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Chemistry

14.5 Polyprotic Acids

Chemistry14.5 Polyprotic Acids
  1. Preface
  2. 1 Essential Ideas
    1. Introduction
    2. 1.1 Chemistry in Context
    3. 1.2 Phases and Classification of Matter
    4. 1.3 Physical and Chemical Properties
    5. 1.4 Measurements
    6. 1.5 Measurement Uncertainty, Accuracy, and Precision
    7. 1.6 Mathematical Treatment of Measurement Results
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  3. 2 Atoms, Molecules, and Ions
    1. Introduction
    2. 2.1 Early Ideas in Atomic Theory
    3. 2.2 Evolution of Atomic Theory
    4. 2.3 Atomic Structure and Symbolism
    5. 2.4 Chemical Formulas
    6. 2.5 The Periodic Table
    7. 2.6 Molecular and Ionic Compounds
    8. 2.7 Chemical Nomenclature
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  4. 3 Composition of Substances and Solutions
    1. Introduction
    2. 3.1 Formula Mass and the Mole Concept
    3. 3.2 Determining Empirical and Molecular Formulas
    4. 3.3 Molarity
    5. 3.4 Other Units for Solution Concentrations
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  5. 4 Stoichiometry of Chemical Reactions
    1. Introduction
    2. 4.1 Writing and Balancing Chemical Equations
    3. 4.2 Classifying Chemical Reactions
    4. 4.3 Reaction Stoichiometry
    5. 4.4 Reaction Yields
    6. 4.5 Quantitative Chemical Analysis
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  6. 5 Thermochemistry
    1. Introduction
    2. 5.1 Energy Basics
    3. 5.2 Calorimetry
    4. 5.3 Enthalpy
    5. Key Terms
    6. Key Equations
    7. Summary
    8. Exercises
  7. 6 Electronic Structure and Periodic Properties of Elements
    1. Introduction
    2. 6.1 Electromagnetic Energy
    3. 6.2 The Bohr Model
    4. 6.3 Development of Quantum Theory
    5. 6.4 Electronic Structure of Atoms (Electron Configurations)
    6. 6.5 Periodic Variations in Element Properties
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  8. 7 Chemical Bonding and Molecular Geometry
    1. Introduction
    2. 7.1 Ionic Bonding
    3. 7.2 Covalent Bonding
    4. 7.3 Lewis Symbols and Structures
    5. 7.4 Formal Charges and Resonance
    6. 7.5 Strengths of Ionic and Covalent Bonds
    7. 7.6 Molecular Structure and Polarity
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  9. 8 Advanced Theories of Covalent Bonding
    1. Introduction
    2. 8.1 Valence Bond Theory
    3. 8.2 Hybrid Atomic Orbitals
    4. 8.3 Multiple Bonds
    5. 8.4 Molecular Orbital Theory
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  10. 9 Gases
    1. Introduction
    2. 9.1 Gas Pressure
    3. 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
    4. 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions
    5. 9.4 Effusion and Diffusion of Gases
    6. 9.5 The Kinetic-Molecular Theory
    7. 9.6 Non-Ideal Gas Behavior
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  11. 10 Liquids and Solids
    1. Introduction
    2. 10.1 Intermolecular Forces
    3. 10.2 Properties of Liquids
    4. 10.3 Phase Transitions
    5. 10.4 Phase Diagrams
    6. 10.5 The Solid State of Matter
    7. 10.6 Lattice Structures in Crystalline Solids
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  12. 11 Solutions and Colloids
    1. Introduction
    2. 11.1 The Dissolution Process
    3. 11.2 Electrolytes
    4. 11.3 Solubility
    5. 11.4 Colligative Properties
    6. 11.5 Colloids
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  13. 12 Kinetics
    1. Introduction
    2. 12.1 Chemical Reaction Rates
    3. 12.2 Factors Affecting Reaction Rates
    4. 12.3 Rate Laws
    5. 12.4 Integrated Rate Laws
    6. 12.5 Collision Theory
    7. 12.6 Reaction Mechanisms
    8. 12.7 Catalysis
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  14. 13 Fundamental Equilibrium Concepts
    1. Introduction
