Limiting reactants and yield
Reactions rarely use exact proportions. The reactant that runs out first limits how much product can form.
The limiting reactant
The limiting reactant is completely used up first and determines the maximum amount of product. The other is in excess. Making sandwiches with 10 slices of bread and 3 slices of cheese (2 bread + 1 cheese each) gives 3 sandwiches: cheese is limiting, and 4 bread slices are left over.
Finding the limiting reactant
Convert each reactant to moles, then use the mole ratio to see how much product each could make. The one giving less product is limiting. Alternatively, compare the available mole ratio with the required ratio.
Worked example
For \(2\text{H}_2 + \text{O}_2 \to 2\text{H}_2\text{O}\), you have 4.0 g \(\text{H}_2\) (2.0 mol) and 48.0 g \(\text{O}_2\) (1.5 mol). Hydrogen could make 2.0 mol water; oxygen could make 3.0 mol. Hydrogen is limiting, giving 2.0 mol (36.0 g) water, with 0.5 mol \(\text{O}_2\) left over.
Theoretical yield
The theoretical yield is the maximum product calculated from the limiting reactant, assuming perfect conversion. It is the benchmark against which real results are judged.
Percent yield
Actual yields are usually lower because of side reactions, incomplete reactions, and losses during purification. Percent yield \(= \frac{\text{actual}}{\text{theoretical}} \times 100\%\). If a reaction should give 36.0 g but gives 30.6 g, the percent yield is 85%.
\text{percent yield} = \frac{\text{actual}}{\text{theoretical}} \times 100\%Atom economy and green chemistry
Atom economy measures what fraction of reactant mass ends up in the desired product. Green chemistry designs reactions with high atom economy and less waste, which matters enormously in pharmaceutical and industrial manufacturing, where waste can outweigh product many times over.
Multi-step syntheses
Yields multiply across steps. A five-step synthesis with 80% yield at each step has an overall yield of \(0.8^5 \approx 33\%\). This is why chemists work hard to shorten routes and improve every step.
Common mistakes
Choosing the limiting reactant by smallest mass instead of by moles and ratios. Calculating theoretical yield from the excess reactant. Reporting percent yields over 100%, which signals errors such as wet or impure product.
Key takeaways
The limiting reactant runs out first and sets the theoretical yield; compare moles using the balanced equation. Percent yield compares actual with theoretical. Atom economy and step counts matter for efficient, greener chemistry.
Flashcard
Used up first
Check your understanding
A reaction's theoretical yield is 50.0 g and 42.0 g is obtained. The percent yield is: