3.4 Theoretical Yield, Actual Yield and Percent Yield

Introduction

In chemistry, when we carry out a reaction, we often want to know how much product we should get and how much product we actually get.

• The amount we calculate from the balanced equation is the theoretical yield.
• The amount we actually obtain in the lab or industry is the actual yield.
• The percentage yield tells us how efficient the reaction was.

Understanding these three quantities is important in:

• Industry — to measure efficiency and reduce costs
• Laboratory work — to evaluate experimental success
• Research — to compare different methods and conditions

Definition

Theoretical Yield: The amount of product as calculated from a balanced chemical equation is known as the theoretical yield of a chemical reaction.

Actual Yield: The actual yield is the amount of product actually produced in the reaction.

Percentage Yield: The percent yield of a chemical reaction is calculated as:

Percentage Yield = Actual YieldTheoretical Yield × 100

In simple words:

• Theoretical yield = what you should get (calculated).
• Actual yield = what you actually get (measured).
• Percentage yield = how close you got to the theoretical yield.

Main Idea

• Theoretical yield is calculated from the balanced equation using stoichiometry.
• Actual yield is measured experimentally.
• Percentage yield compares the actual yield to the theoretical yield.
• For many reactions, the theoretical yield is close to the actual yield. These reactions are quantitative and can be used for chemical analysis.
• For some reactions, the actual yield is below the theoretical yield, and the percent yield is less than 100%.

Core Concept

The relationship between the three quantities is:

Percentage Yield = Actual YieldTheoretical Yield × 100

Key point:

• If actual yield = theoretical yield → percentage yield = 100%.
• If actual yield < theoretical yield → percentage yield < 100%.
• In practice, percentage yield is often less than 100%.

Detailed Explanation

Why Actual Yield is Often Less Than Theoretical Yield

For some reactions, the actual yield is below the theoretical yield, and the percent yield is less than 100%. This is because of the following reasons:

• The reactants may react in a different way than expected, producing unwanted substances.
• This reduces the amount of the desired product.

• The reaction may not go to completion.
• Some product may convert back to reactants.

3. Mechanical loss can occur as a result of filtration or distillation. - Some product may be lost during separation and purification steps.

4. Separation by a funnel, washing or crystallization can also cause mechanical loss. - Product may remain on filter paper, in the flask, or be lost during washing.

Key point: Percentage yield is rarely 100% because of side reactions, reversibility, and mechanical losses.

Reactions That Are Quantitative

For many reactions, the theoretical yield is close to the actual yield. These reactions are quantitative and can be used for chemical analysis.

Examples:

• Acid-base titrations
• Precipitation reactions used in gravimetric analysis

Key point: Quantitative reactions are useful for determining the amount of a substance in a sample.

How to Calculate Percentage Yield

Step 1: Calculate the theoretical yield from the balanced equation.

Step 2: Measure the actual yield experimentally.

Step 3: Use the formula:

Percentage Yield = Actual YieldTheoretical Yield × 100

Step 4: Check that the percentage yield is less than or equal to 100%.

Intermediate Level

Why percentage yield is less than 100%:

• Side reactions — reactants may form unwanted by-products.
• Reversible reactions — reaction may not go to completion.
• Mechanical loss — product lost during filtration, distillation, washing, or crystallization.

Key point: Percentage yield is a measure of the efficiency of a reaction.

How to calculate:

• Find the theoretical yield from the balanced equation.
• Measure the actual yield.
• Use the formula.

Example: Copper from CuSO₄:

• Theoretical yield = 0.5072 g
• Actual yield = 0.392 g
• % yield = 0.3920.5072 × 100 = 77.3\%

Formula / Mathematical Form

Percentage Yield = Actual YieldTheoretical Yield × 100

Where:

• Actual Yield = amount of product actually obtained (g or mol)
• Theoretical Yield = amount of product calculated from the balanced equation (g or mol)

Key point: Both yields must be in the same units (both in grams or both in moles).

Solved Example

Example 3.5

In an industry, copper metal was prepared by the following reaction:

Fe_(s) + CuSO_4(aq) → FeSO_4(aq) + Cu_(s)

1.274 g of CuSO₄ when reacted with excess of Fe metal, a yield of 0.392 g of Cu metal is obtained. Calculate the percentage yield.

