Reaction Yield

A real reaction always returns less than the calculation says it should. That fraction is the yield.

• $Y$ is the yield as a percentage
• $w$ is the mass actually obtained
• $w_0$ is the theoretical yield

The theoretical yield comes from the coefficients of the balanced equation, which the stoichiometry tool here will compute.

Why it is never 100 percent

Several losses stack up. Side reactions produce something other than the target. The reaction stops short and leaves starting material behind. Product clings to filter paper and glassware during purification. Recrystallisation leaves some dissolved in the mother liquor. None of these can be eliminated entirely.

Example

The default input has a theoretical yield of 50 g against an actual 38.5 g.

The yield is $38.5 \div 50 \times 100$, or 77 percent, with 11.5 g lost. For a single step that is a respectable figure.

Steps compound brutally

Here is the point worth internalising: yields multiply. Two steps at 77 percent give $0.77 \times 0.77$, or 59.29 percent. Three give 45.65 percent — already less than half.

Better yields fare no differently. An excellent 90 percent per step, run over ten steps, comes to $0.9^{10}$, only about 34.9 percent.

This is why total synthesis of a natural product is hard. Removing one step from a route is worth roughly as much as a large improvement in the yield of a single step, which is why chemists prize short routes so highly.

Points to watch

A yield above 100 percent means the measurement is wrong, not that the reaction over-performed. The product is impure, or incompletely dried and still holding solvent, or the balance reading is mistaken. Matter does not appear from nowhere.

An error in the theoretical yield carries straight through. Check that the equation is balanced and that the limiting reagent has been identified correctly before trusting the percentage.