Chapter 10: Acids, Bases, and Equilibrium – Study Notes

Chapter 10: Acids, Bases, and Equilibrium

10.1 Acids and Bases

This section introduces the fundamental definitions of acids and bases according to the Arrhenius concept, focusing on their behavior in aqueous solutions.

• Acid: A compound that dissociates into H+ (hydrogen ion) when dissolved in water. Example: $\mathrm{HCl} (g) \rightarrow \mathrm{H}^+ (aq) + \mathrm{Cl}^- (aq)$

• Base: A compound that dissociates into OH- (hydroxide ion) when dissolved in water. Example: $\mathrm{NaOH} (s) \rightarrow \mathrm{Na}^+ (aq) + \mathrm{OH}^- (aq)$

10.5 Dissociation of Water

Water can act as both an acid and a base, undergoing self-ionization to produce hydronium and hydroxide ions.

• Self-ionization of water: Two water molecules react to form hydronium and hydroxide ions. $\mathrm{H_2O} + \mathrm{H_2O} \rightleftharpoons \mathrm{H_3O}^+ + \mathrm{OH}^-$

• Proton transfer reaction: A proton (H+) moves from one water molecule to another.

• Electrolyte: Water is an electrolyte because it produces ions in solution.

Ion Product of Water

The equilibrium constant for the self-ionization of water is called the ion-product constant, Kw.

• $K_w = [\mathrm{H_3O}^+][\mathrm{OH}^-] = 1.0 \times 10^{-14}$ (at 25°C)

• In pure water: $[\mathrm{H_3O}^+] = [\mathrm{OH}^-] = 1.0 \times 10^{-7} \ \mathrm{M}$

Calculations with the Ion Product of Water

Given the concentration of either hydronium or hydroxide ion, the other can be calculated using Kw.

• Example: If $[\mathrm{H_3O}^+] = 0.020 \ \mathrm{M}$, then $[\mathrm{OH}^-] = \dfrac{1.0 \times 10^{-14}}{0.020} = 5.0 \times 10^{-13} \ \mathrm{M}$

Practice Problems

• Calculate $[\mathrm{OH}^-]$ in a solution with $0.00004 \ \mathrm{M} \ \mathrm{H_3O}^+$

• Calculate $[\mathrm{H_3O}^+]$ in a solution with $10^{-5} \ \mathrm{M} \ \mathrm{OH}^-$

• Calculate $[\mathrm{H_3O}^+]$ in a solution with $2.8 \times 10^{-9} \ \mathrm{M} \ \mathrm{OH}^-$

Neutral, Acidic & Basic Solutions

Solutions are classified based on the relative concentrations of hydronium and hydroxide ions.

• Neutral: $[\mathrm{H_3O}^+] = [\mathrm{OH}^-] = 1.0 \times 10^{-7} \ \mathrm{M}$

• Acidic: $[\mathrm{H_3O}^+] > [\mathrm{OH}^-]$

• Basic: $[\mathrm{OH}^-] > [\mathrm{H_3O}^+]$

Example: For a solution with $[\mathrm{OH}^-] = 7.2 \times 10^{-5} \ \mathrm{M}$ and $[\mathrm{H_3O}^+] = 1.38 \times 10^{-10} \ \mathrm{M}$, the solution is basic because $[\mathrm{OH}^-] > [\mathrm{H_3O}^+]$.

Example: For a solution with $[\mathrm{H_3O}^+] = 2.0 \times 10^{-3} \ \mathrm{M}$, the solution is acidic because $[\mathrm{H_3O}^+] > 1.0 \times 10^{-7} \ \mathrm{M}$.

10.6 The pH Scale

The pH scale is a logarithmic scale used to express the acidity or basicity of a solution.

• Definition: $\mathrm{pH} = -\log[\mathrm{H_3O}^+]$

• Range: 0 (most acidic) to 14 (most basic)

• Neutral: pH = 7

• Acidic: pH < 7

• Basic: pH > 7

Example: A sample of seawater has $[\mathrm{H_3O}^+] = 3.67 \times 10^{-9} \ \mathrm{M}$. Calculate pH: $\mathrm{pH} = -\log(3.67 \times 10^{-9}) \approx 8.44$ (basic).

Example: Beer has a pH of 5.0, which is acidic (pH < 7).