    2. 13.1 Chemical Equilibria
    3. 13.2 Equilibrium Constants
    4. 13.3 Shifting Equilibria: Le Châtelier’s Principle
    5. 13.4 Equilibrium Calculations
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  15. 14 Acid-Base Equilibria
    1. Introduction
    2. 14.1 Brønsted-Lowry Acids and Bases
    3. 14.2 pH and pOH
    4. 14.3 Relative Strengths of Acids and Bases
    5. 14.4 Hydrolysis of Salt Solutions
    6. 14.5 Polyprotic Acids
    7. 14.6 Buffers
    8. 14.7 Acid-Base Titrations
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  16. 15 Equilibria of Other Reaction Classes
    1. Introduction
    2. 15.1 Precipitation and Dissolution
    3. 15.2 Lewis Acids and Bases
    4. 15.3 Multiple Equilibria
    5. Key Terms
    6. Key Equations
    7. Summary
    8. Exercises
  17. 16 Thermodynamics
    1. Introduction
    2. 16.1 Spontaneity
    3. 16.2 Entropy
    4. 16.3 The Second and Third Laws of Thermodynamics
    5. 16.4 Free Energy
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  18. 17 Electrochemistry
    1. Introduction
    2. 17.1 Balancing Oxidation-Reduction Reactions
    3. 17.2 Galvanic Cells
    4. 17.3 Standard Reduction Potentials
    5. 17.4 The Nernst Equation
    6. 17.5 Batteries and Fuel Cells
    7. 17.6 Corrosion
    8. 17.7 Electrolysis
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  19. 18 Representative Metals, Metalloids, and Nonmetals
    1. Introduction
    2. 18.1 Periodicity
    3. 18.2 Occurrence and Preparation of the Representative Metals
    4. 18.3 Structure and General Properties of the Metalloids
    5. 18.4 Structure and General Properties of the Nonmetals
    6. 18.5 Occurrence, Preparation, and Compounds of Hydrogen
    7. 18.6 Occurrence, Preparation, and Properties of Carbonates
    8. 18.7 Occurrence, Preparation, and Properties of Nitrogen
    9. 18.8 Occurrence, Preparation, and Properties of Phosphorus
    10. 18.9 Occurrence, Preparation, and Compounds of Oxygen
    11. 18.10 Occurrence, Preparation, and Properties of Sulfur
    12. 18.11 Occurrence, Preparation, and Properties of Halogens
    13. 18.12 Occurrence, Preparation, and Properties of the Noble Gases
    14. Key Terms
    15. Summary
    16. Exercises
  20. 19 Transition Metals and Coordination Chemistry
    1. Introduction
    2. 19.1 Occurrence, Preparation, and Properties of Transition Metals and Their Compounds
    3. 19.2 Coordination Chemistry of Transition Metals
    4. 19.3 Spectroscopic and Magnetic Properties of Coordination Compounds
    5. Key Terms
    6. Summary
    7. Exercises
  21. 20 Organic Chemistry
    1. Introduction
    2. 20.1 Hydrocarbons
    3. 20.2 Alcohols and Ethers
    4. 20.3 Aldehydes, Ketones, Carboxylic Acids, and Esters
    5. 20.4 Amines and Amides
    6. Key Terms
    7. Summary
    8. Exercises
  22. 21 Nuclear Chemistry
    1. Introduction
    2. 21.1 Nuclear Structure and Stability
    3. 21.2 Nuclear Equations
    4. 21.3 Radioactive Decay
    5. 21.4 Transmutation and Nuclear Energy
    6. 21.5 Uses of Radioisotopes
    7. 21.6 Biological Effects of Radiation
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  23. A | The Periodic Table
  24. B | Essential Mathematics
  25. C | Units and Conversion Factors
  26. D | Fundamental Physical Constants
  27. E | Water Properties
  28. F | Composition of Commercial Acids and Bases
  29. G | Standard Thermodynamic Properties for Selected Substances
  30. H | Ionization Constants of Weak Acids
  31. I | Ionization Constants of Weak Bases
  32. J | Solubility Products
  33. K | Formation Constants for Complex Ions
  34. L | Standard Electrode (Half-Cell) Potentials
  35. M | Half-Lives for Several Radioactive Isotopes
  36. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
    18. Chapter 18
    19. Chapter 19
    20. Chapter 20
    21. Chapter 21
  37. Index

