7.S: Buffers, Titrations and Solubility Equilibria (Study Guide)

7.1: Acid-Base Buffers

• The common-ion effect argues that the dissociation of a weak electrolyte is decreased by adding a strong electrolyte to the solution that has a common ion with the weak electrolyte.
• Buffers are solutions that resist a change in pH

• Buffers have both acidic and basic species to neutralize H⁺ and OH^- ions
• Acid dissociation equilibrium in buffered solution \[ HX(aq) \rightleftharpoons H^+ (aq) + X^-(aq) \nonumber \] with \[ K_a = \dfrac{[H^+][X^-]}{[HX]} \nonumber \] or \[[H^+]= K_a \dfrac{[HX]}{[X^-]} \nonumber \]
  • pH determined by: value of K_a and the ratio of [HX]/[X^-]
  • if OH^- added:
    • \[ OH^-(aq) + HX(aq) \rightleftharpoons H_2O(l) + X^-(aq) \nonumber \]
      • Therefore [HX] decreases and [X^-] increases
      • if amounts of HX and X^- present are very much larger than the amount of OH^- added, then the ratio of [HX]/[X^-] will not change much, and so the increase in pH due to the added hydroxide ion is rather small
  • when [HX] and [X^-] are about the same, buffers are most effective: i.e., when \([H^+] = K_a\)

7.2 Practical Aspects of Buffers

• buffer capacity – amount of acid or base buffer can neutralize before the pH changes considerably
• capacity depends on amount of acid or base in buffer
• pH depends on K_a for acid and relative concentrations of the acid and base
• Henderson-Hasselbalch Approximation: \[ pH = pK_a + \log_{10} \dfrac{[base]}{[acid]} \nonumber \]
• [base] and [acid] = concentrations of conjugate acid-base pair
• when [base]=[acid], pH = pK_a
• can use initial concentrations of acid and base components of buffer directly into equation

7.3: Acid-Base Titrations

• solution containing a known [base] added to an acid or acid solution added to base
• acid-base indicators used to signal equivalence point, choose indicator that changes colour as close to equivalence point as possible
• titration curve – pH vs Volume

Strong Acid – Strong base Titrations

• pH starts out low ends high
• pH before equivalence point is pH of acid not neutralized by base
• pH at equivalence point is pH of solution
• pH equals 7.00
• for strong base titrations, the pH starts high ends low

The Addition of a Strong Base to a Weak Acid

• Reactions between weak acid and strong base goes to completion
• calculating pH before equivalence point
  • stoichiometric calculations: allow strong base to react to completion producing a solution containing a weak acid and its conjugate base
• equilibrium calculation: use K_a and equilibrium expression to find equilibrium concentrations of the weak acid and its conjugate base, and H⁺

Titration Curves for Weak Acids or Weak Bases

• Differences between strong acid-strong base titrations

1. solution of weak acid as higher initial pH than solution of a strong acid with same concentration
2. solution of weak acid rises more rapidly in early part of titration and more slowly as it reached the equivalence point
3. pH is not 7.00 at equivalence point

• before equivalence point solution has mixture of weak acid and its salt
• also called the buffer region of curve
• at equivalence point solution contains only salt
• weakly basic due to hydrolysis of anion
• after equivalence point solution has mixture of salt and excess strong base
• pH determined by [base]

• Titrations of Polyprotic Acids
  • reaction occurs in series of steps
  • titration curve shows multiple equivalence points

7.4: Solving Titration Problems

• Solving weak acid or base titration problems, look at where you are on the titration curve
  • initial pH before titrant added, acid or base equilibrium calculation
  • buffer region, use H-H
  • pH at equivalence point look at salt solution
  • pH after equivalence point, excess of titrant added
  • make sure to remember volume changes

7.5: Solubility Equilibria

• The Solubility-Product Constant, K_sp
• saturated solution – dissolved and undissolved solute are at equilibrium
• expressed by g/L
• molar solubility – moles of solute dissolved to form a liter of saturated solution (mol/L)
• K_sp equilibrium constant for the equilibrium between an ionic solid and its saturated solution
• Solubility of compound (g/L) à molar solubility of compound (mol/L) à [molar] of ions à K_sp of ions
• solubility affected by temperature and presence of other solutes. The solubility of ionic compound affected by:
• the presence of common ions
• pH of solution
• presence of complexing agent

• solubility of slightly soluble salt decreases when a second solute has a common ion

• solubility of any ionic compound affected if solution is acidic or basic
• change only noticeable if both ions are moderately acidic or basic
• solubility of slightly soluble salts containing basic anions increase as [H⁺] increases (as pH is lowered)
• the more basic an anion is, the greater the solubility will be affected by pH

• Q = ion product
  • If Q > K_sp, precipitation occurs until Q = K_sp
  • If Q = K_sp, equilibrium exists, have a saturated solution
  • If Q < K_sp, solid dissolves until Q = K_sp