Theoretical Yield Formula and Worked Example

The theoretical yield formula is theoretical yield = moles of limiting reactant × (balanced-equation product coefficient ÷ limiting-reactant coefficient) × product molar mass. This calculator estimates the maximum product mass from a reactant’s mass, its molar mass, the balanced reaction’s coefficients, and the product’s molar mass; it returns theoretical yield in grams.

Formula

In words: convert the limiting reactant’s mass to moles, multiply by the product-to-reactant coefficient ratio in the balanced chemical equation, then convert product moles to mass.

moles of limiting reactant = m_r ÷ M_r
theoretical yield = (m_r ÷ M_r) × (ν_p ÷ ν_r) × M_p

• m_r is the available mass of the limiting reactant, in grams.
• M_r is its molar mass, in grams per mole.
• ν_p is the balanced-equation coefficient for the product of interest.
• ν_r is the coefficient for the limiting reactant.
• M_p is the product’s molar mass, in grams per mole.

The coefficient ratio has no units. The result is grams of product. The calculator assumes the coefficients come from a correctly balanced equation and that the stated reactant mass is pure, available reactant. Enter a positive coefficient for each species; the coefficient of 1 is usually omitted in written equations but still counts as 1.

Worked Example

For the calculator’s example, use a 10 g limiting reactant with molar mass 58.44 g/mol, a 1:1 reactant-to-product coefficient ratio, and a product molar mass of 58.44 g/mol.

1. Convert reactant mass to moles: 10 g ÷ 58.44 g/mol = 0.1711157 mol.
2. Apply the stoichiometric ratio: 0.1711157 mol × (1 ÷ 1) = 0.1711157 mol product.
3. Convert product moles to mass: 0.1711157 mol × 58.44 g/mol = 10.000 g.

Rounded to the calculator’s three decimal places, the theoretical yield is 10.000 g. The corresponding product amount is 0.1711 mol when rounded to four decimal places. These identical molar masses and a 1:1 ratio make the example’s product mass equal the reactant mass; that coincidence does not hold for most reactions.

Assumptions

• The reaction equation is balanced and its coefficients describe the reaction being considered.
• The entered reactant mass is pure, and the limiting reactant is known.
• The reaction proceeds according to the equation, with no competing reactions or loss of material.
• Molar masses are appropriate for the chemical forms represented in the equation.

This is study and lab-planning arithmetic, not a prediction that a real experiment will produce that amount. For bench work, follow your lab method, the safety data sheet (SDS), and your supervisor.

What Theoretical Yield Means

Theoretical yield is the maximum product amount calculated from the limiting reactant under the reaction’s stated stoichiometry. It is a calculated upper bound, not the amount guaranteed to form or the amount recovered after separation. It assumes the limiting reactant is fully consumed in the desired reaction and that all product is retained.

In practice, a reaction may be incomplete, side reactions may consume reactants, or product may be lost during transfer and purification. The isolated product mass is therefore often lower than the theoretical yield. A result above the theoretical yield usually points to a measurement or calculation issue, or to product that is still wet or contains impurities.

Find the Limiting Reactant First

The calculator needs the mass of the limiting reactant, not simply the mass of whichever reactant you have most of. For a reaction with multiple reactants, calculate how much product each reactant could form from its available amount. The reactant that predicts the least product is limiting; the others are in excess.

For example, for A + 2B → C, 0.50 mol A could form 0.50 mol C, while 0.60 mol B could form only 0.30 mol C because two moles of B are needed for each mole of C. B is limiting, and the theoretical yield is 0.30 mol C. If using this calculator, enter B’s mass and molar mass, set the product coefficient to 1, and the limiting-reactant coefficient to 2. If the product coefficient differs from 1, use its actual balanced-equation coefficient.

Using the Result and Avoiding Errors

Use the balanced equation’s coefficients as mole ratios; they are not mass ratios. Convert each measured reactant amount to moles before applying the ratio. Then convert product moles to mass with the product molar mass. The formula performs those conversions algebraically, but the units should still cancel correctly: grams divided by grams per mole gives moles, and moles multiplied by grams per mole gives grams.

• Balance the chemical equation before using its coefficients.
• Use the actual limiting reactant and its available amount, accounting for purity if the material is not pure.
• Keep units consistent. If mass is entered in milligrams, convert it to grams first; if a different mass unit is used throughout, adapt the calculation consistently.
• Use molar masses for the chemical formulas and forms in the equation, including waters of hydration where applicable.
• Keep extra digits during intermediate steps and round the final answer to a precision justified by the measurements.

Purity can matter: if a sample’s stated mass includes inert material, its reactive mass is less than its total mass. For a known purity expressed as a fraction, multiply the sample mass by that fraction before calculating. This calculator does not include a purity input, so enter the corrected mass when purity is relevant.

Theoretical Yield, Actual Yield, and Percent Yield

Actual yield is the amount of product obtained and measured in an experiment. Percent yield compares actual yield with theoretical yield: percent yield = (actual yield ÷ theoretical yield) × 100%. Both yields must be expressed in the same units. For instance, an actual yield of 7.5 g against a theoretical yield of 10.0 g gives 75% percent yield.

Theoretical yield alone does not reveal whether a reaction is efficient in practice. A low percent yield can result from incomplete conversion, side reactions, or product loss; it does not identify which cause applies. A percent yield above 100% commonly suggests residual solvent, moisture, impurities, or inconsistent measurements rather than creation of extra product beyond the stoichiometric limit.

Frequently Asked Questions

What is the simplest formula for theoretical yield?
Multiply the limiting reactant’s moles by the balanced-equation product-to-reactant coefficient ratio. To get yield in grams, multiply the resulting product moles by the product’s molar mass.

Can theoretical yield be greater than the amount of reactant?
Yes. Product and reactant have different molar masses and stoichiometric proportions, so the product mass can be larger or smaller than the reactant mass. The calculation concerns conservation of atoms, not equal masses of substances.

Does theoretical yield equal actual yield?
Usually not. Theoretical yield assumes complete conversion to the desired product and no losses. Actual yield is measured, and commonly falls below the theoretical value because of incomplete reaction, competing reactions, or handling losses.

How do I calculate theoretical yield when two reactants are given?
Convert each reactant amount to moles, use the balanced equation to find the product amount each could make, and choose the smaller product amount. That reactant is limiting; use its amount and coefficient in the yield calculation.

Why is my percent yield over 100%?
A value above 100% often means the isolated material includes water, solvent, or impurities, or that masses, units, or calculations are inconsistent. Check the sample’s condition, measurements, balanced equation, and limiting-reactant calculation.

Related

• Mole Calculator From a Chemical Equation: Moles of Product From the Mole Ratio
• Percent Yield Calculator: Actual Yield ÷ Theoretical Yield × 100

in rm | Limiting reactant mass | g | 10 | 0
in rmm | Limiting reactant molar mass | g/mol | 58.44 | 0.001
in pc | Product coefficient | - | 1 | 1
in rc | Limiting reactant coefficient | - | 1 | 1
in pmm | Product molar mass | g/mol | 58.44 | 0.001
out ty | Theoretical yield | g | (rm / rmm) * (pc / rc) * pmm | 3
out tm | Theoretical yield | mol | (rm / rmm) * (pc / rc) | 4