\( \newcommand{\xrightleftharpoons}[2]{\overset{#1}{\underset{#2}{\rightleftharpoons}}} \) \( \newcommand{\conc}[1]{\left[\mathrm{#1}\right]} \) \( \newcommand{\chem}[1]{\mathrm{#1}} \)

Chapter 14
Acids and Bases

Shaun Williams, PhD

Models of Acids and Bases

$$ \chem{\underbrace{HCl}_{acid} + \underbrace{H_2O}_{base} \rightleftharpoons Cl^- + H_3O^+} $$

Acid in Water

$$ \chem{\underbrace{HA(aq)}_{Acid} + \underbrace{H_2O(l)}_{Base} \rightleftharpoons \underbrace{H_3O^+(aq)}_{\text{Conjugate base}} + \underbrace{A^-(aq)}_{\text{Conjugate base}}} $$

Acid Strength

Acid Strength

100% of strong acids molecules in water break up into their ions. Only a small fraction of weak acid molecules break up into their ions in water.

Various Ways to Describe Acid Strength

Property Strong Acid Weak Acid
\(K_a\) value \(K_a\) is large \(K_a\) is small
Position of the dissociation (ionization) equilibrium Far to the right Far to the left
Equilibrium concentration of \(\conc{H^+}\) compared with original \(\conc{H^+}\approx \conc{HA}_0\) \(\conc{H^+}\ll \conc{HA}_0\)
Strength of conjugate base compared with that of water \(\chem{A^-}\) much weakber base than \(\chem{H_2O}\) \(\chem{A^-}\) much stronger base than \(\chem{H_2O}\)

Water as an Acid and a Base

The pH Scale

The pH Scale and pH Values of Some Common Substances

A scale showing 1 M HCl at a pH of 1 up to 1 M NaOH at a pH of 14.

Exercise

Calculate the pH for each of the following solutions.

  1. \(1.0 \times 10^{-4}\,\mathrm{M}\,\chem{H^+}\)
  2. \(pH=4.00\)

  3. \(0.0400\,\mathrm{M}\,\chem{OH^-}\)
  4. \(pH=12.60\)

pH and pOH

$$ K_w=\conc{H^+}\conc{OH^-} $$ $$ -\log K_w = -\log \conc{H^+} - \log \conc{OH^-} $$ $$ \mathrm{p}K_w=\mathrm{pH}+\mathrm{pOH} $$ $$ 14.00 = \mathrm{pH} + \mathrm{pOH} $$

Exercise

Calculate the pOH for each of the following solutions.

  1. \( 1.0 \times 10^{-4}\,\mathrm{M}\,\chem{H^+} \)
  2. \(\mathrm{pOH}=10.00\)

  3. \( 0.040\,\mathrm{M}\,\chem{OH^-} \)
  4. \(\mathrm{pOH}=1.40\)

Exercise

The pH of a solution is 5.85. What is the [OH–] for this solution?

\( \conc{OH^-}=7.1\times 10^{-9}\,\mathrm{M} \)

Thinking About Acid-Base Problems

Concept Check

Calculate the pH of a \( 1.5 \times 10^{–11}\,\mathrm{M} \) solution of \(\chem{HCl}\).

\(\mathrm{pH}=7.00\)

Concept Check

Calculate the pH of a \( 1.5 \times 10^{–2}\,\mathrm{M} \) solution of \(\chem{HNO_3}\).

\(\mathrm{pH}=1.82\)

Solving Weak Acid Equilibrium Problems

  1. List the major species in the solution.
  2. Choose the species that can produce \(\chem{H^+}\), and write balanced equations for the reactions producing \(\chem{H^+}\).
  3. Using the values of the equilibrium constants for the reactions you have written, decide which equilibrium will dominate in producing \(\chem{H^+}\).
  4. Write the equilibrium expression for the dominant equilibrium.
  5. List the initial concentrations of the species participating in the dominant equilibrium.
  6. Define the change needed to achieve equilibrium; that is, define \(x\).
  7. Write the equilibrium concentrations in terms of \(x\).
  8. Substitute the equilibrium concentrations into the equilibrium expression.

Solving Weak Acid Equilibrium Problems (cont.)

  1. Solve for \(x\) the “easy” way, that is, by assuming that \(\conc{HA}_0-x\) about equals \(\conc{HA}_0\).
  2. Use the 5% rule to verify whether the approximation is valid.
  3. Calculate \(\conc{H^+}\) and \(\mathrm{pH}\).

Consider This

$$\begin{align} \chem{HCN(aq)+H_2O(l)} &\rightleftharpoons \chem{H_3O^+(aq)+CN^-(aq)} & K_a&=6.2 \cdot 10^{-1} \\ \chem{H_2O(l)+H_2O(l)} &\rightleftharpoons \chem{H_3O^+(aq)+OH^-(aq)} & K_w&=1.0 \cdot 10^{-14} \end{align}$$ Which reaction controls the pH? Explain.

Exercise

Calculate the pH of a \(0.50\,\mathrm{M}\) aqueous solution of the weak acid \(\chem{HF}\). (\(K_a=7.2\times 10^{-4}\))

$$ \begin{align} & \chem{HF(aq)} &+& \chem{H_2O} &\rightleftharpoons& \chem{H_3O^+(aq)} &+& \chem{F^-(aq)} \\ \mathrm{Initial}\;\; & 0.50\,\mathrm{M} && - && \sim 0 && \sim 0 \\ \mathrm{Change}\;\; & -x && - && +x && +x \\ \mathrm{Equilibrium}\;\; & 0.50-x && - && x && x \\ \end{align} $$ $$ \mathrm{pH}=1.72 $$

Percent Dissociation (Ionization)

$$ \text{Percent dissociation}=\frac{\text{amount dissociated}\,\left(\bfrac{\mathrm{mol}}{\mathrm{L}}\right)}{\text{initial concentration}\,\left(\bfrac{\mathrm{mol}}{\mathrm{L}}\right)} \times 100% $$

Exercise

A solution of \(8.00\,\mathrm{M}\) formic acid (\(\chem{HCHO_2}\)) is 0.47% ionized in water.

