Acids and Bases Equilibrium: Bronsted-Lowry Theory, pH Calculations, and Salt Solutions

Acids and Bases Equilibrium

Bronsted-Lowry Definition of Acids and Bases

The Bronsted-Lowry theory defines acids and bases based on their ability to donate or accept protons (H+). This concept expands upon the Arrhenius definition and is fundamental to understanding acid-base reactions in aqueous solutions.

• Acid: A substance that donates a proton (H+) to another substance.

• Base: A substance that accepts a proton (H+) from another substance.

• Conjugate Acid-Base Pair: Two species that differ by a single proton. The acid becomes its conjugate base after donating a proton, and the base becomes its conjugate acid after accepting a proton.

Example: In the reaction between acetic acid and water:

• CH3COOH (acid) + H2O (base) → CH3COO- (conjugate base) + H3O+ (conjugate acid)

Acid and Base Ionization Reactions

Acids and bases ionize in water to produce hydronium (H3O+) or hydroxide (OH-) ions. The extent of ionization depends on the strength of the acid or base.

• Strong acids/bases: Ionize completely in water.

• Weak acids/bases: Ionize partially, establishing an equilibrium.

Example: Ionization of acetic acid:

• CH3COOH + H2O → CH3COO- + H3O+

Ion-Product Constant for Water (Kw)

Water undergoes auto-ionization, producing hydronium and hydroxide ions. The equilibrium constant for this process is known as the ion-product constant for water, Kw.

• Equation:

$K_{w} = [H_{3}O^{+}][OH^{-}]$

• At 25°C, $K_{w} = 1.0 \times 10^{-14}$

• In pure water, $[H_{3}O^{+}] = [OH^{-}] = 1.0 \times 10^{-7}$ M

Amphiprotic Substances

An amphiprotic substance can act as either an acid or a base, depending on the reaction context. Water is the most common example.

• Example: Water acts as a base with HCl and as an acid with NH3.

pH and pOH Scales

The concentration of hydronium and hydroxide ions is often expressed using the pH and pOH scales, which are logarithmic measures of acidity and basicity.

• pH: $pH = -\log [H_{3}O^{+}]$

• pOH: $pOH = -\log [OH^{-}]$

• Relationship: $pH + pOH = 14$ (at 25°C)

Calculations Relating pH, pOH, Ka, and Kb

For weak acids and bases, equilibrium calculations are necessary to determine pH and pOH. The acid dissociation constant (Ka) and base dissociation constant (Kb) quantify the strength of weak acids and bases.

• Acid dissociation: $HA + H_{2}O \rightleftharpoons H_{3}O^{+} + A^{-}$

• Ka expression: $K_{a} = \frac{[H_{3}O^{+}][A^{-}]}{[HA]}$

• Base dissociation: $B + H_{2}O \rightleftharpoons BH^{+} + OH^{-}$

• Kb expression: $K_{b} = \frac{[BH^{+}][OH^{-}]}{[B]}$

Example: Calculate the pH of a 0.50 M CH3COOH solution, $K_{a} = 1.76 \times 10^{-5}$.

• Set up an ICE table for the equilibrium.

• Solve for $[H_{3}O^{+}]$ using the quadratic formula or approximation.

• Calculate pH using $pH = -\log [H_{3}O^{+}]$.

Example: Calculate the pH of a 0.50 M NH3 solution, $K_{b} = 1.79 \times 10^{-5}$.

• Set up an ICE table for the equilibrium.

• Solve for $[OH^{-}]$.

• Calculate pOH and then pH.

Equilibrium Calculations for Weak Acid–Base Systems

Weak acids and bases do not fully dissociate, so equilibrium calculations are required to determine the concentrations of all species present.

• Use ICE tables to track changes in concentration.

• Apply the equilibrium constant expressions (Ka or Kb).

• Calculate pH or pOH as needed.

Acid-Base Properties of Salt Solutions

Salt solutions can be acidic, basic, or neutral depending on the nature of the ions produced from the salt. Predicting the pH involves analyzing the parent acid and base.

• Acidic salt: Derived from a strong acid and weak base.

• Basic salt: Derived from a weak acid and strong base.

• Neutral salt: Derived from a strong acid and strong base.

Example: NH4Cl solution is acidic because NH4+ is a weak acid.

Equilibrium Concepts for Polyprotic Acids and Bases

Some acids and bases can donate or accept more than one proton. These are called polyprotic acids or bases, and their dissociation occurs in steps, each with its own equilibrium constant.

• Example: H2SO4 (sulfuric acid) dissociates in two steps.

• Each step has a different Ka value.

Summary Table: Acid-Base Properties and Calculations

Concept	Equation/Definition	Example
Bronsted-Lowry Acid	Donates H+	CH3COOH
Bronsted-Lowry Base	Accepts H+	NH3
Kw	$K_{w} = [H_{3}O^{+}][OH^{-}]$	1.0 × 10-14 at 25°C
pH	$pH = -\log [H_{3}O^{+}]$	pH of pure water = 7
Ka	$K_{a} = \frac{[H_{3}O^{+}][A^{-}]}{[HA]}$	Acetic acid: $K_{a} = 1.76 \times 10^{-5}$
Kb	$K_{b} = \frac{[BH^{+}][OH^{-}]}{[B]}$	Ammonia: $K_{b} = 1.79 \times 10^{-5}$

Additional info: ICE tables and quadratic approximations are commonly used for equilibrium calculations involving weak acids and bases. Polyprotic acids require sequential equilibrium analysis for each dissociation step.