Learning Objectives

By the end of this section, you will be able to:
  • Extend previously introduced equilibrium concepts to acids and bases that may donate or accept more than one proton

We can classify acids by the number of protons per molecule that they can give up in a reaction. Acids such as HCl, HNO3, and HCN that contain one ionizable hydrogen atom in each molecule are called monoprotic acids. Their reactions with water are:

HCl(aq)+H2O(l)H3O+(aq)+Cl(aq)HNO3(aq)+H2O(l)H3O+(aq)+NO3(aq)HCN(aq)+H2O(l)H3O+(aq)+CN(aq)HCl(aq)+H2O(l)H3O+(aq)+Cl(aq)HNO3(aq)+H2O(l)H3O+(aq)+NO3(aq)HCN(aq)+H2O(l)H3O+(aq)+CN(aq)

Even though it contains four hydrogen atoms, acetic acid, CH3CO2H, is also monoprotic because only the hydrogen atom from the carboxyl group (COOH) reacts with bases:

This image contains two equilibrium reactions. The first shows a C atom bonded to three H atoms and another C atom. The second C atom is double bonded to an O atom and also forms a single bond to another O atom. The second O atom is bonded to an H atom. There is a plus sign and then the molecular formula H subscript 2 O. An equilibrium arrow follows the H subscript 2 O. To the right of the arrow is H subscript 3 O superscript positive sign. There is a plus sign. The final structure shows a C atom bonded the three H atoms and another C atom. This second C atom is double bonded to an O atom and single bonded to another O atom. The entire structure is in brackets and a superscript negative sign appears outside the brackets. The second reaction shows C H subscript 3 C O O H ( a q ) plus H subscript 2 O ( l ) equilibrium arrow H subscript 3 O ( a q ) plus C H subscript 3 C O O superscript negative sign ( a q ).

Similarly, monoprotic bases are bases that will accept a single proton.

Diprotic acids contain two ionizable hydrogen atoms per molecule; ionization of such acids occurs in two steps. The first ionization always takes place to a greater extent than the second ionization. For example, sulfuric acid, a strong acid, ionizes as follows:

First ionization:H2SO4(aq)+H2O(l)H3O+(aq)+HSO4(aq)Ka1=more than102; complete dissociationSecond ionization:HSO4(aq)+H2O(l)H3O+(aq)+SO42−(aq)Ka2=1.2×10−2First ionization:H2SO4(aq)+H2O(l)H3O+(aq)+HSO4(aq)Ka1=more than102; complete dissociationSecond ionization:HSO4(aq)+H2O(l)H3O+(aq)+SO42−(aq)Ka2=1.2×10−2

This stepwise ionization process occurs for all polyprotic acids. When we make a solution of a weak diprotic acid, we get a solution that contains a mixture of acids. Carbonic acid, H2CO3, is an example of a weak diprotic acid. The first ionization of carbonic acid yields hydronium ions and bicarbonate ions in small amounts.

First ionization:H2CO3(aq)+H2O(l)H3O+(aq)+HCO3(aq)KH2CO3=[H3O+][HCO3][H2CO3]=4.3×10−7First ionization:H2CO3(aq)+H2O(l)H3O+(aq)+HCO3(aq)KH2CO3=[H3O+][HCO3][H2CO3]=4.3×10−7

The bicarbonate ion can also act as an acid. It ionizes and forms hydronium ions and carbonate ions in even smaller quantities.

Second ionization:HCO3(aq)+H2O(l)H3O+(aq)+CO32−(aq)KHCO3=[H3O+][CO32−][HCO3]=5.6×10−11Second ionization:HCO3(aq)+H2O(l)H3O+(aq)+CO32−(aq)KHCO3=[H3O+][CO32−][HCO3]=5.6×10−11

KH2CO3KH2CO3 is larger than KHCO3KHCO3 by a factor of 104, so H2CO3 is the dominant producer of hydronium ion in the solution. This means that little of the HCO3HCO3 formed by the ionization of H2CO3 ionizes to give hydronium ions (and carbonate ions), and the concentrations of H3O+ and HCO3HCO3 are practically equal in a pure aqueous solution of H2CO3.

