Limiting Reactants and Theoretical Yields

Introduction

In chemical reactions, the concept of limiting reactants and theoretical yields is essential for predicting the amount of product that can be formed. These concepts are fundamental in stoichiometry and are widely applied in laboratory and industrial chemistry.

Limiting Reactant

Definition and Analogy

• Limiting Reactant: The reactant that is completely consumed first in a chemical reaction, thus limiting the amount of product that can be formed.

• Excess Reactant: The reactant(s) that remain after the limiting reactant is used up.

• Analogy: Making sandwiches: If each sandwich requires 2 slices of bread and 1 slice of cheese, the number of sandwiches you can make is limited by whichever ingredient runs out first.

Example: If you have 28 slices of bread and 17 slices of cheese, you can make 14 sandwiches (since 2 slices of bread per sandwich). Bread is the limiting reactant.

Identifying the Limiting Reactant

• Write the balanced chemical equation for the reaction.

• Convert all given quantities (mass, volume, moles) to moles.

• Calculate the mole ratio from the balanced equation.

• Determine which reactant will produce the least amount of product; this is the limiting reactant.

Worked Example: Hydrogen and Oxygen Reaction

• Reaction:

• Given: 14 mol , 4 mol

• Calculation:

  • From the balanced equation, 2 mol reacts with 1 mol .

  • 14 mol would require 7 mol to react completely, but only 4 mol $O_2$ is available.

  • Limiting reactant:

  • All 4 mol will react with 8 mol (since ratio).

  • Product formed: mol

  • Excess remaining: mol

Theoretical Yield

Definition

• Theoretical Yield: The maximum amount of product that can be formed from the limiting reactant, as calculated from the balanced chemical equation.

• Actual Yield: The amount of product actually obtained from a reaction.

• Percent Yield: The ratio of actual yield to theoretical yield, expressed as a percentage.

Formula:

Worked Example: Sandwich Analogy (Mass-Based)

• Given: 160 g cheese, 500 g bread; 2 slices bread + 1 slice cheese = 1 sandwich

• Assume: 1 slice bread = 25 g, 1 slice cheese = 20 g (Additional info: typical values for calculation)

• Number of bread slices: slices

• Number of cheese slices: slices

• Maximum sandwiches: Limited by cheese (8 slices), so 8 sandwiches can be made.

Stoichiometric Calculations with Limiting Reactants

General Steps

1. Write the balanced chemical equation.

2. Convert all reactant quantities to moles.

3. Use mole ratios to determine the limiting reactant.

4. Calculate the theoretical yield of product (in moles or grams).

5. Calculate the amount of excess reactant remaining.

Worked Example: Iron(III) Sulfide and Hydrobromic Acid

• Reaction:

• Given: 4.24 mol , 14.5 mol

• Limiting Reactant Calculation:

  • 1 mol requires 6 mol

  • 4.24 mol would require mol

  • Only 14.5 mol is available, so $HBr$ is the limiting reactant.

  • Amount of that reacts: mol

  • Excess remaining: mol

  • Mass remaining: mol molar mass of

Worked Example: Ammonia Synthesis

• Reaction:

• Given: 15.12 g , 33.62 g

• Convert to moles:

  • Moles : mol

  • Moles : mol

• Limiting Reactant:

  • 1 mol requires 3 mol

  • 1.20 mol would require mol

  • 7.50 mol is available, so is the limiting reactant.

  • Theoretical yield of : mol

  • Mass of : g

  • Excess remaining: mol ( g)

Percent Yield

Definition and Calculation

• Percent Yield: A measure of the efficiency of a reaction, calculated as the ratio of actual yield to theoretical yield.

• Formula:

Worked Example: Chloroethane Synthesis

• Reaction: (simplified for illustration)

• Given: 100 g , 100 g ; actual yield = 150 g

• Steps:

  • Convert reactants to moles:

  • Moles : mol

  • Moles : mol

  • From the equation, 1:1 ratio; is limiting reactant (1.41 mol)

  • Theoretical yield of : 1.41 mol 64.51 g/mol = 91.0 g

  • Percent yield: (Note: This is over 100%, which suggests a calculation or measurement error; in practice, percent yield should not exceed 100%)

Summary Table: Key Terms and Formulas

Additional info:

• Some molar masses and slice weights in the sandwich analogy were inferred for calculation purposes.

• Percent yield should not exceed 100% in practice; values above 100% indicate experimental or calculation errors.