Acid-Base Equilibria and Classifications

• Acid-base equilibria involve the study of acids, bases, and their interactions in solutions

Acid-Base Classifications

• Arrhenius acids increase H⁺ concentration in water.
• Arrhenius bases increase OH⁻ concentration in water.
• The Arrhenius definition is limited to aqueous solutions
• Bronsted-Lowry acids are proton (H⁺) donors.
• Bronsted-Lowry bases are proton (H⁺) acceptors.
• Bronsted-Lowry definition is broader and includes non-aqueous solutions
• Amphiprotic substances can act as acids or bases.
• A conjugate acid-base pair differs by a single proton (H⁺).
• A conjugate base is formed by removing a proton from the acid
• A conjugate acid is formed by adding a proton to the base
• Acid strength is inversely related to the strength of its conjugate base

Autoionization of Water

• Water undergoes autoionization where one molecule acts as an acid and another acts as a base
• 2H₂O ⇌ H₃O⁺ + OH⁻
• Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C
• In neutral solution [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M
• Acidic Solutions: [H₃O⁺] > [OH⁻]
• Basic Solutions: [H₃O⁺] < [OH⁻]
• Kw is temperature-dependent increasing with higher temperatures

Strong and Weak Acids and Bases

• Strong acids completely dissociate into ions in water
• Common Strong Acids: HCl, HBr, HI, HNO₃, HClO₃, HClO₄, and H₂SO₄ (first proton only).
• pH of a strong acid solution is directly calculated from the initial acid concentration
• Strong bases completely dissociate in water, producing OH⁻ ions
• Common Strong Bases: Group 1 hydroxides (NaOH, KOH, etc) and heavier group 2 hydroxides (Ca(OH)₂, Sr(OH)₂, Ba(OH)₂)
• pH of a strong base solution is calculated using the OH⁻ concentration and Kw = [H₃O⁺][OH⁻]
• Weak acids only partially dissociate in water establishing equilibrium
• Ka is the acid dissociation constant
• A larger Ka indicates a stronger weak acid
• The pH of a weak acid solution is calculated using the Ka expression and an ICE table
• Percent ionization measures the extent of dissociation of a weak acid
• Weak bases partially react with water accepting protons to form conjugate acids and OH⁻ ions
• Kb is the base dissociation constant
• A larger Kb indicates a stronger weak base
• pH of a weak base solution is calculated using the Kb expression and an ICE table

Relationship Between Ka and Kb

• For a conjugate acid-base pair, Ka × Kb = Kw
• Shows the inverse relationship between the strength of an acid and its conjugate base.
• Knowing either Ka or Kb, the other can be calculated
• This relationship is valid for conjugate acid-base pairs at a given temperature

Acid-Base Properties of Salt Solutions

• Hydrolysis is the reaction of an ion with water to produce H₃O⁺ or OH⁻ ions
• Cations of weak bases (e.g. NH₄⁺) undergo hydrolysis to produce acidic solutions
• Highly charged metal cations also hydrolyze to produce acidic solutions
• Anions of weak acids (e.g, CH₃COO⁻) undergo hydrolysis to produce basic solutions
• Salts formed from strong acids and strong bases produce neutral solutions
• The pH of a salt solution depends on the relative strengths of the conjugate acid and base formed by hydrolysis

Acid-Base Behavior and Chemical Structure

• In binary acids (HX), acid strength increases down a group and across a period
• Example: HI > HBr > HCl > HF
• In oxyacids (YOₓ(OH)ₙ), acid strength increases with the electronegativity of Y and the number of oxygen atoms bonded to Y
• Example: HClO₄ > HClO₃ > HClO₂ > HClO
• Carboxylic acids contain the -COOH group.
• The acidity of carboxylic acids is enhanced by the electron-withdrawing effect of the carbonyl group (C=O) and resonance stabilization of the carboxylate anion
• Lewis acids are electron-pair acceptors
• Lewis bases are electron-pair donors
• The Lewis definition encompasses reactions without proton transfer
• Many metal ions act as Lewis acids forming complex ions with Lewis bases

The Common Ion Effect

• The common-ion effect describes the decrease in solubility of a slightly soluble salt when a soluble salt containing a common ion is added
• Adding a common ion shifts the solubility equilibrium to the left, decreasing the solubility of the slightly soluble salt
• The solubility of a slightly soluble salt in the presence of a common ion is calculated using the Ksp expression and an ICE table
• The common-ion effect is more pronounced for ions with higher charges

Buffers

• A buffer is a solution that resists changes in pH upon addition of small amounts of strong acid or base
• Buffers consist of a weak acid and its conjugate base (or a weak base and its conjugate acid) in roughly equal concentrations
• The pH of a buffer can be calculated using the Henderson-Hasselbalch equation: pH = pKa + log([base]/[acid])
• Buffer capacity is the amount of acid or base a buffer can neutralize before its pH changes significantly.
• The effective pH range of a buffer is typically within ±1 pH unit of the pKa of the weak acid

Acid-Base Titrations

• A titration curve is a graph of pH versus volume of titrant added during a titration
• In strong acid-strong base titration the equivalence point is at pH 7
• There is a sharp pH change near the equivalence point
• In weak acid-strong base titration the equivalence point is above pH 7
• The pH change near the equivalence point is less sharp than in a strong acid-strong base titration
• Halfway to the equivalence point, pH = pKa
• In weak base-strong acid titrations the equivalence point is below pH 7
• The pH change near the equivalence point is less sharp than in a strong acid-strong base titration
• Halfway to the equivalence point, pH = pKb
• Polyprotic Acid Titration: Multiple equivalence points are observed, one for each ionizable proton
• Halfway to each equivalence point, pH = pKa for that ionization step
• Acid-base indicators change color over a specific pH range and are used to signal the endpoint of a titration
• Indicators should be chosen to have a color change near the equivalence point