If the first ionization constant of a weak diprotic acid is larger than the second by a factor of at least 20, it is appropriate to treat the first ionization separately and calculate concentrations resulting from it before calculating concentrations of species resulting from subsequent ionization. This can simplify our work considerably because we can determine the concentration of H3O+ and the conjugate base from the first ionization, then determine the concentration of the conjugate base of the second ionization in a solution with concentrations determined by the first ionization.

Example 14.19

Ionization of a Diprotic Acid

When we buy soda water (carbonated water), we are buying a solution of carbon dioxide in water. The solution is acidic because CO2 reacts with water to form carbonic acid, H2CO3. What are [H3O+],[H3O+], [HCO3],[HCO3], and [CO32−][CO32−] in a saturated solution of CO2 with an initial [H2CO3] = 0.033 M?
H2CO3(aq)+H2O(l)H3O+(aq)+HCO3(aq)Ka1=4.3×10−7H2CO3(aq)+H2O(l)H3O+(aq)+HCO3(aq)Ka1=4.3×10−7
HCO3(aq)+H2O(l)H3O+(aq)+CO32−(aq)Ka2=5.6×10−11HCO3(aq)+H2O(l)H3O+(aq)+CO32−(aq)Ka2=5.6×10−11

Solution

As indicated by the ionization constants, H2CO3 is a much stronger acid than HCO3,HCO3, so H2CO3 is the dominant producer of hydronium ion in solution. Thus there are two parts in the solution of this problem: (1) Using the customary four steps, we determine the concentration of H3O+ and HCO3HCO3 produced by ionization of H2CO3. (2) Then we determine the concentration of CO32−CO32− in a solution with the concentration of H3O+ and HCO3HCO3 determined in (1). To summarize: Four tan rectangles are shown that are connected with right pointing arrows. The first is labeled “left bracket H subscript 2 C O subscript 3 right bracket.” The second is labeled “left bracket H subscript 3 O superscript plus right bracket and left bracket H C O subscript 3 superscript negative right bracket from H subscript 2 C O subscript 3.” The third is labeled “left bracket C O subscript 3 superscript 2 negative right bracket from H C O subscript 3 superscript negative.”
  1. Step 1. Determine the concentrations of H3O+H3O+ and HCO3.HCO3.
    H2CO3(aq)+H2O(l)H3O+(aq)+HCO3(aq)Ka1=4.3×10−7H2CO3(aq)+H2O(l)H3O+(aq)+HCO3(aq)Ka1=4.3×10−7

    As for the ionization of any other weak acid:
    Four tan rectangles are shown that are connected with right pointing arrows. The first is labeled “Determine the direction of change.” The second is labeled “Determine x and the equilibrium concentrations.” The third is labeled “Solve for x and the equilibrium concentrations.” The fourth is labeled “Check the math.”
    An abbreviated table of changes and concentrations shows:
    This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium constant ( M ). The second column has the header of “H subscript 2 C O subscript 3 plus sign H subscript 2 O equilibrium arrow H subscript 3 O superscript positive sign plus sign H C O subscript 3 superscript negative sign.” Under the second column is a subgroup of three columns and three rows. The first column has the following: 0.033, negative sign x, 0.033 minus sign x. The second column has the following: approximately 0, x, x. The third column has the following: 0, x, x.
    Substituting the equilibrium concentrations into the equilibrium gives us:
    KH2CO3=[H3O+][HCO3][H2CO3]=(x)(x)0.033x=4.3×10−7KH2CO3=[H3O+][HCO3][H2CO3]=(x)(x)0.033x=4.3×10−7

    Solving the preceding equation making our standard assumptions gives:
    x=1.2×10−4x=1.2×10−4

