Chemical Analysis Notes

Monoprotic Acid-Base Equilibria

• Overview: Chapter 9 focuses on the analysis of monoprotic acid-base equilibria in quantitative chemical analysis.

Strong Acids and Bases (Section 9-1)

• Dissociation and Equilibrium:

  • Large dissociation constants ($K_a$) signify strong acids.

  • General dissociation reaction:
    HX + H2O \rightleftharpoons H3O^+ + X^-

  • Example acids with $K_a$ values:

    • HCl: $K_a = 10^{3.9}$

    • HBr: $K_a = 10^{5.8}$

    • HI: $K_a = 10^{10.4}$

    • HNO3: $K_a = 10^{1.4}$

  • For Sulfuric Acid (H2SO4), only the first dissociation is complete:
    H2SO4 \rightarrow H^+ + HSO_4^-

  • Second dissociation: $K_{a2} = 1.0 imes 10^{-2}$

• Common Strong Bases:

  • Hydroxides of alkali metals (e.g., LiOH, NaOH, KOH, RbOH, CsOH)

  • Quaternary ammonium hydroxides (e.g., tetrabutylammonium hydroxide)

pH Calculations

• pH of Strong Acid:

  • Calculation for 0.10 M HBr:

  1. Reaction completion assumption:

  • [H_3O^+] = 0.10 M

  1. pH Calculation:
     ext{pH} = - ext{log}[H_3O^+] = - ext{log}(0.10) = 1.00

• pH of Strong Base:

  • Calculation for 0.10 M KOH:
    [OH^-] = 0.10 M

  • pH can be found from $[H^+]$ using the relationship with $Kw$: Kw = [H^+][OH^-] = 1.0 imes 10^{-14}

Example Calculation with Activity Coefficient

• pH of 0.10 M HBr with activity coefficient ($eta$):

  • Ionic strength ($c$):

  • Calculate pH using:
    ext{pH} = - ext{log}(eta [H^+])

  • Use:
    eta = 0.83

Dilute Base Calculations

• pH of 1 × 10^{-8} M KOH and water contribution:

  • Systematic treatment is required as the concentration of $OH^-$ from water ionization can influence pH calculations.

Weak Acids and Bases (Section 9-2)

• Dissociation Constants:

  • Acid dissociation constant ($K_a$) for weak acids reflects partial dissociation in water.

  • Base hydrolysis constant ($K_b$) reflects weak base reactions.

• Understanding pK Values:

  • Negative logarithm of equilibrium constants:
    pK = - ext{log}(K)

  • In general, higher $K$ results in lower $pK$ values, correlating strength.

Weak Acid Equilibria (Section 9-3)

• Typical Weak Acid Problem:

  • Reaction illustrative approach with equilibrium constants and charge/mass balance equations:

  1. HA \rightleftharpoons H^+ + A^-

  2. Charge Balance: [H^+] = [A^-] + [OH^-]

  3. Mass Balance: Total concentration in weak acid form, $F$.

  4. Incorporate equilibrium properties:
     K_a = \frac{[H^+][A^-]}{[HA]}

• Fraction of Dissociation:

  • (α = Fraction of acid dissociated).

  • Concentration's relation leads to simplifications in calculations at different dilution states.

Buffers Section (Section 9-5)

• Buffer Properties:

  • A buffered solution minimizes pH changes upon acid/base addition or dilution, relying on equilibria between weak acids and their conjugate bases.

  • Ideal mix: acid + conjugate base in near-equal concentrations.

• Henderson-Hasselbalch Equation:

  • Used for calculating pH of buffer solutions,

  • For Acid:
    ext{pH} = pK_a + ext{log}\left(\frac{[A^-]}{[HA]}\right)

  • Changes in pH based on the ratio of acid/base concentrations.

• Example - Buffer Calculation:

  • If given a pH and pK, calculate the concentration ratio of conjugate species using the Henderson-Hasselbalch equation.