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Introductory Chemistry - 1st Canadian Edition: The pH Scale

Introductory Chemistry - 1st Canadian Edition
The pH Scale
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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

The pH Scale

Learning Objectives

  1. Define pH.
  2. Determine the pH of acidic and basic solutions.

As we have seen, [H+] and [OH−] values can be markedly different from one aqueous solution to another. So chemists defined a new scale that succinctly indicates the concentrations of either of these two ions.

pH is a logarithmic function of [H+]:

\text{pH}=-\log[\ce{H+}]

pH is usually (but not always) between 0 and 14. Knowing the dependence of pH on [H+], we can summarize as follows:

  • If pH < 7, then the solution is acidic.
  • If pH = 7, then the solution is neutral.
  • If pH > 7, then the solution is basic.

This is known as the pH scale. You can use pH to make a quick determination whether a given aqueous solution is acidic, basic, or neutral.

Example 12.13

Label each solution as acidic, basic, or neutral based only on the stated pH.

  1. milk of magnesia, pH = 10.5
  2. pure water, pH = 7
  3. wine, pH = 3.0

Solution

  1. With a pH greater than 7, milk of magnesia is basic. (Milk of magnesia is largely Mg(OH)2.)
  2. Pure water, with a pH of 7, is neutral.
  3. With a pH of less than 7, wine is acidic.

Test Yourself
Identify each substance as acidic, basic, or neutral based only on the stated pH.

  1. human blood, pH = 7.4
  2. household ammonia, pH = 11.0
  3. cherries, pH = 3.6

Answers

  1. basic
  2. basic
  3. acidic

Table 12.3 “Typical pH Values of Various Substances” gives the typical pH values of some common substances. Note that several food items are on the list, and most of them are acidic.

Table 12.3 Typical pH Values of Various Substances[1]
SubstancepH
stomach acid1.7
lemon juice2.2
vinegar2.9
soda3.0
wine3.5
coffee, black5.0
milk6.9
pure water7.0
blood7.4
seawater8.5
milk of magnesia10.5
ammonia solution12.5
1.0 M NaOH14.0

pH is a logarithmic scale. A solution that has a pH of 1.0 has 10 times the [H+] as a solution with a pH of 2.0, which in turn has 10 times the [H+] as a solution with a pH of 3.0 and so forth.

Using the definition of pH, it is also possible to calculate [H+] (and [OH−]) from pH and vice versa. The general formula for determining [H+] from pH is as follows:

[\ce{H+}]=10^{-\text{pH}}

You need to determine how to evaluate the above expression on your calculator. Ask your instructor if you have any questions.

The other issue that concerns us here is significant figures. Because the number(s) before the decimal point in a logarithm relate to the power on 10, the number of digits after the decimal point is what determines the number of significant figures in the final answer:

X and Y

Example 12.14

What are [H+] and [OH−] for an aqueous solution whose pH is 4.88?

Solution
We need to evaluate the following expression:

[\ce{H+}]=10^{-4.88}

Depending on the calculator you use, the method for solving this problem will vary. In some cases, the “−4.88” is entered and a “10x” key is pressed; for other calculators, the sequence of keystrokes is reversed. In any case, the correct numerical answer is as follows:

[\ce{H+}]=1.3\times 10^{-5}\text{ M}

Because 4.88 has two digits after the decimal point, [H+] is limited to two significant figures. From this, [OH−] can be determined:

[\ce{OH-}]=\dfrac{1\times 10^{-14}}{1.3\times 10^{-5}}=7.7\times 10^{-10}\text{ M}

Test Yourself
What are [H+] and [OH−] for an aqueous solution whose pH is 10.36?

Answer
[H+] = 4.4 × 10−11 M; [OH−] = 2.3 × 10−4 M

There is an easier way to relate [H+] and [OH−]. We can also define pOH similar to pH:

\text{pOH}=-\log[\ce{OH-}]

(In fact, p“anything” is defined as the negative logarithm of that anything.) This also implies that:

[\ce{OH-}]=10^{-\text{pOH}}

A simple and useful relationship is that, for any aqueous solution:

\text{pH}+\text{pOH}=14

This relationship makes it simple to determine pH from pOH or pOH from pH and then calculate the resulting ion concentration.

Example 12.15

The pH of a solution is 8.22. What are pOH, [H+], and [OH−]?

Solution
Because the sum of pH and pOH equals 14, we have:

8.22+\text{pOH}=14

Subtracting 8.22 from 14, we get:

\text{pOH}=5.78

Now we evaluate the following two expressions:

\begin{array}{rcl} \left[\ce{H+}\right]&=&10^{-8.22} \\ \\ \left[\ce{OH-}\right]&=&10^{-5.78} \end{array}

So:

\begin{array}{rcl} \left[\ce{H+}\right]&=&6.0\times 10^{-9}\text{ M} \\ \\ \left[\ce{OH-}\right]&=&1.7\times 10^{-6}\text{ M} \end{array}

Test Yourself
The pOH of a solution is 12.04. What are pH, [H+], and [OH−]?

Answer
pH = 1.96; [H+] = 1.1 × 10−2 M; [OH−] = 9.1 × 10−13 M

Key Takeaways

  • pH is a logarithmic function of [H+].
  • [H+] can be calculated directly from pH.
  • pOH is related to pH and can be easily calculated from pH.

Exercises

Questions

  1. Define pH. How is it related to pOH?
  2. Define pOH. How is it related to pH?
  3. What is the pH range for an acidic solution?
  4. What is the pH range for a basic solution?
  5. What is [H+] for a neutral solution?
  6. What is [OH−] for a neutral solution? Compare your answer to Exercise 5. Does this make sense?
  7. Which substances in Table 12.3 “Typical pH Values of Various Substances” are acidic?
  8. Which substances in Table 12.3 are basic?
  9. What is the pH of a solution when [H+] is 3.44 × 10−4 M?
  10. What is the pH of a solution when [H+] is 9.04 × 10−13 M?
  11. What is the pH of a solution when [OH−] is 6.22 × 10−7 M?
  12. What is the pH of a solution when [OH−] is 0.0222 M?
  13. What is the pOH of a solution when [H+] is 3.44 × 10−4 M?
  14. What is the pOH of a solution when [H+] is 9.04 × 10−13 M?
  15. What is the pOH of a solution when [OH−] is 6.22 × 10−7 M?
  16. What is the pOH of a solution when [OH−] is 0.0222 M?
  17. If a solution has a pH of 0.77, what is its pOH, [H+], and [OH−]?
  18. If a solution has a pOH of 13.09, what is its pH, [H+], and [OH−]?

Answers

  1. pH is the negative logarithm of [H+] and is equal to 14 − pOH.
  1. pH < 7
  1. 1.0 × 10−7 M
  1. Every entry above pure water is acidic.
  1. pH of 3.46
  1. pH of 7.79
  1. pOH of 10.54
  1. pOH of 6.21
  1. pOH = 13.23; [H+] = 1.70 × 10−1 M; [OH−] = 5.89 × 10−14 M

  1. Actual values may vary depending on conditions. ↵

Annotate

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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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