Theoretical Yield Formula and Worked Example

The theoretical yield formula is: theoretical yield = moles of limiting reactant × (product’s stoichiometric coefficient ÷ limiting reactant’s coefficient) × product molar mass. Enter the balanced reaction’s reactant and product coefficients, the limiting reactant amount, and the product molar mass to calculate the maximum product mass predicted by stoichiometry.

Formula

In symbols, theoretical yield (g) = n_LR × (ν_P ÷ ν_LR) × M_P. Here, n_LR is the available amount of limiting reactant in moles (mol); ν_LR is its coefficient in the balanced chemical equation; ν_P is the coefficient of the desired product; and M_P is that product’s molar mass in grams per mole (g/mol). The result is a mass in grams.

If the limiting reactant amount is supplied as a mass rather than moles, first convert it: n_LR = mass in grams ÷ reactant molar mass in g/mol. If it is supplied as a solution volume, use its concentration and volume to find moles, ensuring the units are compatible. The calculator’s inputs are already in moles, so it does not perform either conversion.

Worked Example

Use the default values in the calculator: 0.1 mol limiting reactant, a limiting-reactant coefficient of 1, a product coefficient of 1, and product molar mass 180.156 g/mol. The formula gives:

1. Product moles = 0.1 mol × (1 ÷ 1) = 0.1 mol.
2. Theoretical yield = 0.1 mol × 180.156 g/mol = 18.0156 g.
3. Rounded to the calculator’s three decimal places, the theoretical yield is 18.016 g.

This result is the maximum predicted product mass for the stated limiting-reactant amount and reaction ratio, assuming the reaction follows the balanced equation completely. It is not a prediction that a real experiment will produce exactly that mass.

Assumptions

• The chemical equation is balanced and represents the reaction that forms the product of interest.
• The limiting-reactant amount is correctly expressed in moles, and its coefficient and the product coefficient come from that equation.
• The product molar mass is appropriate for the formula and form being counted; no purity, side-reaction, or isolation correction is applied.
• The stoichiometric calculation assumes complete conversion of the limiting reactant into the specified product.

How to Find the Limiting Reactant

The limiting reactant is the reactant that runs out first according to the balanced equation. It caps how much product can form. You cannot determine it from the amount of just one reactant when multiple reactants are involved; compare the available amount of each reactant with its required stoichiometric ratio.

For each reactant, divide its available moles by its coefficient in the balanced equation. The smallest quotient identifies the limiting reactant. For example, in A + 2B → C, suppose a reaction has 0.30 mol A and 0.40 mol B. The quotients are 0.30 ÷ 1 = 0.30 mol and 0.40 ÷ 2 = 0.20 mol. B is limiting, and the maximum amount of C is 0.40 mol × (1 ÷ 2) = 0.20 mol. This comparison accounts for the equation’s ratio rather than merely choosing the reactant with fewer moles.

For more than two reactants, do the same division for each one. If quantities are given in grams, convert each to moles before comparing them. For solutions, calculate dissolved reactant moles from concentration and volume first. Only after identifying the limiting reactant should you use its amount in the theoretical-yield formula.

Using the Result and Comparing Yield

Theoretical yield is a stoichiometric ceiling under the stated assumptions. It is useful for planning calculations, checking reaction results, and calculating percent yield. To compare an experiment with the prediction, first express the actual isolated product amount and theoretical yield in the same units and on the same product basis.

Percent yield = (actual yield ÷ theoretical yield) × 100%. If the theoretical yield is 18.016 g and the actual isolated product is 14.4 g, the percent yield is (14.4 ÷ 18.016) × 100% ≈ 79.93%. Actual yield may be lower because a reaction is incomplete, competing reactions form other products, or product is lost during transfer, separation, washing, or purification. A measured yield above 100% can result when the collected material contains solvent, water, or impurities, or when measurements are inaccurate; it does not mean that stoichiometry created extra product.

Keep significant figures consistent with the precision of the input measurements. The calculator displays three decimal places for convenience, but those digits do not make an imprecise input more accurate. Carry unrounded values through intermediate steps and round the reported result only at the end.

Common Mistakes and Limits

• Using an unbalanced equation: coefficients set the mole ratios. Balance the equation before calculating; subscripts in chemical formulas are not reaction coefficients.
• Using grams as if they were moles: convert each reactant mass by dividing by its molar mass. The calculator’s first input specifically requires mol.
• Choosing the wrong reactant: a reactant present in the smallest mass or mole amount is not necessarily limiting. Compare moles divided by coefficients.
• Reversing the ratio: multiply by product coefficient divided by limiting-reactant coefficient, not the other way around.
• Mixing product forms: use the molar mass of the product form whose mass you want to report. A hydrated compound, salt, or different protonation form can have a different molar mass from the anhydrous or neutral form.

The equation gives a theoretical mass, not a reaction-rate estimate, a purity measurement, or a guarantee of recoverable product. It does not account for equilibrium, kinetic limitations, side reactions, incomplete conversion, solubility, or handling losses. Those effects influence actual yield and require chemical and experimental information beyond the stoichiometric inputs. For bench work, follow your lab method, the safety data sheet (SDS) and your supervisor.

Frequently Asked Questions

What is the formula for theoretical yield in grams?
Multiply limiting-reactant moles by the product-to-reactant coefficient ratio, then by the product molar mass: g = n_LR × (ν_P ÷ ν_LR) × M_P.

Can I calculate theoretical yield from grams?
Yes. Convert the limiting reactant’s mass to moles by dividing grams by its molar mass, then apply the balanced-equation ratio and multiply product moles by the product molar mass.

How do I know which reactant is limiting?
Convert each reactant quantity to moles and divide by its coefficient in the balanced equation. The smallest result identifies the limiting reactant.

Is theoretical yield the same as actual yield?
No. Theoretical yield is the stoichiometric maximum under the calculation’s assumptions. Actual yield is the amount obtained and measured in practice, often lower because of incomplete reaction or product loss.

Can percent yield be over 100%?
A calculated value can exceed 100% if the collected sample contains impurities or retained liquid, or if measurements are inaccurate. It usually signals that the sample mass is not the mass of pure, correctly identified product.

Related

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

in n | Limiting reactant amount | mol | 0.1 | 0
in cr | Limiting reactant coefficient | - | 1 | 0
in cp | Product coefficient | - | 1 | 0
in mm | Product molar mass | g/mol | 180.156 | 0
out y | Theoretical yield | g | n * (cp / cr) * mm | 3