AI Tutor
If a pharmaceutical company needs to produce 100 kilograms of aspirin, simply buying 100 kilograms worth of starting chemicals guarantees failure.
Side reactions, incomplete conversions, and mechanical losses during filtration mean real chemical processes rarely produce all the product that balanced equations predict.
The theoretical yield is the maximum mass of product that could form if all limiting reactant converted perfectly into product, while the actual yield is the measured mass collected in the lab.
The ratio between what you actually isolate and what you theoretically calculated gives the percent yield:
Percent Yield=(Actual YieldTheoretical Yield)×100%\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%
When you know your reaction's typical efficiency, how do you work backward to figure out how much starting material to weigh out?

The Reverse Yield Calculation

To target a specific final mass of product (mactualm_{\text{actual}}) in a reaction with a fractional yield (%Y/100\%\text{Y}/100), your starting reactants must target an inflated required theoretical yield.
Rearranging the percent yield formula shows that you must divide the desired mass by the yield percentage:
mtheoretical=mactual(%Yield100)m_{\text{theoretical}} = \frac{m_{\text{actual}}}{\left( \frac{\%\text{Yield}}{100} \right)}
Let's synthesize aspirin (acetylsalicylic acid, C9H8O4\text{C}_9\text{H}_8\text{O}_4, M=180.16 g/molM = 180.16\text{ g/mol}) from salicylic acid (C7H6O3\text{C}_7\text{H}_6\text{O}_3, M=138.12 g/molM = 138.12\text{ g/mol}) and excess acetic anhydride:
C7H6O3+C4H6O3→C9H8O4+C2H4O2\text{C}_7\text{H}_6\text{O}_3 + \text{C}_4\text{H}_6\text{O}_3 \rightarrow \text{C}_9\text{H}_8\text{O}_4 + \text{C}_2\text{H}_4\text{O}_2