Reaction yield and sample purity
yield = obtained / theoretical × 100
The yield of a synthesis is computed in three directions that are easily confused: measuring it afterwards, predicting what you will recover, or sizing what theory must predict to obtain a wanted amount. The tool asks which of the three, then returns the percentage, the missing amount and, if you give the product formula, its molar mass and your amounts converted into moles. A fourth mode computes the purity of a sample. A yield above 100% is shown as is with its warning, never rounded down to 100: that value is precisely what tells you what went wrong.
50 %
- Calculation
- yield = obtained / theoretical × 100 = 9.01 / 18.02 × 100 = 50%
180.159 g/mol
- Theoretical amount in moles
- 0.100023
- Amount obtained in moles
- 0.0500114
The yield is 50%. 9.01 is missing against the prediction.
Both amounts must be in the same unit: the ratio keeps none, and comparing grams to moles would give a meaningless number.
Mass yield and molar yield are equal as long as the same substance is meant, the molar mass cancelling in the ratio. They differ as soon as a reagent is compared to a product.
A yield below 100% is not a mistake: part of the product stays in the mother liquor, sticks to the glass, or is lost to filtration and recrystallisation. Over a multi-step synthesis, yields multiply, which is why a run of good steps gives a poor total.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasyield = obtained / theoretical × 100
yield = obtained / theoretical × 100
obtained = theoretical × yield / 100
theoretical = obtained × 100 / yield
purity = pure mass / sample mass × 100
n = m / M
The first three lines are one equation, solved in turn for each of its three unknowns. That is why the mode is an explicit choice rather than a deduction: the number "80%" does not say by itself whether it is a measurement or a working assumption, and a tool that guessed would be wrong half the time.
- Theoretical amount
- · what stoichiometry predicts from the limiting reagent, assuming the reaction goes to completion.
- Amount obtained
- · what the balance gives after purification and drying.
- Yield
- · the ratio of the two, as a percentage. Unitless: both amounts must share the same unit.
- Purity
- · the share of the weighed mass that really is the wanted product; the rest is solvent, water or impurity.
- M
- · molar mass of the product, in g/mol, computed from its formula.
Validity domainThe theoretical amount must come from the limiting reagent, the one that runs out first: computing it on a reagent in excess gives a falsely low yield.
The theoretical amount must come from the limiting reagent, the one that runs out first: computing it on a reagent in excess gives a falsely low yield. Both amounts must share the same unit, the ratio keeping none. A yield above 100% is physically impossible and the tool does not correct it: it shows it with its three ordinary causes, a damp product, a weighing including its support, or a theoretical amount computed on the wrong reagent. A yield entered as data, however, is refused above 100%, because the prediction drawn from it would mean nothing. The molar mass used is that of the IUPAC standard atomic weights, with the tool convention for the fourteen interval elements.
Reading the resultA yield below 100% is not a mistake: part of the product stays in the mother liquor, sticks to the glass, or is lost to filtration and recrystallisation.
A yield below 100% is not a mistake: part of the product stays in the mother liquor, sticks to the glass, or is lost to filtration and recrystallisation. The figure worth remembering on a multi-step synthesis is that yields multiply: three steps at 80% do not make 80% but 51%. Mass yield and molar yield coincide as long as the same substance is meant, the molar mass cancelling in the ratio; they diverge as soon as a reagent is compared to a product.