Percent Yield

Overview

In real chemical reactions, the amount of product obtained is often less than the theoretical maximum. Percent yield compares the actual yield to the theoretical yield, measuring the efficiency of a reaction.

Key Definitions

Theoretical Yield

The maximum amount of product that could form based on stoichiometry and the limiting reagent. Calculated from balanced equation.

Actual Yield

The amount of product actually obtained from the experiment. Measured in the lab.

Percent Yield

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

Why Actual Yield < Theoretical Yield

1. Incomplete reactions - Not all reactants convert to products
2. Side reactions - Competing reactions form byproducts
3. Loss during transfer - Product left on equipment
4. Purification losses - Some product lost during isolation
5. Equilibrium limitations - Reversible reactions don't go to completion
6. Impure reactants - Starting materials contain contaminants

Calculation Steps

Step 1: Balance the equation

Step 2: Identify limiting reagent (if given multiple reactants)

Step 3: Calculate theoretical yield from stoichiometry

Step 4: Apply percent yield formula

Examples

Example 1: Basic Calculation

In a reaction, the theoretical yield of NaCl is 25.0 g. A student obtains 22.5 g.

$$\text{Percent Yield} = \frac{22.5 \text{ g}}{25.0 \text{ g}} \times 100\% = 90.0\%$$

Example 2: Complete Problem

Zinc reacts with hydrochloric acid:

$$\text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2$$

Given: 13.1 g Zn reacts, producing 24.5 g ZnCl₂

Step 1: Calculate theoretical yield

$$\text{mol Zn} = \frac{13.1 \text{ g}}{65.38 \text{ g/mol}} = 0.200 \text{ mol}$$ $$\text{mol ZnCl}_2 = 0.200 \text{ mol} \quad \text{(1:1 ratio)}$$ $$\text{Theoretical yield} = 0.200 \times 136.29 = 27.3 \text{ g}$$

Step 2: Calculate percent yield

$$\text{Percent Yield} = \frac{24.5}{27.3} \times 100\% = 89.7\%$$

Example 3: Finding Actual Yield

If the theoretical yield is 50.0 g and percent yield is 85%, what is the actual yield?

$$\text{Actual Yield} = \text{Theoretical Yield} \times \frac{\text{Percent Yield}}{100\%}$$ $$\text{Actual Yield} = 50.0 \text{ g} \times 0.85 = 42.5 \text{ g}$$

Example 4: Finding Theoretical Yield

A reaction has 75% yield and produces 30.0 g of product. What was the theoretical yield?

$$\text{Theoretical Yield} = \frac{\text{Actual Yield}}{\text{Percent Yield}/100\%}$$ $$\text{Theoretical Yield} = \frac{30.0 \text{ g}}{0.75} = 40.0 \text{ g}$$

Multi-Step Reactions

For reactions with multiple steps, the overall percent yield is the product of individual yields.

$$\text{Overall Yield} = (\text{Yield}_1 \times \text{Yield}_2 \times \text{Yield}_3 \times \cdots) \times 100\%$$

Example: Two-Step Synthesis

Step 1: 80% yield Step 2: 90% yield

$$\text{Overall} = 0.80 \times 0.90 \times 100\% = 72\%$$

Three-Step Synthesis

Each step has 90% yield:

$$\text{Overall} = 0.90^3 \times 100\% = 72.9\%$$

Percent Yield in Planning

How Much Reactant Is Needed?

If you need 50.0 g of product and expect 80% yield:

$$\text{Required theoretical yield} = \frac{\text{Desired amount}}{\text{Percent Yield}/100\%}$$ $$= \frac{50.0 \text{ g}}{0.80} = 62.5 \text{ g}$$

Then calculate reactant needed for 62.5 g product.

Atom Economy

Related concept measuring efficiency:

$$\text{Atom Economy} = \frac{\text{Mass of desired product}}{\text{Total mass of all products}} \times 100\%$$

Summary Table

Find	Formula
Percent Yield	$\frac{\text{Actual}}{\text{Theoretical}} \times 100\%$
Actual Yield	$\text{Theoretical} \times \frac{\%}{100}$
Theoretical Yield	$\frac{\text{Actual}}{\%/100}$
Overall Yield (multi-step)	$\text{Yield}_1 \times \text{Yield}_2 \times \cdots$