Topic 1 · page 8 of 10

Yield and atom economy

Percentage yield measures how well an experiment went. Atom economy measures how much of the reactants could ever end up in the product, and it comes from the equation alone.

10 min read1.9

Read first: Masses from equations

Percentage yield 1.9

The theoretical yield is the mass of product you would get if every bit of the limiting reactant turned into product. You calculate it with the three-step method. The actual yield is what you weigh at the end.

percentage yield=actual mass of producttheoretical mass of product×100% \text{percentage yield} = \frac{\text{actual mass of product}}{\text{theoretical mass of product}} \times 100\%

Worked exampleYield of iron

10.0 g of iron(III) oxide is reduced with carbon monoxide, and 5.60 g of iron is collected. Find the percentage yield.

FeX2OX3(s)+3 CO(g)→2 Fe(s)+3 COX2(g) \ce{Fe2O3(s) + 3CO(g) -> 2Fe(s) + 3CO2(g)}
  1. n(Fe₂O₃) = 10.0 ÷ 159.6 = 0.06266 mol
  2. n(Fe) = 2 × 0.06266 = 0.1253 mol
  3. Theoretical mass = 0.1253 × 55.8 = 6.99 g
  4. Percentage yield = 5.60 ÷ 6.99 × 100 = 80.1%

Yields are lower than 100% because:

Atom economy 1.9

atom economy=molar mass of the desired productsum of the molar masses of all products×100% \text{atom economy} = \frac{\text{molar mass of the desired product}}{\text{sum of the molar masses of all products}} \times 100\%

Use the balanced equation, and multiply each molar mass by its coefficient.

Worked exampleTwo ways to make ethanol

Route Equation Atom economy
hydration of ethene C₂H₄ + H₂O → C₂H₅OH 46.0 ÷ 46.0 × 100 = 100%
fermentation of glucose C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ 2(46.0) ÷ [2(46.0) + 2(44.0)] × 100 = 92.0 ÷ 180.0 × 100 = 51.1%

A useful check: by conservation of mass, the total mass of products equals the total mass of reactants. So you can use the sum of the reactant molar masses on the bottom instead, and get the same answer.

Why industry cares

A high atom economy means less waste, fewer by-products to separate, sell or dispose of, and better use of raw materials. It is one measure of how sustainable a process is. A by-product with a use (for example, selling CO₂) can make a low atom economy process more acceptable.

Yield and atom economy are different 1.9

Percentage yield Atom economy
Comes from an experiment the balanced equation alone
Measures how much product you actually got the most that could ever be product
Improved by better technique, conditions or catalysts choosing a different reaction

A reaction can have 100% atom economy and still a low yield, for example an addition reaction that reaches equilibrium before it is complete.

Check yourself

  1. 4.86 g of magnesium should give 8.06 g of magnesium oxide, but only 7.25 g is collected. Calculate the percentage yield.
  2. Calculate the atom economy for making hydrogen by steam reforming: CH₄ + H₂O → CO + 3H₂
  3. Calculate the atom economy for making iron: Fe₂O₃ + 3CO → 2Fe + 3CO₂
  4. Calcium oxide is made by heating calcium carbonate: CaCO₃ → CaO + CO₂. Calculate the atom economy. Suggest one way the process could be made less wasteful.
  5. 12.0 g of ethanoic acid (M = 60.0 g mol⁻¹) reacts with excess ethanol to give 12.3 g of ethyl ethanoate (M = 88.0 g mol⁻¹). The ratio is 1 : 1. Calculate the percentage yield.

Answers cover these until you have tried the questions

  1. 7.25 ÷ 8.06 × 100 = 90.0%
  2. Desired: 3(2.0) = 6.0. All products: 28.0 + 6.0 = 34.0. Atom economy = 6.0 ÷ 34.0 × 100 = 17.6%
  3. Desired: 2(55.8) = 111.6. All products: 111.6 + 3(44.0) = 243.6. Atom economy = 111.6 ÷ 243.6 × 100 = 45.8%
  4. 56.1 ÷ (56.1 + 44.0) × 100 = 56.0%. The CO₂ could be captured and sold or used, so it is no longer waste.
  5. n(acid) = 12.0 ÷ 60.0 = 0.200 mol, so the theoretical mass is 0.200 × 88.0 = 17.6 g. Yield = 12.3 ÷ 17.6 × 100 = 69.9%