General Chemistry II Unit 4 Review: pH Equations & Curves

Key Concepts

• Buffers resist changes in pH when small amounts of acid or base are added
• Consist of a weak acid and its conjugate base (or weak base and conjugate acid) in roughly equal concentrations
• Henderson-Hasselbalch equation relates pH, pKa, and ratio of conjugate base to weak acid concentrations: $pH = pKa + log\frac{[A^-]}{[HA]}$
• Titrations quantitatively analyze the concentration of an unknown solution by reacting it with a known solution
• Equivalence point occurs when the moles of titrant equal the moles of analyte and the reaction is complete
• pH curves graphically represent the pH changes during a titration, with the steepest point indicating the equivalence point
• Buffer capacity measures a buffer's ability to resist pH changes upon addition of acid or base
  • Depends on the concentrations of the weak acid and conjugate base components

Buffer Basics

• Formed by combining a weak acid (HA) and its conjugate base (A^-) in solution
• Weak acid partially dissociates in water: $HA + H_2O \rightleftharpoons H_3O^+ + A^-$
• Conjugate base is the species formed when the weak acid loses a proton (H^+)
• Common buffer systems include acetic acid/acetate (CH₃COOH/CH₃COO^-) and carbonic acid/bicarbonate (H₂CO₃/HCO₃^-)
• Maintain relatively constant pH by neutralizing added acid (H^+) or base (OH^-)
  • Added H^+ reacts with conjugate base: $H^+ + A^- \rightarrow HA$
  • Added OH^- reacts with weak acid: $OH^- + HA \rightarrow A^- + H_2O$
• Most effective when pH is close to the pKa of the weak acid component

Buffer Calculations

• Henderson-Hasselbalch equation calculates buffer pH from pKa and ratio of conjugate base to weak acid concentrations
  • pKa is the negative logarithm of the acid dissociation constant (Ka): $pKa = -log(Ka)$
• Rearranging the equation allows calculation of the conjugate base to weak acid ratio needed to achieve a target pH: $\frac{[A^-]}{[HA]} = 10^{pH - pKa}$
• Buffer preparation involves combining appropriate amounts of weak acid and conjugate base
  • Example: To prepare a pH 4.75 acetate buffer (pKa = 4.76), mix equal volumes of 0.1 M acetic acid and 0.1 M sodium acetate
• pH changes can be calculated when small amounts of strong acid or base are added to a buffer
  • Use an ICE table (Initial, Change, Equilibrium) to determine the new equilibrium concentrations

Titration Fundamentals

• Titration is a technique used to determine the concentration of an unknown solution (analyte) by reacting it with a solution of known concentration (titrant)
• Titrant is added gradually to the analyte until the reaction is complete, indicated by a color change in an indicator or a steep change in pH
• Endpoint is the point at which the indicator changes color, ideally close to the equivalence point
• Equivalence point occurs when the moles of titrant added equal the moles of analyte in the solution
  • Calculated using the balanced chemical equation and stoichiometry
• Common titrations include acid-base, redox, and complexometric titrations
• Titration setup consists of a burette (to dispense titrant), Erlenmeyer flask (to hold analyte), and a stirring device
• Accurate results require precise measurement of the analyte volume and careful titrant addition

Acid-Base Titrations

• Involve the reaction of an acid with a base to form water and a salt
• Strong acid-strong base titration (e.g., HCl vs. NaOH): $H^+ + OH^- \rightarrow H_2O$
  • Equivalence point occurs at pH 7 (neutral)
• Weak acid-strong base titration (e.g., CH₃COOH vs. NaOH): $CH_3COOH + OH^- \rightarrow CH_3COO^- + H_2O$
  • Equivalence point occurs at pH > 7 due to hydrolysis of the conjugate base
• Weak base-strong acid titration (e.g., NH₃ vs. HCl): $NH_3 + H^+ \rightarrow NH_4^+$
  • Equivalence point occurs at pH < 7 due to hydrolysis of the conjugate acid
• Indicators are weak acids or bases that change color at specific pH ranges
  • Selected based on the expected pH at the equivalence point

pH Curves

• Graphical representation of pH changes during a titration
• x-axis represents the volume of titrant added, while y-axis represents the pH of the solution
• Shape of the curve depends on the strengths of the acid and base involved
• Strong acid-strong base titration curve has a steep rise in pH near the equivalence point
  • Equivalence point occurs at pH 7 (neutral)
• Weak acid-strong base titration curve has a more gradual rise in pH and a buffer region near the pKa of the weak acid
  • Equivalence point occurs at pH > 7
• Weak base-strong acid titration curve has a more gradual decrease in pH and a buffer region near the pKa of the conjugate acid
  • Equivalence point occurs at pH < 7
• Half-equivalence point is the point at which half of the analyte has been neutralized
  • Occurs at a pH equal to the pKa of the weak acid or conjugate acid of the weak base

Buffer Capacity

• Measure of a buffer's ability to resist pH changes when small amounts of acid or base are added
• Depends on the concentrations of the weak acid and conjugate base components
  • Higher concentrations provide greater buffer capacity
• Maximum buffer capacity occurs when the concentrations of weak acid and conjugate base are equal (pH = pKa)
• Buffer capacity decreases as the pH moves further from the pKa of the weak acid component
• Can be quantified by the Van Slyke equation: $\beta = 2.3C \frac{K_a[H^+]}{(K_a+[H^+])^2}$
  • C is the total buffer concentration (sum of weak acid and conjugate base concentrations)
• Buffer capacity is important in maintaining stable pH in biological systems and industrial processes

Real-World Applications

• Maintaining pH in biological systems (blood, cytoplasm)
  • Bicarbonate buffer system (H₂CO₃/HCO₃^-) maintains blood pH around 7.4
  • Phosphate buffer system (H₂PO₄^-/HPO₄²^-) maintains intracellular pH around 7.2
• pH control in industrial processes (fermentation, wastewater treatment)
  • Acetate buffers maintain optimal pH for yeast growth in beer brewing
  • Carbonate buffers maintain pH in anaerobic digesters for wastewater treatment
• Environmental monitoring (ocean acidification, soil pH)
  • Carbonate buffer system (CO₂/HCO₃^-/CO₃²^-) regulates ocean pH
  • Soil pH affects nutrient availability and plant growth
• Analytical chemistry (titrations, chromatography)
  • Acid-base titrations determine the concentration of acids or bases in solutions
  • Buffer solutions control pH in high-performance liquid chromatography (HPLC) mobile phases
• Consumer products (food, cosmetics, cleaning agents)
  • Citrate buffers maintain pH in citrus-flavored beverages
  • Phosphate buffers control pH in shampoos and conditioners