Chapter 17: Aqueous Equilibria: Buffers, Titrations, and Solubility

Chapter 17: Aqueous Equilibria: Buffers, Titrations, and Solubility

17.1 The Common-Ion Effect

Definition and Principles

• Common-Ion Effect: When a weak electrolyte and a strong electrolyte containing a common ion are present in solution, the weak electrolyte ionizes less than it would if it were alone.

• The equilibrium constant ($K$) does not change, but the equilibrium concentrations of reactants and products do.

• These changes follow Le Châtelier's Principle: the system shifts to counteract the addition of the common ion.

Example: Acetic Acid and Sodium Acetate

• Acetic acid is a weak acid: $\mathrm{CH_3COOH(aq) \rightleftharpoons H^+(aq) + CH_3COO^-(aq)}$

• Sodium acetate is a strong electrolyte: $\mathrm{NaCH_3COO(aq) \rightarrow Na^+(aq) + CH_3COO^-(aq)}$

• Both provide the acetate ion ($\mathrm{CH_3COO^-}$), the common ion.

• The presence of acetate from sodium acetate shifts the acetic acid equilibrium to the left, decreasing $[H^+]$.

Application to Weak Bases

• The common-ion effect also applies to weak bases. For example:

• $\mathrm{NH_3(aq) + H_2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)}$

• Adding $\mathrm{NH_4^+}$ (from a salt) shifts equilibrium left, lowering $[OH^-]$.

Calculating pH with a Common Ion

• Given: 0.30 mol acetic acid and 0.30 mol sodium acetate in 1.0 L solution.

• Assume sodium acetate dissociates completely.

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

• $K_a = \dfrac{[H^+][CH_3COO^-]}{[CH_3COOH]} = 1.8 \times 10^{-5}$

• Set up ICE table and solve:

	CH3COOH	H+	CH3COO-
Initial (M)	0.30	0	0.30
Change (M)	-x	+x	+x
Equilibrium (M)	0.30-x	x	0.30+x

• Assume $x$ is small: $K_a = \dfrac{x(0.30)}{0.30} = x = 1.8 \times 10^{-5}$

• $pH = -\log[H^+] = 4.74$

17.2 Buffers

Definition and Properties

• Buffer: A solution of a weak conjugate acid-base pair that resists drastic changes in pH when small amounts of acid or base are added.

• Buffers contain relatively high concentrations ($10^{-3}$ M or more) of both the acid and its conjugate base, with concentrations approximately equal.

Preparation of Buffers

• Mix a weak acid and a salt of its conjugate base, or a weak base and a salt of its conjugate acid.

• Alternatively, add strong acid to partially neutralize a weak base, or strong base to partially neutralize a weak acid.

• Prepackaged buffers at specific pH values are available for laboratory use.

How Buffers Work

• Adding a small amount of acid or base only slightly neutralizes one component of the buffer, so the pH changes very little.

Henderson-Hasselbalch Equation

• For a weak acid: $K_a = \dfrac{[H^+][A^-]}{[HA]}$

• Taking $-\log$ of both sides and rearranging gives:

$\mathrm{pH} = \mathrm{p}K_a + \log\left(\dfrac{[A^-]}{[HA]}\right)$

• This equation is used for buffer and weak acid/base titration calculations. If three variables are known, the fourth can be calculated.

Example Calculation

• Buffer: 0.12 M lactic acid ($\mathrm{CH_3CH(OH)COOH}$), 0.10 M sodium lactate, $K_a = 1.4 \times 10^{-4}$

• $\mathrm{pH} = -\log(1.4 \times 10^{-4}) + \log\left(\dfrac{0.10}{0.12}\right) = 3.85 + (-0.08) = 3.77$

Buffer Capacity and pH Range

• Buffer capacity: The amount of acid or base a buffer can neutralize before the pH changes significantly.

• Buffers with higher concentrations of acid and base can neutralize more added acid or base.

• Buffers are most effective within ±1 pH unit of the $pK_a$ of the acid.

Addition of Strong Acid or Base to a Buffer

• Addition of strong acid or base is a neutralization reaction.

• First, calculate the new amounts of acid and base using stoichiometry (limiting reagent).

• Then, use the Henderson-Hasselbalch equation to find the new pH.

