General Chemistry II Unit 3 Review: pH and Brønsted-Lowry

Key Concepts and Definitions

• Acids donate protons (H⁺) in aqueous solutions, while bases accept protons
• Brønsted-Lowry theory defines acids as proton donors and bases as proton acceptors
• Conjugate acid-base pairs consist of a species and its corresponding proton-transfer product (HCl and Cl⁻)
• Amphoteric substances can act as both acids and bases depending on the environment (water, amino acids)
• Autoionization of water produces H⁺ and OH⁻ ions with a constant product of $K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C
• pH is a logarithmic scale that measures the concentration of H⁺ ions in a solution, defined as $pH = -\log[H^+]$
• pOH is a logarithmic scale that measures the concentration of OH⁻ ions in a solution, defined as $pOH = -\log[OH^-]$
• The relationship between pH and pOH is $pH + pOH = 14$ at 25°C

Acid-Base Theories

• Arrhenius theory defines acids as substances that produce H⁺ ions and bases as substances that produce OH⁻ ions in aqueous solutions
• Brønsted-Lowry theory expands the definition of acids and bases to include proton transfer reactions
• Lewis theory further broadens the definition of acids as electron pair acceptors and bases as electron pair donors
• Brønsted-Lowry acids and bases exist in conjugate pairs, with the acid having one more proton than its conjugate base (HNO₃ and NO₃⁻)
• Stronger acids have weaker conjugate bases, while stronger bases have weaker conjugate acids
• Acid-base reactions involve the transfer of a proton from an acid to a base, forming their respective conjugate base and acid
• The leveling effect occurs when a strong acid or base is dissolved in water, as the acid or base cannot be stronger than the solvent itself (H₃O⁺ or OH⁻)

pH Scale and Calculations

• The pH scale ranges from 0 to 14, with 7 being neutral, values below 7 acidic, and values above 7 basic
• To calculate pH from [H⁺], use the equation $pH = -\log[H^+]$
  • For example, if $[H^+] = 1.0 \times 10^{-5}$ M, then $pH = -\log(1.0 \times 10^{-5}) = 5$
• To calculate [H⁺] from pH, use the equation $[H^+] = 10^{-pH}$
  • For example, if pH = 3.2, then $[H^+] = 10^{-3.2} = 6.3 \times 10^{-4}$ M
• pOH can be calculated from [OH⁻] using the equation $pOH = -\log[OH^-]$
• [OH⁻] can be calculated from pOH using the equation $[OH^-] = 10^{-pOH}$
• The relationship between pH and pOH can be used to convert between the two scales
  • For example, if pH = 4.7, then pOH = 14 - 4.7 = 9.3

Strong vs. Weak Acids and Bases

• Strong acids and bases completely dissociate in aqueous solutions, while weak acids and bases only partially dissociate
• Strong acids have a large Ka value (>1), indicating a high degree of dissociation (HCl, HNO₃, H₂SO₄)
• Strong bases have a small Kb value (<10⁻¹⁴), indicating a high degree of dissociation (NaOH, KOH)
• Weak acids have a small Ka value (<1), indicating a low degree of dissociation (CH₃COOH, HF)
• Weak bases have a large Kb value (>10⁻¹⁴), indicating a low degree of dissociation (NH₃, CH₃NH₂)
• The strength of an acid or base depends on its ability to donate or accept protons, respectively
• The dissociation of a weak acid or base can be represented by an equilibrium expression (HA ⇌ H⁺ + A⁻)

Equilibrium Constants (Ka and Kb)

• The acid dissociation constant, Ka, represents the equilibrium constant for the dissociation of a weak acid (HA ⇌ H⁺ + A⁻)
  • $K_a = \frac{[H^+][A^-]}{[HA]}$
• The base dissociation constant, Kb, represents the equilibrium constant for the dissociation of a weak base (B + H₂O ⇌ BH⁺ + OH⁻)
  • $K_b = \frac{[BH^+][OH^-]}{[B]}$
• The relationship between Ka and Kb for a conjugate acid-base pair is $K_a \times K_b = K_w = 1.0 \times 10^{-14}$ at 25°C
• pKa and pKb are the negative logarithms of Ka and Kb, respectively
  • $pK_a = -\log K_a$ and $pK_b = -\log K_b$
• Smaller pKa values indicate stronger acids, while larger pKb values indicate stronger bases
• Equilibrium constants can be used to calculate the pH of weak acid or base solutions

Buffer Solutions

• Buffer solutions resist changes in pH when small amounts of acid or base are added
• Buffers consist of a weak acid and its conjugate base, or a weak base and its conjugate acid
• The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the conjugate base and acid
  • $pH = pK_a + \log \frac{[A^-]}{[HA]}$
• Buffer capacity is the amount of acid or base that can be added to a buffer solution before a significant change in pH occurs
• The optimal buffering range is within ±1 pH unit of the pKa of the acid or pKb of the base
• Buffers are important in biological systems to maintain stable pH environments (blood, cytoplasm)
• Common buffer systems include acetate (CH₃COOH/CH₃COO⁻), phosphate (H₂PO₄⁻/HPO₄²⁻), and carbonate (H₂CO₃/HCO₃⁻)

Titrations and Indicators

• Titrations are used to determine the concentration of an acid or base by reacting it with a known concentration of the opposite (standard solution)
• The equivalence point is reached when the moles of acid and base are equal, and the reaction is complete
• The endpoint is the point at which the indicator changes color, signaling the end of the titration
• Indicators are weak acids or bases that change color at specific pH ranges, typically near the equivalence point (phenolphthalein, methyl orange)
• Strong acid-strong base titrations have a sharp equivalence point at pH 7
• Weak acid-strong base titrations have an equivalence point at a pH > 7, while weak base-strong acid titrations have an equivalence point at a pH < 7
• Titration curves plot the pH of the solution against the volume of titrant added, showing the change in pH during the titration
• The shape of the titration curve depends on the strengths of the acid and base being titrated

Real-World Applications

• pH plays a crucial role in biological systems, as enzymes and other proteins function optimally within specific pH ranges (pepsin in the stomach, pH 1.5-2.5)
• Buffers maintain stable pH in the body, such as the bicarbonate buffer system in blood (pH 7.35-7.45)
• Acid-base reactions are used in the production of various products (soap, detergents, fertilizers)
• pH control is essential in water treatment, agriculture, and food processing to ensure quality and safety
• Acidic and basic solutions are used in cleaning products, with acidic solutions effective against mineral deposits and basic solutions effective against grease and oils
• Antacids neutralize excess stomach acid (HCl) to relieve heartburn and indigestion
• Ocean acidification, caused by increased absorption of atmospheric CO₂, has negative impacts on marine life (coral reefs, shellfish)
• Soil pH affects nutrient availability and plant growth, with most plants thriving in slightly acidic to neutral soils (pH 6.0-7.5)