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Introductory Chemistry - 1st Canadian Edition: Limiting Reagents

Introductory Chemistry - 1st Canadian Edition
Limiting Reagents
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table of contents
  1. Cover
  2. Title Page
  3. Copyright
  4. Table Of Contents
  5. Acknowledgments
  6. Dedication
  7. About BCcampus Open Education
  8. Chapter 1. What is Chemistry
    1. Some Basic Definitions
    2. Chemistry as a Science
  9. Chapter 2. Measurements
    1. Expressing Numbers
    2. Significant Figures
    3. Converting Units
    4. Other Units: Temperature and Density
    5. Expressing Units
    6. End-of-Chapter Material
  10. Chapter 3. Atoms, Molecules, and Ions
    1. Acids
    2. Ions and Ionic Compounds
    3. Masses of Atoms and Molecules
    4. Molecules and Chemical Nomenclature
    5. Atomic Theory
    6. End-of-Chapter Material
  11. Chapter 4. Chemical Reactions and Equations
    1. The Chemical Equation
    2. Types of Chemical Reactions: Single- and Double-Displacement Reactions
    3. Ionic Equations: A Closer Look
    4. Composition, Decomposition, and Combustion Reactions
    5. Oxidation-Reduction Reactions
    6. Neutralization Reactions
    7. End-of-Chapter Material
  12. Chapter 5. Stoichiometry and the Mole
    1. Stoichiometry
    2. The Mole
    3. Mole-Mass and Mass-Mass Calculations
    4. Limiting Reagents
    5. The Mole in Chemical Reactions
    6. Yields
    7. End-of-Chapter Material
  13. Chapter 6. Gases
    1. Pressure
    2. Gas Laws
    3. Other Gas Laws
    4. The Ideal Gas Law and Some Applications
    5. Gas Mixtures
    6. Kinetic Molecular Theory of Gases
    7. Molecular Effusion and Diffusion
    8. Real Gases
    9. End-of-Chapter Material
  14. Chapter 7. Energy and Chemistry
    1. Formation Reactions
    2. Energy
    3. Stoichiometry Calculations Using Enthalpy
    4. Enthalpy and Chemical Reactions
    5. Work and Heat
    6. Hess’s Law
    7. End-of-Chapter Material
  15. Chapter 8. Electronic Structure
    1. Light
    2. Quantum Numbers for Electrons
    3. Organization of Electrons in Atoms
    4. Electronic Structure and the Periodic Table
    5. Periodic Trends
    6. End-of-Chapter Material
  16. Chapter 9. Chemical Bonds
    1. Lewis Electron Dot Diagrams
    2. Electron Transfer: Ionic Bonds
    3. Covalent Bonds
    4. Other Aspects of Covalent Bonds
    5. Violations of the Octet Rule
    6. Molecular Shapes and Polarity
    7. Valence Bond Theory and Hybrid Orbitals
    8. Molecular Orbitals
    9. End-of-Chapter Material
  17. Chapter 10. Solids and Liquids
    1. Properties of Liquids
    2. Solids
    3. Phase Transitions: Melting, Boiling, and Subliming
    4. Intermolecular Forces
    5. End-of-Chapter Material
  18. Chapter 11. Solutions
    1. Colligative Properties of Solutions
    2. Concentrations as Conversion Factors
    3. Quantitative Units of Concentration
    4. Colligative Properties of Ionic Solutes
    5. Some Definitions
    6. Dilutions and Concentrations
    7. End-of-Chapter Material
  19. Chapter 12. Acids and Bases
    1. Acid-Base Titrations
    2. Strong and Weak Acids and Bases and Their Salts
    3. Brønsted-Lowry Acids and Bases
    4. Arrhenius Acids and Bases
    5. Autoionization of Water
    6. Buffers
    7. The pH Scale
    8. End-of-Chapter Material
  20. Chapter 13. Chemical Equilibrium
    1. Chemical Equilibrium
    2. The Equilibrium Constant
    3. Shifting Equilibria: Le Chatelier’s Principle
    4. Calculating Equilibrium Constant Values
    5. Some Special Types of Equilibria
    6. End-of-Chapter Material
  21. Chapter 14. Oxidation and Reduction
    1. Oxidation-Reduction Reactions
    2. Balancing Redox Reactions
    3. Applications of Redox Reactions: Voltaic Cells
    4. Electrolysis
    5. End-of-Chapter Material
  22. Chapter 15. Nuclear Chemistry
    1. Units of Radioactivity
    2. Uses of Radioactive Isotopes
    3. Half-Life
    4. Radioactivity
    5. Nuclear Energy
    6. End-of-Chapter Material
  23. Chapter 16. Organic Chemistry
    1. Hydrocarbons
    2. Branched Hydrocarbons
    3. Alkyl Halides and Alcohols
    4. Other Oxygen-Containing Functional Groups
    5. Other Functional Groups
    6. Polymers
    7. End-of-Chapter Material
  24. Chapter 17. Kinetics
    1. Factors that Affect the Rate of Reactions
    2. Reaction Rates
    3. Rate Laws
    4. Concentration–Time Relationships: Integrated Rate Laws
    5. Activation Energy and the Arrhenius Equation
    6. Reaction Mechanisms
    7. Catalysis
    8. End-of-Chapter Material
  25. Chapter 18. Chemical Thermodynamics
    1. Spontaneous Change
    2. Entropy and the Second Law of Thermodynamics
    3. Measuring Entropy and Entropy Changes
    4. Gibbs Free Energy
    5. Spontaneity: Free Energy and Temperature
    6. Free Energy under Nonstandard Conditions
    7. End-of-Chapter Material
  26. Appendix A: Periodic Table of the Elements
  27. Appendix B: Selected Acid Dissociation Constants at 25°C
  28. Appendix C: Solubility Constants for Compounds at 25°C
  29. Appendix D: Standard Thermodynamic Quantities for Chemical Substances at 25°C
  30. Appendix E: Standard Reduction Potentials by Value
  31. Glossary
  32. About the Authors
  33. Versioning History