Solubility Equilibria

• Solubility is the amount of a substance that dissolves to form a saturated solution
• It is expressed in g/L or mol/L (molar solubility).
• Ksp the solubility-product constant
• The Ksp is the equilibrium constant for the dissolution of a slightly soluble ionic compound
• A smaller Ksp indicates lower solubility.
• The Ksp expression is written as the product of the ion concentrations, each raised to the power of its stoichiometric coefficient in the balanced dissolution equation
• Ksp can be calculated from solubility, and solubility can be calculated from Ksp
• Ionic strength and other simultaneous equilibria (e.g., hydrolysis) can affect solubility and deviate from values calculated solely from Ksp

Factors Affecting Solubility

• The solubility of a slightly soluble salt is decreased by the presence of a common ion
• Solubility in the presence of a common ion is calculated using the Ksp expression and an ICE table
• The common-ion effect is more pronounced for ions with higher charges
• The solubility of salts containing basic anions increases as the solution becomes more acidic (pH decreases)
• H⁺ ions react with the basic anion, shifting the solubility equilibrium to the right
• Solubility at different pH values is calculated by considering both the solubility equilibrium and the acid-base equilibrium of the anion
• The effect of pH on solubility is more pronounced for more basic anions
• The solubility of metal salts increases in the presence of Lewis bases that form stable complex ions with the metal cation
• Kf is the formation constant with a larger Kf indicating a more stable complex ion
• Solubility in the presence of a complexing agent is calculated by considering both the solubility equilibrium and the complex ion formation equilibrium
• The overall equilibrium constant for the dissolution of a metal salt in the presence of a complexing agent is the product of Ksp and Kf
• Amphoteric substances are slightly soluble in water but dissolve in both acidic and basic solutions
• They dissolve in acid because of the reaction of their basic anion with H⁺ and in base because of the formation of soluble complex ions
• The amphoteric behavior of metal hydroxides is often due to the formation of hydroxo complexes

Precipitation and Separation of Ions

• The reaction quotient (Q) is calculated like the Ksp expression but using non-equilibrium concentrations
• Predicting Precipitation: If Q > Ksp, precipitation occurs, if Q < Ksp, no precipitation occurs, and if Q = Ksp, the solution is saturated.
• Q is calculated from the initial ion concentrations and compared to Ksp to predict precipitation
• Selective precipitation separates ions based on the different solubilities of their salts
• A reagent is added that precipitates one or more ions but not others
• Example: Separating Ag⁺ from Pb²⁺ by adding Cl⁻ (AgCl precipitates, PbCl₂ remains soluble)
• Careful control of pH and the use of complexing agents can enhance the selectivity of precipitation reactions

Qualitative Analysis for Metallic Elements

• Qualitative analysis systematically separates and identifies metal ions in a mixture
• Ions are separated into groups based on the solubility of their salts
• After group separation, individual tests are used to identify specific metal ions
• Flame tests are used to identify alkali and alkaline earth metals based on the characteristic colors they impart to a flame
• The success of qualitative analysis depends on the careful control of reaction conditions (pH, reagent concentrations) to ensure complete separation of ions.

ICE and BCA Tables

• ICE (Initial, Change, Equilibrium) tables organize concentration information at different stages
• Use ICE Tables to calculate concentrations at equilibrium, problems involving equilibrium constants (Kc or Kp), when dealing with weak acids and bases.
• BCA (Before, Change, After) tables are similar to ICE tables but are often used in stoichiometry problems
• Use BCA Tables to determine amounts of reactants and products before and after a reaction, and in stoichiometric calculations to find limiting reactants or theoretical yields.
• ICE Tables are used for equilibrium problems, while BCA Tables are used for stoichiometric calculations

Facts to Memorize

• Arrhenius Definition: Acids increase [H⁺], bases increase [OH⁻] in water
• Brønsted-Lowry Definition: Acids donate H⁺, bases accept H⁺
• Conjugate Pairs: Differ by one H⁺; strong acid has weak conjugate base
• Autoionization of Water: 2H₂O ⇌ H₃O⁺ + OH⁻; Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C
• pH: -log[H⁺]; pH 7 is neutral, 7 is basic
• Strong Acids: HCl, HBr, HI, HNO₃, HClO₃, HClO₄, H₂SO₄ (first proton)
• Strong Bases: Group 1 hydroxides, heavier group 2 hydroxides
• Weak Acids/Bases: Partially dissociate/react with water; Ka/Kb values indicate strength
• Ka × Kb = Kw: For conjugate acid-base pairs at a given temperature
• Salt Hydrolysis: Anions of weak acids form basic solutions; cations of weak bases form acidic solutions
• Common Ion Effect: Decreases solubility of slightly soluble salts
• Buffers: Resist pH changes; contain weak acid/base and conjugate; pH ≈ pKa
• Henderson-Hasselbalch: pH = pKa + log([base]/[acid])
• Solubility Equilibria: Ksp = product of ion concentrations (each raised to its stoichiometric coefficient)
• Factors Affecting Solubility: Common ion effect, pH, complex ion formation
• Precipitation: Occurs when Q > Ksp
• Qualitative Analysis: Systematic separation and identification of metal ions