Limiting reactant calculator
Type a reaction and the amounts you have; leave a reactant blank if it is in excess.
How the limiting reactant is found
The calculator first balances the equation exactly (the same engine as the Equation balancer); if the equation cannot be balanced, or balances in more than one way, it stops and says so, because amounts cannot be compared without a single recipe. Then, for each reactant you give:[1]
- the amount is converted to moles: n = m/M, using the molar mass from the Molar mass calculator;
- the moles are divided by the reactant's coefficient ν, giving the number of times the recipe could run on that reactant alone;
- the smallest of these is the limiting reactant, and its value is how far the reaction can go, the extent of reaction ξ (defined by dn = ν dξ).[2]
Every product then forms ν × ξ moles (its theoretical yield), every reactant uses ν × ξ moles, and what remains of the others is left over. The working shows the chain of conversion factors from the limiting reactant to each product. A blank amount means that reactant is in excess. An actual yield gives the percent yield, actual ÷ theoretical × 100 %.
Precision and close calls
Arithmetic is exact (fractions, never floating point) until the final display. Each result is rounded to the significant figures of the least precise number it depends on: your amounts, and molar masses to their tabulated precision; coefficients and the Avogadro constant are exact.[1][3] A whole number typed without a decimal point (2, 16, 100) is read as three significant figures, as textbook problems usually intend; type 2.0 or 16. to say exactly how many. Every rounded yield is shown beside its value before rounding, and amounts left over follow the subtraction rule, keeping only the decimal places both numbers share.
When two reactants supply nearly the same number of batches, the last digit of a measurement can decide which runs out. The calculator checks this exactly: if moving any amount by half a unit in its last significant digit could make another reactant limiting, it says “close call” and names it. The answer it gives is still exact for the numbers as typed.
Valid range and assumptions
Amounts from 10−9 g to 109 g, or 10−12 mol to 107 mol, with at most 12 significant figures. Electrons cannot be weighed, so equations containing e− are refused here. The calculation assumes the reaction goes to completion as written, with no side reactions and pure reactants; the theoretical yield is an upper bound, not a prediction.
Worked examples
| Reaction and amounts | Limiting | Theoretical yield |
|---|---|---|
| 2H2 + O2 → 2H2O; 10.0 g H2, 10.0 g O2 | O2 | 11.3 g H2O (8.74 g H2 left) |
| 3Si + 2N2 → Si3N4; 2.00 g Si, 1.50 g N2 | Si | 0.0237 mol Si3N4 |
| CH4 + 2O2 → CO2 + 2H2O; 16.0 g CH4, 48.0 g O2 | O2 | 33.0 g CO2, 27.0 g H2O |
| CuSO4 + Zn → Cu + ZnSO4; 1.274 g CuSO4, excess Zn; 0.392 g Cu collected | CuSO4 | 0.5073 g Cu; 77.3 % yield |
The silicon nitride and copper examples are OpenStax's worked examples 4.12 and 4.13; the copper theoretical yield differs from OpenStax's 0.5072 g in the last digit because the calculator divides by the molar mass as displayed, 159.60 g/mol (the unrounded 159.602 gives 0.5072 g).[1]
Sources
- (2019). Chemistry 2e. OpenStax, Rice University. book §1.5 Measurement uncertainty, accuracy, and precision; §3.1 Formula mass and the mole concept; §4.1 Writing and balancing chemical equations; §4.3 Reaction stoichiometry; §4.4 Reaction yields.
- (2019). extent of reaction, ξ. International Union of Pure and Applied Chemistry. doi:10.1351/goldbook.E02283. standard
- (2019). The International System of Units (SI), 9th edition. BIPM. standard Section 2.3.1, the mole; the molar mass of carbon 12 after the 2019 redefinition.