Limiting Reagents

Learning Objectives

  1. Identify a limiting reagent from a set of reactants.
  2. Calculate how much product will be produced from the limiting reagent.
  3. Calculate how much reactant(s) remains when the reaction is complete.

One additional assumption we have made about chemical reactions—in addition to the assumption that reactions proceed all the way to completion—is that all the reactants are present in the proper quantities to react to products. This is not always the case.

Consider Figure 5.1 “Making Water”. Here we are taking hydrogen atoms and oxygen atoms (left) to make water molecules (right). However, there are not enough oxygen atoms to use up all the hydrogen atoms. We run out of oxygen atoms and cannot make any more water molecules, so the process stops when we run out of oxygen atoms.

3 oxygen atoms and 8 hydrogen atoms make 3 water molecules, with 2 hydrogen atoms left over.
Figure 5.1 “Making Water.” In this scenario for making water molecules, we run out of O atoms before we use up all the H atoms. Similar situations exist for many chemical reactions when one reactant runs out before the other.

A similar situation exists for many chemical reactions: you usually run out of one reactant before all of the other reactant has reacted. The reactant you run out of is called the limiting reagent; the other reactant or reactants are considered to be in excess. A crucial skill in evaluating the conditions of a chemical process is to determine which reactant is the limiting reagent and which is in excess.

The key to recognizing which reactant is the limiting reagent is based on a mole-mass or mass-mass calculation: whichever reactant gives the lesser amount of product is the limiting reagent. What we need to do is determine an amount of one product (either moles or mass) assuming all of each reactant reacts. Whichever reactant gives the least amount of that particular product is the limiting reagent. It does not matter which product we use, as long as we use the same one each time. It does not matter whether we determine the number of moles or grams of that product; however, we will see shortly that knowing the final mass of product can be useful.

For example, consider this reaction:

4As(s) + 3O2(g) → 2As2O3(s)

Suppose we start a reaction with 50.0 g of As and 50.0 g of O2. Which one is the limiting reagent? We need to perform two mole-mass calculations, each assuming that each reactant reacts completely. Then we compare the amount of the product produced by each and determine which is less.

