4.4 Reaction Yields

Reaction Yields and Limiting Reactants

In any chemical reaction, the amount of product you can actually make depends on which reactant runs out first and how efficiently the reaction proceeds. This section covers how to identify the limiting reactant, calculate theoretical and percent yields, and understand why actual yields fall short.

Limiting Reactants and Theoretical Yield

The limiting reactant is the reactant that gets completely used up first in a reaction. Once it's gone, the reaction stops, no matter how much of the other reactants remain. Those leftover reactants are called excess reactants.

Think of it like making sandwiches: if you have 10 slices of bread and 3 slices of cheese, the cheese limits you to 3 sandwiches. The bread is in excess.

To figure out which reactant is limiting, you compare the mole amounts you actually have to the mole ratio from the balanced equation. Here's the process:

1. Convert the mass of each reactant to moles (using molar mass).
2. Divide each reactant's moles by its coefficient in the balanced equation.
3. The reactant with the smallest value from step 2 is the limiting reactant.

For example, in the reaction $2H_2 + O_2 \rightarrow 2H_2O$, hydrogen and oxygen react in a 2:1 mole ratio. If you have 3 mol of $H_2$ and 2 mol of $O_2$, dividing gives $3/2 = 1.5$ for hydrogen and $2/1 = 2$ for oxygen. Hydrogen is the limiting reactant because 1.5 is smaller.

Calculation of Chemical Yields

Theoretical yield is the maximum amount of product you could possibly get, assuming the limiting reactant converts perfectly with no losses. You calculate it using stoichiometry:

1. Start with the moles of the limiting reactant.
2. Use the mole ratio from the balanced equation to find moles of product.
3. Convert moles of product to grams (using the product's molar mass).

$\text{Theoretical Yield} = \text{Moles of Limiting Reactant} \times \frac{\text{Coefficient of Product}}{\text{Coefficient of Limiting Reactant}} \times \text{Molar Mass of Product}$

Actual yield is the amount of product you actually collect in the lab. It's almost always less than the theoretical yield.

Percent yield tells you how efficient the reaction was by comparing actual to theoretical:

$\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

For example, if your theoretical yield is 48 g of NaOH but you only collect 42 g, your percent yield is:

$\frac{42}{48} \times 100\% = 87.5\%$

A percent yield above 100% usually signals an error, like impurities in your product adding extra mass or a measurement mistake.

Factors Affecting Actual Yield

Several things can cause your actual yield to fall below the theoretical yield:

• Incomplete reactions occur when not all of the limiting reactant converts to product. Some reactions reach equilibrium before going to completion, meaning both reactants and products coexist. The Haber process ($N_2 + 3H_2 \rightleftharpoons 2NH_3$) is a classic example.
• Side reactions use up reactants to form unwanted byproducts. For instance, a reaction meant to produce $CO_2$ might also generate some $CO$.
• Impurities in your starting materials mean that not all of the measured mass is actually the reactant you need, so fewer moles are available to react.
• Product loss during purification is common. Techniques like filtration and recrystallization inevitably leave some product behind on glassware or in solution.
• Experimental errors such as inaccurate measurements, spills, or incorrect temperature settings also reduce yield.

Green Chemistry and Reaction Efficiency

Atom economy measures what fraction of the atoms in your reactants end up in the desired product (rather than in waste byproducts):

$\text{Atom Economy} = \frac{\text{Molar Mass of Desired Product}}{\text{Total Molar Mass of All Products}} \times 100\%$

A reaction can have a high percent yield but low atom economy if it efficiently produces a lot of waste byproduct. Ideally, you want both values to be high.

Mass balance is the principle that total mass is conserved: the mass of all reactants equals the mass of all products (including byproducts). This follows directly from the law of conservation of mass and is useful for tracking where atoms end up.

Green chemistry applies these ideas to design processes that minimize waste and environmental harm. The goal is to maximize both atom economy and percent yield so that reactions use fewer resources and generate less waste.