Calculate the \(K_a\) value for formic acid.

$$ K_a=1.8 \times 10^{-4} $$

Exercise

Calculate the pH of an \(8.00\,\mathrm{M}\) solution of formic acid. Use the data from the previous slide to help you solve this problem.

$$ \mathrm{pH}=1.42 $$

Bases

Concept Check

Calculate the \(\mathrm{pH}\) of a \( 1.0 \times 10^{–3}\,\mathrm{M} \) solution of sodium hydroxide.

$$ \mathrm{pH}=11.00 $$

Concept Check

Calculate the \(\mathrm{pH}\) of a \( 1.0 \times 10^{–3}\,\mathrm{M} \) solution of calcium hydroxide.

$$ \mathrm{pH}=11.30 $$

Weak Bases

Concept Check

Calculate the \(\mathrm{pH}\) of a \( 2.0\,\mathrm{M} \) solution of ammonia (\(\chem{NH_3}\)). $$(K_b=1.8 \times 10^{-5})$$

$$ \mathrm{pH}=11.78 $$

Polyprotic Acids

Exercise

Calculate the \(\mathrm{pH}\) of a \( 1.00\,\mathrm{M} \) solution of \(\chem{H_3PO_4}\). $$ \begin{align} K_{a1} &= 7.5 \times 10^{-3} \\ K_{a2} &= 6.2 \times 10^{-8} \\ K_{a3} &= 4.8 \times 10^{-13} \end{align} $$

$$ \mathrm{pH}=1.08 $$

Concept Check

Calculate the equilibrium concentration of \(\chem{PO_4^{3-}}\) in a \( 1.00\,\mathrm{M} \) solution of \(\chem{H_3PO_4}\). $$ \begin{align} K_{a1} &= 7.5 \times 10^{-3} \\ K_{a2} &= 6.2 \times 10^{-8} \\ K_{a3} &= 4.8 \times 10^{-13} \end{align} $$

$$ \conc{PO_4^{3-}}=3.6 \times 10^{-19}\,\mathrm{M} $$

Salts

More of Salts

Summary of Properties of Salts

Cation Anion Acidic or Basic Example
neutral neutral neutral \(\chem{NaCl}\)
neutral conjugate base of weak acid basic \(\chem{NaF}\)
conjugate acid of a weak base neutral acidic \(\chem{NH_4Cl}\)
conjugate acid of a weak base conjugate acid of a weak acid depends on \(K_a\) & \(K_b\) values \(\chem{Al_2(SO_4)_3}\)

Qualitative Prediction of pH of Salt Solutions (from Weak Parents)

\(K_a>K_b\) \(\mathrm{pH}<7\) (acidic)
\(K_b>K_a\) \(\mathrm{pH}>7\) (basic)
\(K_a=K_b\) \(\mathrm{pH}=7\) (neutral)

Exercise

Calculate the \(\mathrm{pH}\) of a \(0.75\,\mathrm{M}\) aqueous solution of \(\chem{NaCN}\).\(K_a\) for \(\chem{HCN}\) is \(6.2 \times 10^{–10}\).

$$ \begin{align} & \chem{CN^-(aq)} &+& \chem{H_2O} &\rightleftharpoons& \chem{HCN(aq)} &+& \chem{OH^-(aq)} \\ \mathrm{Initial}\;\; & 0.75\,\mathrm{M} && - && 0 && \sim 0 \\ \mathrm{Change}\;\; & -x && - && +x && +x \\ \mathrm{Equilibrium}\;\; & 0.75-x && - && x && x \\ \end{align} $$ $$ \mathrm{pH}=11.54 $$

Models of Acids and Bases

H-X Bond Bond Strength (kJ/mol) Acid Strength in Water
H-F 565 Weak
H-Cl 427 Strong
H-Br 363 Strong
H-I 295 Strong

Oxyacids

Comparison of Electronegativitiy of X and \(K_a\) Value for a Series of Oxyacids

Acid X Electronegativity of X \(K_a\) for Acid
\(\chem{HOCl}\) \(\chem{Cl}\) 3.0 \( 4 \times 10^{-8} \)
\(\chem{HOBr}\) \(\chem{Br}\) 2.8 \( 2 \times 10^{-9} \)
\(\chem{HOI}\) \(\chem{I}\) 2.5 \( 2 \times 10^{-11} \)
\(\chem{HOCH_3}\) \(\chem{CH_3}\) 2.3 (for carbon \(\chem{CH_3}\)) \( \sim 10^{-15} \)

Oxides

Lewis Acids and Bases

A pictoral representation of aluminum ion with six waters to form the aluminum hexahydrate ion with a plus 3 charge.

Three Models for Acids and Bases

Model Definition of Acid Definition of Base
Arrhenius \(\chem{H^+}\) producer \(\chem{OH^-}\) producer
Brønsted-Lowry \(\chem{H^+}\) donor \(\chem{H^+}\) acceptor
Lewis Electron-pair acceptor Electron-pair donor

When analyzing an acid-base equilibrium problem:

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