The calculations are as follows:

50.0\text{ \cancel{g As}}\times \dfrac{1\text{ \cancel{mol As}}}{74.92\text{ \cancel{g As}}}\times \dfrac{2\text{ mol }\ce{As2O3}}{4\text{ \cancel{mol As}}}=0.334\text{ mol }\ce{As2O3}

50.0\cancel{\text{ g }\ce{O2}}\times \dfrac{1\cancel{\text{ mol }\ce{O2}}}{32.00\cancel{\text{ g }\ce{O2}}}\times \dfrac{2\text{ mol }\ce{As2O3}}{3\cancel{\text{ mol }\ce{O2}}}=1.04\text{ mol }\ce{As2O3}

Comparing these two answers, it is clear that 0.334 mol of As2O3 is less than 1.04 mol of As2O3, so arsenic is the limiting reagent. If this reaction is performed under these initial conditions, the arsenic will run out before the oxygen runs out. We say that the oxygen is “in excess.”

Identifying the limiting reagent, then, is straightforward. However, there are usually two associated questions:

  1. What mass of product (or products) is then actually formed?
  2. What mass of what reactant is left over?

The first question is straightforward to answer: simply perform a conversion from the number of moles of product formed to its mass, using its molar mass. For As2O3, the molar mass is 197.84 g/mol; knowing that we will form 0.334 mol of As2O3 under the given conditions, we will get:

0.334\cancel{\text{ mol }\ce{As2O3}}\times \dfrac{197.84\text{ g }\ce{As2O3}}{1\cancel{\text{ mol }\ce{As2O3}}}=66.1\text{ g }\ce{As2O3}

The second question is somewhat more convoluted to answer. First, we must do a mass-mass calculation relating the limiting reagent (here, As) to the other reagent (O2). Once we determine the mass of O2 that reacted, we subtract that from the original amount to determine the amount left over. According to the mass-mass calculation:

50.0\text{ \cancel{g As}}\times \dfrac{1\text{ \cancel{mol As}}}{74.92\text{ \cancel{g As}}}\times \dfrac{3\cancel{\text{ mol }\ce{O2}}}{4\text{ \cancel{mol As}}}\times \dfrac{32.00\text{ g }\ce{O2}}{1\cancel{\text{ mol }\ce{O2}}}=16.0\text{ g }\ce{O2}\text{ reacted}

Because we reacted 16.0 g of our original O2, we subtract that from the original amount, 50.0 g, to get the mass of O2 remaining:

50.0 g O2 − 16.0 g O2 reacted = 34.0 g O2 left over

You must remember to perform this final subtraction to determine the amount remaining; a common error is to report the 16.0 g as the amount remaining.

Example 5.11

Problem

A 5.00 g quantity of Rb are combined with 3.44 g of MgCl2 according to this chemical reaction:

2Rb(s) + MgCl2(s) → Mg(s) + 2RbCl(s)

What mass of Mg is formed, and what mass of what reactant is left over?

Solution

Because the question asks what mass of magnesium is formed, we can perform two mass-mass calculations and determine which amount is less.

5.00\text{ \cancel{g Rb}}\times \dfrac{1\text{ \cancel{mol Rb}}}{85.47\text{ \cancel{g Rb}}}\times \dfrac{1\text{ \cancel{mol Mg}}}{2\text{ \cancel{mol Rb}}}\times \dfrac{24.31\text{ g Mg}}{1\text{ \cancel{mol Mg}}}=0.711\text{ g Mg}

3.44\cancel{\text{ g }\ce{MgCl2}}\times \dfrac{1\cancel{\text{ mol }\ce{MgCl2}}}{95.21\cancel{\text{ g }\ce{MgCl2}}}\times \dfrac{1\text{ \cancel{mol Mg}}}{1\cancel{\text{ mol }\ce{MgCl2}}}\times \dfrac{24.31\text{ g Mg}}{1\text{ \cancel{mol Mg}}}=0.878\text{ g Mg}

The 0.711 g of Mg is the lesser quantity, so the associated reactant — 5.00 g of Rb — is the limiting reagent. To determine how much of the other reactant is left, we have to do one more mass-mass calculation to determine what mass of MgCl2 reacted with the 5.00 g of Rb and then subtract the amount reacted from the original amount.