Solution:

Given: Mass of CuSO₄ = 1.274\ g Actual yield of Cu = 0.392\ g

Molar mass of CuSO₄:

= 63.5 + 32 + (4 × 16) \] \[ = 63.5 + 32 + 64 = 159.5\ g/mol

Number of moles of CuSO₄:

n = 1.274159.5 = 7.982 × 10^-3\ mol

From the balanced equation:

1\ mol of CuSO₄ = 1\ mol of Cu

7.982 × 10^-3\ moles of CuSO₄ = 7.982 × 10^-3\ mol of Cu

Theoretical yield of Cu:

Mass = moles × molar mass

= 7.982 × 10^-3 × 63.5

= 0.5072\ g

Theoretical yield = 0.5072\ g

Actual yield = 0.392\ g

Percentage yield:

\%\ yield = Actual yieldTheoretical yield × 100

= 0.3920.5072 × 100

= 77.3\%

Final Answer: The percentage yield is 77.3%.

Concept Assessment Exercise 3.6

1. In a reaction, 2.00 moles of CH₄ were reacted with an excess of Cl₂. As a result, 177.0 g of CCl₄ is obtained. What is the (a) theoretical yield (b) actual yield (c) % yield of this reaction?

CH_4(g) + 4Cl_2(g) → CCl_4(g) + 4HCl_(g)

Solution:

Moles of CH₄ = 2.00 mol

From the equation:

1\ mol CH₄ → 1\ mol CCl₄

2.00\ mol CH₄ → 2.00\ mol CCl₄

Molar mass of CCl₄:

= 12 + (4 × 35.5) = 12 + 142 = 154\ g/mol

(a) Theoretical yield:

= 2.00 × 154 = 308\ g

(b) Actual yield:

= 177.0\ g

(c) Percentage yield:

\%\ yield = 177.0308 × 100 = 57.47\%

Answer: (a) Theoretical yield = 308 g (b) Actual yield = 177.0 g (c) Percentage yield = 57.47%

2. Phosphorus reacts with bromine to form phosphorus tribromide. When 35 g of bromine is reacted with 27.9 g of phosphorus tribromide is produced. What is the (a) theoretical yield (b) actual yield (c) % yield of this reaction?

2P_(s) + 3Br_2(l) → 2PBr_3(s)

Solution:

Moles of Br₂:

n = 35160 = 0.21875\ mol

From the equation:

3\ mol Br₂ → 2\ mol PBr₃

0.21875\ mol Br₂ → 23 × 0.21875 = 0.1458\ mol PBr₃

Molar mass of PBr₃:

= 31 + (3 × 80) = 31 + 240 = 271\ g/mol

(a) Theoretical yield:

= 0.1458 × 271 = 39.5\ g

(b) Actual yield:

= 27.9\ g

(c) Percentage yield:

\%\ yield = 27.939.5 × 100 = 70.6\%

Answer: (a) Theoretical yield = 39.5 g (b) Actual yield = 27.9 g (c) Percentage yield = 70.6%

Summary Table

Important Points

• - Theoretical yield = amount of product calculated from the balanced equation.
• - Actual yield = amount of product actually produced in the reaction.
• - Percentage yield = (Actual Yield/Theoretical Yield) × 100.
• - Percentage yield is often less than 100% because of:
• - side reactions
• - reversible reactions
• - mechanical loss during filtration, distillation, washing, or crystallization
• - For many reactions, theoretical yield is close to actual yield. These are quantitative reactions.
• - Percentage yield measures the efficiency of a reaction.
• - Both actual and theoretical yields must be in the same units.

Remember

• - Theoretical yield = calculated from equation.
• - Actual yield = measured in lab.
• - % yield = (Actual/Theoretical) × 100.
• - % yield is usually less than 100%.
• - Reasons: side reactions, reversible reactions, mechanical loss.
• - Quantitative reactions: theoretical ≈ actual.
• - % yield measures efficiency.
• - Same units for actual and theoretical.

Common Mistakes

Quick Revision

• Theoretical Yield:
• The amount of product as calculated from a balanced chemical equation is known as the theoretical yield of a chemical equation.

• Actual Yield:
• The actual yield is the amount of product actually produced in the reaction.

Percentage Yield:

• Percentage Yield = Actual YieldTheoretical Yield × 100

Why Percentage Yield is Less Than 100%:

• Side reactions may result in by-products.
• Some reactions may be reversible.
• Mechanical loss can occur as a result of filtration or distillation.
• Separation by a funnel, washing or crystallization can also cause mechanical loss.

• Quantitative Reactions:
• For many reactions, the theoretical yield is close to the actual yield. These reactions are quantitative and can be used for chemical analysis.

60-Second Revision

• Theoretical yield = calculated from balanced equation.
• Actual yield = measured in lab.
• % yield = (Actual/Theoretical) × 100.
• % yield is usually less than 100%.
• Reasons: side reactions, reversible reactions, mechanical loss.
• Quantitative reactions: theoretical ≈ actual.
• % yield measures efficiency.
• Limiting reactant determines theoretical yield.
• ⚠️ Warning: percentage yield cannot exceed 100% (unless there is an error in measurement or calculation).