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In a perfect chemistry world, every mole of limiting reagent would convert entirely to product. The mass calculated from the stoichiometric equation assumes this perfect outcome — the theoretical yield.
In reality, chemists almost never achieve the theoretical yield. Reasons include:
The mass actually obtained at the end of the experiment is the actual yield.
Percentage yield=theoretical yieldactual yield×100
Yields can also be calculated in moles:
Percentage yield=moles of product expectedmoles of product obtained×100
Note: percentage yield can never exceed 100%. If it does, the product has not been fully dried, or contains impurities, or there has been a weighing error. A yield over 100% is a sign the student should dry the product more thoroughly before weighing.
In the preparation of aspirin, 5.00 g of salicylic acid (Mr = 138.1) is converted into aspirin (Mr = 180.2). The experiment produces 4.82 g of pure aspirin. Calculate the percentage yield.
Equation: C₇H₆O₃ + (CH₃CO)₂O → C₉H₈O₄ + CH₃COOH
Step 1: Theoretical yield
Step 2: Percentage yield
% yield=6.5254.82×100=73.9%
The Haber process reacts hydrogen and nitrogen to form ammonia:
N₂(g) + 3H₂(g) → 2NH₃(g)
If 14.0 g of N₂ is reacted with excess H₂ and 12.8 g of NH₃ is obtained, calculate the percentage yield.
Theoretical yield:
Percentage yield:
% yield=17.012.8×100=75.3%
5.40 g of aluminium reacts with 16.0 g of bromine:
2Al + 3Br₂ → 2AlBr₃
The actual yield of AlBr₃ is 12.5 g. Calculate the percentage yield.
Find limiting reagent:
Theoretical yield of AlBr₃:
Percentage yield:
% yield=17.7912.5×100=70.3%
A three-step organic synthesis has yields of 80%, 70% and 60% at each step. Calculate the overall percentage yield.
Overall yield = 0.80 × 0.70 × 0.60 = 0.336 = 33.6%
This illustrates why multi-step syntheses suffer dramatic losses: even modest yields at each step multiply together. Pharmaceutical syntheses of 10+ steps may give overall yields of just a few per cent, making the drugs very expensive to produce.
Percentage yield measures how efficiently the limiting reagent is converted to product in a specific experiment. It says nothing about whether the equation itself is efficient — some reactions produce large amounts of by-product waste even at 100% yield. The concept of atom economy was introduced by Barry Trost in 1991 to quantify this. Trost's original paper argued that traditional yield metrics hid the inherent wastefulness of many classical synthetic reactions.
Atom economy=sum of Mr of all productsMr of desired product×100
Equivalently, for a balanced equation where we consider the total mass of products equals total mass of reactants (conservation of mass):
Atom economy=total Mr of all reactants (including coefficients)Mr of desired product×100
A high atom economy means most of the atoms from the reactants end up in the desired product, rather than in waste by-products.
Aspirin synthesis:
C₇H₆O₃ + (CH₃CO)₂O → C₉H₈O₄ + CH₃COOH
% atom economy=240.2180.2×100=75.0%
Industrial iron production in a blast furnace:
Fe₂O₃ + 3CO → 2Fe + 3CO₂
% atom economy=243.6111.6×100=45.8%
Over half the mass in the products is "wasted" CO₂ — an inherent inefficiency of carbon reduction. This is one reason why iron production is such a large source of CO₂ emissions globally.
CO + 2H₂ → CH₃OH
% atom economy=32.032.0×100=100%
Addition reactions with a single product always have 100% atom economy. This is ideal from a green chemistry perspective.
Titanium is extracted by the Kroll process:
TiCl₄(g) + 2Mg(l) → Ti(s) + 2MgCl₂(s)
% atom economy=238.547.9×100=20.1%
The extraction is atom-inefficient — for every tonne of titanium, 4 tonnes of waste MgCl₂ are produced. Recycling the MgCl₂ back to Mg and Cl₂ (by electrolysis) is essential for the economics and environmental impact of the process.
Ethanol is now mainly produced by hydration of ethene:
CH₂=CH₂ + H₂O → CH₃CH₂OH
Compare with the alternative fermentation route:
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
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