5.00\text{ \cancel{g Rb}}\times \dfrac{1\text{ \cancel{mol Rb}}}{85.47\text{ \cancel{g Rb}}} \times \dfrac{1\cancel{\text{ mol }\ce{MgCl2}}}{2\text{ \cancel{mol Rb}}} \times \dfrac{95.21\text{ g Mg}}{1\cancel{\text{ mol }\ce{MgCl2}}} = 2.78\text{ g }\ce{MgCl2}\text{ reacted}

Because we started with 3.44 g of MgCl2, we have:

3.44 g MgCl2 − 2.78 g MgCl2 reacted = 0.66 g MgCl2 left

Test Yourself

Given the initial amounts listed, what is the limiting reagent, and what is the mass of the leftover reagent?

22.7 g MgO(s) + 17.9 H2S(g) → MgS(s) + H2O(ℓ)

Answer

H2S is the limiting reagent; 1.5 g of MgO are left over.

Key Takeaways

  • The limiting reagent is that reactant that produces the least amount of product.
  • Mass-mass calculations can determine how much product is produced and how much of the other reactants remain.

Exercises

Questions

  1. The box below shows a group of nitrogen and hydrogen molecules that will react to produce ammonia, NH3. What is the limiting reagent?

    10 hydrogen atoms reacting with 3 nitrogen atoms.

  2. The box below shows a group of hydrogen and oxygen molecules that will react to produce water, H2O. What is the limiting reagent?

    5 hydrogen atoms reacting with 3 oxygen atoms.

  3. Given the statement “20.0 g of methane is burned in excess oxygen,” is it obvious which reactant is the limiting reagent?
  4. Given the statement “the metal is heated in the presence of excess hydrogen,” is it obvious which substance is the limiting reagent despite not specifying any quantity of reactant?
  5. Acetylene (C2H2) is formed by reacting 7.08 g of C and 4.92 g of H2.

    2C(s) + H2(g) → C2H2(g)

    What is the limiting reagent? How much of the other reactant is in excess?

  6. Ethane (C2H6) is formed by reacting 7.08 g of C and 4.92 g of H2.

    2C(s) + 3H2(g) → C2H6(g)

    What is the limiting reagent? How much of the other reactant is in excess?

  7. Given the initial amounts listed, what is the limiting reagent, and how much of the other reactant is in excess?

    35.6 g P4O6(s) + 4.77 g 6H2O(ℓ) → 4H3PO4

  8. Given the initial amounts listed, what is the limiting reagent, and how much of the other reactant is in excess?

    377 g 3NO2(g) + 244 g H2O(ℓ) → 2HNO3(aq) + NO(g)

  9. To form the precipitate PbCl2, 2.88 g of NaCl and 7.21 g of Pb(NO3)2 are mixed in solution. How much precipitate is formed? How much of which reactant is in excess?
  10. In a neutralization reaction, 18.06 g of KOH are reacted with 13.43 g of HNO3. What mass of H2O is produced, and what mass of which reactant is in excess?

Answers

  1. Nitrogen is the limiting reagent.
  1. Yes; methane is the limiting reagent.
  1. C is the limiting reagent; 4.33 g of H2 are left over.
  1. H2O is the limiting reagent; 25.9 g of P4O6 are left over.
  1. 6.06 g of PbCl2 are formed; 0.33 g of NaCl is left over.

Media Attributions

  • “Making Water” by David W. Ball © CC BY-NC-SA (Attribution-NonCommercial-ShareAlike)
  • “NH3 Reaction” by David W. Ball © CC BY-NC-SA (Attribution-NonCommercial-ShareAlike)
  • “H2O Reaction” by David W. Ball © CC BY-NC-SA (Attribution-NonCommercial-ShareAlike)

Annotate

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The Mole in Chemical Reactions
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Chemistry

Copyright © 2014

                                by Jessie A. Key

            Introductory Chemistry - 1st Canadian Edition by Jessie A. Key is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.
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