    Thus:
    [H2CO3]=0.033M[H2CO3]=0.033M

    [H3O+]=[HCO3]=1.2×10−4M[H3O+]=[HCO3]=1.2×10−4M
  2. Step 2. Determine the concentration of CO32−CO32− in a solution at equilibrium with [H3O+][H3O+] and [HCO3][HCO3] both equal to 1.2 ×× 10−4 M.
    HCO3(aq)+H2O(l)H3O+(aq)+CO32−(aq)HCO3(aq)+H2O(l)H3O+(aq)+CO32−(aq)

    KHCO3=[H3O+][CO32−][HCO3]=(1.2×10−4)[CO32−]1.2×10−4KHCO3=[H3O+][CO32−][HCO3]=(1.2×10−4)[CO32−]1.2×10−4

    [CO32−]=(5.6×10−11)(1.2×10−4)1.2×10−4=5.6×10−11M[CO32−]=(5.6×10−11)(1.2×10−4)1.2×10−4=5.6×10−11M

To summarize: In part 1 of this example, we found that the H2CO3 in a 0.033-M solution ionizes slightly and at equilibrium [H2CO3] = 0.033 M; [H3O+][H3O+] = 1.2 ×× 10−4; and [HCO3]=1.2×10−4M.[HCO3]=1.2×10−4M. In part 2, we determined that [CO32−]=5.6×10−11M.[CO32−]=5.6×10−11M.

Check Your Learning

The concentration of H2S in a saturated aqueous solution at room temperature is approximately 0.1 M. Calculate [H3O+],[H3O+], [HS], and [S2−] in the solution:
H2S(aq)+H2O(l)H3O+(aq)+HS(aq)Ka1=8.9×10−8H2S(aq)+H2O(l)H3O+(aq)+HS(aq)Ka1=8.9×10−8
HS(aq)+H2O(l)H3O+(aq)+S2−(aq)Ka2=1.0×10−19HS(aq)+H2O(l)H3O+(aq)+S2−(aq)Ka2=1.0×10−19

Answer:

[H2S] = 0.1 M; [H3O+][H3O+] = [HS] = 0.000094 M; [S2−] = 1 ×× 10−19 M
We note that the concentration of the sulfide ion is the same as Ka2. This is due to the fact that each subsequent dissociation occurs to a lesser degree (as acid gets weaker).

A triprotic acid is an acid that has three dissociable protons that undergo stepwise ionization: Phosphoric acid is a typical example:

First ionization:H3PO4(aq)+H2O(l)H3O+(aq)+H2PO4(aq)Ka1=7.5×10−3Second ionization:H2PO4(aq)+H2O(l)H3O+(aq)+HPO42−(aq)Ka2=6.2×10−8Third ionization:HPO42−(aq)+H2O(l)H3O+(aq)+PO43−(aq)Ka3=4.2×10−13First ionization:H3PO4(aq)+H2O(l)H3O+(aq)+H2PO4(aq)Ka1=7.5×10−3Second ionization:H2PO4(aq)+H2O(l)H3O+(aq)+HPO42−(aq)Ka2=6.2×10−8Third ionization:HPO42−(aq)+H2O(l)H3O+(aq)+PO43−(aq)Ka3=4.2×10−13

As with the diprotic acids, the differences in the ionization constants of these reactions tell us that in each successive step the degree of ionization is significantly weaker. This is a general characteristic of polyprotic acids and successive ionization constants often differ by a factor of about 105 to 106.

This set of three dissociation reactions may appear to make calculations of equilibrium concentrations in a solution of H3PO4 complicated. However, because the successive ionization constants differ by a factor of 105 to 106, the calculations can be broken down into a series of parts similar to those for diprotic acids.

Polyprotic bases can accept more than one hydrogen ion in solution. The carbonate ion is an example of a diprotic base, since it can accept up to two protons. Solutions of alkali metal carbonates are quite alkaline, due to the reactions:

H2O(l)+CO32−(aq)HCO3(aq)+OH(aq)andH2O(l)+HCO3(aq)H2CO3(aq)+OH(aq)H2O(l)+CO32−(aq)HCO3(aq)+OH(aq)andH2O(l)+HCO3(aq)H2CO3(aq)+OH(aq)
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