Aqueous Ionic Equilibrium: Buffers, Titrations, and Solubility

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Aqueous Ionic Equilibrium

Buffered Solutions

Buffered solutions are essential in chemistry because they resist changes in pH when small amounts of strong acids or bases are added. Buffers are typically composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.

Definition: A buffer is a solution that minimizes pH changes upon the addition of acid or base.
Composition: Buffers contain significant amounts of both a weak acid and its conjugate base (or weak base and its conjugate acid).
Mechanism: Added H+ ions react with the conjugate base, while added OH− ions react with the weak acid.
Buffering Capacity: The amount of acid or base a buffer can neutralize before the pH changes significantly.

Test tubes with buffer solutions of different colors

Example: A buffer made from 0.50 M acetic acid (CH3COOH) and 0.50 M sodium acetate (CH3COONa) has a pH of 4.74. Adding 0.010 mol NaOH only raises the pH to 4.76, demonstrating the buffer's resistance to pH change.

Calculating the pH of a Buffer Solution

The pH of a buffer can be calculated using equilibrium tables or the Henderson-Hasselbalch equation. The equilibrium approach involves setting up an ICE (Initial, Change, Equilibrium) table for the weak acid dissociation.

ICE table for acetic acid buffer equilibrium

Henderson-Hasselbalch Equation:

$\mathrm{pH} = \mathrm{p}K_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right)$

This equation is especially useful when the concentrations of the acid and its conjugate base are known.

Henderson-Hasselbalch equation calculation example

Basic Buffers

Basic buffers are prepared by mixing a weak base with a soluble salt of its conjugate acid. For example, a buffer can be made from ammonia (NH3) and ammonium chloride (NH4Cl).

Reaction: NH3(aq) + H2O(l) → NH4+(aq) + OH−(aq)
Buffering Action: Added acid reacts with NH3; added base reacts with NH4+.

Formation of a buffer from ammonia and ammonium chloride

Buffering Capacity and Range

The effectiveness of a buffer depends on the absolute and relative concentrations of the acid and base components.

Buffering Capacity: Increases with higher concentrations of buffer components.
Buffering Range: Most effective when the ratio [base]:[acid] is between 0.1 and 10. The effective pH range is pKa ± 1.

Concentrated vs. dilute buffer solutions

Titrations and Titration Curves

Strong Acid–Strong Base Titration

In a titration, a solution of known concentration (titrant) is added to a solution of unknown concentration until the reaction reaches the equivalence point. For strong acid–strong base titrations, the pH changes rapidly near the equivalence point.

Titration curve for strong acid-strong base titration Titration curve for strong base-strong acid titration

Weak Acid–Strong Base Titration

When titrating a weak acid with a strong base, the titration curve differs from that of a strong acid. The initial pH is higher, and the equivalence point pH is above 7 due to the formation of a weak conjugate base.

Titration curve for weak acid-strong base titration Titration curves for various weak acids with different Ka values

Strong Acid–Weak Base Titration

In this titration, the initial pH is high, and the equivalence point pH is below 7 due to the formation of a weak conjugate acid.

Titration curve for strong acid-weak base titration

Comparing Titration Curves

Titration curves can be compared to understand the differences between strong and weak acids and bases.

Titration curve: Weak acid vs. strong base Titration curve: Strong acid vs. strong base Titration curve: Weak base vs. strong acid

Titration of Polyprotic Acids

Polyprotic acids have more than one ionizable proton and thus show multiple equivalence points in their titration curves. The separation between equivalence points depends on the difference between their Ka values.

Titration curve for a polyprotic acid

Acid-Base Indicators

Indicators and End Points

Acid-base indicators are weak acids or bases that change color at specific pH ranges. They are used to mark the end point of a titration, which should be as close as possible to the equivalence point.

Color change of phenolphthalein indicator Color change of bromothymol blue indicator Color change of methyl red indicator

Selection of Indicator: Choose an indicator with a pKa near the equivalence point pH.

Indicator color change during titration Indicator color in 0.1 M HCl Indicator color in 0.1 M acetic acid Table of indicator pH ranges Indicator color change on titration curve

Solubility Equilibria

Solubility-Product Constant (Ksp)

The solubility-product constant, Ksp, is the equilibrium constant for the dissolution of a sparingly soluble ionic compound in water.

General Form: For MnXm(s) ↔ nMm+(aq) + mXn−(aq),

$K_{sp} = [M^{m+}]^n [X^{n-}]^m$

Example: For PbCl2(s) ↔ Pb2+(aq) + 2Cl−(aq),

$K_{sp} = [Pb^{2+}][Cl^-]^2$

Table of selected Ksp values

Common Ion Effect

The solubility of an ionic compound decreases in the presence of a common ion due to Le Châtelier's principle. For example, the solubility of Ag2CrO4 is lower in a solution already containing Ag+ ions.

Predicting Precipitation

Precipitation occurs when the ionic product (Q) exceeds Ksp. If Q > Ksp, precipitation occurs; if Q < Ksp, no precipitation occurs; if Q = Ksp, the solution is saturated.

Precipitation of Ag2CrO4 from mixing solutions Supersaturated solution forming a precipitate upon seeding

Complex Ion Formation

Transition metals can form complex ions with ligands, which increases their solubility. The equilibrium constant for complex ion formation is called the formation constant (Kf).

Table of formation constants for complex ions

Solubility of Amphoteric Hydroxides

Some metal hydroxides are amphoteric, meaning they can dissolve in both acidic and basic solutions. For example, Al(OH)3 is more soluble in both acidic and basic conditions due to its ability to react as either an acid or a base.

pH-dependent solubility of amphoteric hydroxide

Additional info: Amphoteric substances can act as both acids and bases. Water is a classic example of an amphoteric molecule.