Common Ion Effect, Buffers, and pH Calculations

Common Ion Effect and Buffer Solutions

Calculating the pH When a Common Ion Is Involved

The common ion effect refers to the shift in equilibrium that occurs when a solution contains two substances that share a common ion. This effect is important in solutions of weak acids or bases mixed with their salts, as it influences the pH and ion concentrations.

• Key Steps for pH Calculation:

  1. Identify which solutes are strong electrolytes and which are weak electrolytes.

  2. Determine the major species present in solution.

  3. Write the important equilibrium reaction that determines [H+].

  4. Set up initial and equilibrium concentrations for all relevant species.

  5. Use the equilibrium-constant expression to solve for [H+] and then calculate pH.

• Example: Mixing 0.30 mol acetic acid (CH3COOH) and 0.30 mol sodium acetate (CH3COONa) in 1.0 L solution.

• Major species: CH3COOH (weak acid), Na+ (spectator ion), CH3COO- (conjugate base).

• Equilibrium: $\mathrm{CH_3COOH(aq) \rightleftharpoons H^+(aq) + CH_3COO^-(aq)}$

• Initial concentrations: CH3COOH = 0.30 M, CH3COO- = 0.30 M

• Equilibrium-constant expression: $K_a = \frac{[H^+][CH_3COO^-]}{[CH_3COOH]}$

• Calculation: $K_a = 1.8 \times 10^{-5} = \frac{x(0.30)}{0.30}$, so $x = 1.8 \times 10^{-5}$ M

• pH: $\mathrm{pH} = -\log(1.8 \times 10^{-5}) = 4.74$

• Effect of common ion: Addition of CH3COONa decreases [H+] and increases pH compared to pure acetic acid solution.

Calculating Ion Concentrations When a Common Ion Is Involved

When a strong acid or base is added to a solution containing a weak acid or base, the common ion effect suppresses the ionization of the weak acid/base, reducing its ion concentration.

• Example: Solution with 0.20 M HF (weak acid) and 0.10 M HCl (strong acid).

• Major species: HF, H+, Cl-

• Equilibrium: $\mathrm{HF(aq) \rightleftharpoons H^+(aq) + F^-(aq)}$

• Initial concentrations: HF = 0.20 M, H+ = 0.10 M

• Equilibrium-constant expression: $K_a = \frac{[H^+][F^-]}{[HF]}$

• Calculation: $K_a = 6.8 \times 10^{-4} = \frac{(0.10)(x)}{0.20}$, so $x = 1.4 \times 10^{-3}$ M (F- concentration)

• pH: Since [H+] is dominated by HCl, $\mathrm{pH} = 1.00$

• Effect of common ion: The presence of H+ from HCl suppresses the ionization of HF, lowering [F-].

Calculating the pH of a Buffer

A buffer solution contains a weak acid and its conjugate base (or a weak base and its conjugate acid). Buffers resist changes in pH upon addition of small amounts of strong acid or base.

• Example: Buffer with 0.12 M lactic acid (HC3H5O3) and 0.10 M sodium lactate (NaC3H5O3).

• Equilibrium: $\mathrm{HC_3H_5O_3(aq) \rightleftharpoons H^+(aq) + C_3H_5O_3^-(aq)}$

• Initial concentrations: HC3H5O3 = 0.12 M, C3H5O3- = 0.10 M

• Equilibrium-constant expression: $K_a = \frac{[H^+][C_3H_5O_3^-]}{[HC_3H_5O_3]}$

• Calculation: $K_a = 1.4 \times 10^{-4} = \frac{x(0.10)}{0.12}$, so $x = 1.7 \times 10^{-4}$ M

• pH: $\mathrm{pH} = -\log(1.7 \times 10^{-4}) = 3.77$

• Buffer action: The buffer maintains pH by neutralizing added acid or base via the weak acid/conjugate base pair.

Table: Some Weak Acids in Water at 25°C

This table compares the acid dissociation constants ($K_a$) and conjugate bases for several weak acids.

Acid	Structural Formula	Conjugate Base	$K_a$
Trichloroacetic acid	CCl3COOH	CCl3COO-	0.76 × 10-1
Benzoic acid	C6H5COOH	C6H5COO-	6.3 × 10-5
Acetic acid	CH3COOH	CH3COO-	1.8 × 10-5
Hypochlorous acid	HOCl	OCl-	3.5 × 10-8
Phenol	C6H5OH	C6H5O-	1.3 × 10-10

Additional info: The table above is reconstructed from the image and may omit some entries. The $K_a$ values indicate acid strength; lower $K_a$ means weaker acid.