = 20.0 ÷ 70.90 = 0.2821 mol.
- Divide by the coefficients: Al = 0.3706 ÷ 2 = 0.1853, and Cl2 = 0.2821 ÷ 3 = 0.0940.
- Cl2 gives the smaller value, so Cl2 is the limiting reactant.
- AlCl3 = 0.2821 mol × 2 ÷ 3 = 0.1881 mol. Mass = 0.1881 mol × 133.332 g/mol = 25.1 g.
Answer: 25.1 g AlCl3
Problem 4
The reaction in problem 3 gives 20.0 g of AlCl3. What is the percent yield?
- Percent yield = 20.0 g ÷ 25.07 g × 100 = 79.8%.
Answer: 79.8%
How to use this calculator
- Enter the chemical equation.
- Enter one known reactant formula, quantity, and unit.
- Enter the desired product formula and select its mass unit.
- Calculate and review the balanced coefficient ratio and product mass.
Formula and variables
product moles = reactant moles x product coefficient / reactant coefficient
| Symbol | Meaning | Unit |
|---|---|---|
| n | amount | mol |
| nu | stoichiometric coefficient | integer |
Worked example
2 mol H2 with coefficients 2 H2 : 2 H2O can theoretically produce 2 mol H2O, about 36.03 g.
Interpretation
Theoretical yield assumes the supplied reactant is fully available for the stated reaction and no competing loss occurs.
Common mistakes
- Use coefficients from a verified balanced equation.
- Do not confuse theoretical and actual yield.
Frequently asked questions
Do I need to balance the equation first?
No. The calculator balances the equation and uses the verified coefficients.
Can I enter reactant mass instead of moles?
Yes. Enter a mass, amount, or particle count for the known reactant.
What does theoretical yield assume?
It assumes complete conversion by the stated reaction with no product loss or side reaction.
What is the theoretical yield formula?
Theoretical yield = moles of limiting reactant × product-to-reactant coefficient ratio × product molar mass.
How do you find theoretical yield with two reactants?
Find the limiting reactant first. Then calculate the product from that reactant only.
Can I use scientific notation?
Yes. Enter values such as 6.022e23 or 1.0e-6 in a numeric field.
How should I round the result?
Keep extra digits during the calculation. Round the final result to the precision required by your data.