Example: Buffer after Strong Base Addition

• Buffer: 0.300 mol $\mathrm{HC_2H_3O_2}$ and 0.300 mol $\mathrm{NaC_2H_3O_2}$ in 1.00 L; add 0.020 mol NaOH.

	HC2H3O2	OH-	CH3COO-
Before reaction (mol)	0.300	0.020	0.300
Change (mol)	-0.020	-0.020	+0.020
After reaction (mol)	0.280	0	0.320

• $\mathrm{pH} = 4.74 + \log\left(\dfrac{0.320}{0.280}\right) = 4.80$

Comparison: Buffer vs. Water

• Adding 5.00 mL of 4.0 M NaOH to 1.000 L of buffer (0.300 M each component): pH changes from 4.80 to 4.75 (0.05 units).

• Adding same base to pure water: pH changes from 7.00 to 12.30 (5.30 units).

• Conclusion: Buffers minimize pH changes upon addition of acid or base.

17.3 Acid-Base Titrations

Principles of Titration

• An acid (or base) solution of known concentration is slowly added to a base (or acid) solution of unknown concentration.

• A pH meter or indicator is used to determine the equivalence point—the point at which the amount of acid equals the amount of base.

Titration of a Strong Acid with a Strong Base

• Plot pH versus mL of strong base added.

• pH rises slowly at first, then rapidly near the equivalence point (pH = 7), then levels off as more base is added.

Titration of a Strong Base with a Strong Acid

• The titration curve is the mirror image of the strong acid/strong base titration.

• Start with high pH; pH = 7 at equivalence point; pH levels off as more acid is added.

Titration of a Weak Acid with a Strong Base

• Four regions:

  1. Initial pH (use $K_a$ calculation)

  2. Between initial pH and equivalence point (excess acid): use limiting reactant and Henderson-Hasselbalch equation

  3. At equivalence point: only anion of weak acid remains; pH > 7

  4. After equivalence point: excess base determines pH

Calculating pH at Various Points

• Before equivalence: calculate moles, write neutralization equation, use ICE table, then Henderson-Hasselbalch equation.

• At equivalence: all weak acid converted to its conjugate base; calculate new concentration and use $K_b$ or $K_a$ to find pH.

Key Differences: Weak vs. Strong Acid Titrations

• Weak acid solutions have higher initial pH than strong acids.

• pH change near equivalence is smaller for weak acids.

• At halfway to equivalence, pH = $pK_a$.

• At equivalence, pH > 7 for weak acids.

Indicators and Polyprotic Acids

• Indicators: Weak acids with different colors in acid and base forms; each has a specific pH range for color change.

• Choose an indicator that changes color near the equivalence point of the titration.

• Polyprotic acids: Have multiple equivalence points; treat each step with its own $K_a$ and polyanion.

• At halfway to each equivalence point, pH = $pK_a$ for that step.

17.4 Solubility Equilibria

Solubility-Product Constant ($K_{sp}$)

• Ionic compounds are strong electrolytes and dissociate completely to the extent that they dissolve.

• Equilibrium: solid is reactant, ions in solution are products.

• Solubility-product constant ($K_{sp}$): The equilibrium constant for the dissolution of a sparingly soluble salt.

• Example: $\mathrm{Ba_3(PO_4)_2(s) \rightleftharpoons 3Ba^{2+}(aq) + 2PO_4^{3-}(aq)}$

• $K_{sp} = [Ba^{2+}]^3[PO_4^{3-}]^2$

Solubility vs. $K_{sp}$

• $K_{sp}$ is not the same as solubility.

• Solubility: The quantity of a substance that dissolves to form a saturated solution.

• Common units: grams per liter (g/L), moles per liter (mol/L).

Concept	Definition
Solubility	Amount of solute that dissolves (g/L or mol/L)
$K_{sp}$	Equilibrium constant for dissolution

• Solubility and $K_{sp}$ are related through the stoichiometry of the dissolution reaction.

*Additional info: These notes are based on slides from "Chemistry: The Central Science," 15th Edition, Chapter 17, and cover all major topics relevant to aqueous equilibria, including buffers, titrations, and solubility equilibria, as outlined in a standard General Chemistry curriculum.*