Limiting Reagent and Theoretical Yield Calculator (Synthesis / Biochemical Reactions)

Core Formulas and Derivation

Step 1: Convert mass to moles

Moles of reactant i:

n_i = m_i / MW_i

m_i is the mass used (g), MW_i is the molar mass (g/mol).

Step 2: Calculate “available equivalents” and identify the limiting reagent

A chemical reaction proceeds according to the molar ratios in the balanced equation. For reactant i with stoichiometric coefficient ν_i, the number of reaction “equivalents” it can support is:

equivalents_i = n_i / ν_i

The reactant with the smallest equivalents value is the limiting reagent — it is consumed first and sets the upper limit on product yield.

limiting reagent = argmin_i (n_i / ν_i)

Intuition: For the reaction A + 2B → C, each 1 mol A requires 2 mol B. If you have 0.01 mol A and 0.015 mol B, available equivalents for B = 0.015/2 = 0.0075, less than A’s 0.01/1 = 0.01, so B is the limiting reagent — it can support only 0.0075 equivalents of reaction.

Step 3: Calculate theoretical yield

With ν_P as the product’s stoichiometric coefficient and MW_P as its molar mass:

n_P = min_i(n_i / ν_i) × ν_P
m_P(g) = n_P × MW_P

Step 4 (optional): Percent yield

Compare the mass of isolated product m_actual (g) to the theoretical value:

% yield = (m_actual / m_P) × 100

Worked Example: Aspirin Synthesis

The default values in this tool come from this classic teaching experiment. Balanced equation (all stoichiometric coefficients equal 1):

Salicylic acid  +  Acetic anhydride  →  Aspirin  +  Acetic acid
(MW 138.12)        (MW 102.09)          (MW 180.16)

Using 1.00 g salicylic acid and 2.00 g acetic anhydride:

Salicylic acid has the smaller available equivalents and is the limiting reagent.

Theoretical yield = 0.007240 mol × 180.16 g/mol = 1.304 g

If 0.85 g of pure product is isolated, percent yield = 0.85 / 1.304 × 100 = 65.2%, within the normal range for this experiment (60–80%).

Scope and Assumptions

• Two reactants: The form supports two reactants and one product, covering the vast majority of single-step laboratory syntheses. For three or more reactants, compare all n_i/ν_i values individually — the method is identical; extend manually.
• Single-step, unidirectional reaction: Not applicable to cascade reactions, reversible equilibria, or multi-step transformations.
• 100% selectivity assumed: Side reactions are not accounted for. A percent yield below 100% is normal; if it exceeds 100%, the product contains impurities or there is a weighing error, not a calculation error.
• Units: The tool uses g and g/mol throughout. If your data are in mmol, convert first: m(g) = n(mmol) × MW / 1000.

Common Mistakes

Mistake 1: Comparing masses directly to judge excess. “2 g acetic anhydride is more than 1 g salicylic acid, so acetic anhydride is in excess” — this only holds when both reagents have identical molar masses. The correct approach is to divide each mass by its molar mass before comparing.

Mistake 2: Omitting the stoichiometric coefficient. If the equation is A + 2B → C, the moles of B must be divided by 2 before comparing with moles of A on the same basis; skipping this step overestimates the available amount of B by a factor of two.

Mistake 3: Equating percent yield with reaction conversion. A low yield can arise from incomplete reaction, side reactions, or mechanical losses during workup (filtration mother liquors, aqueous layers in extraction, product dissolution in solvent). Percent yield alone cannot distinguish between these causes.