Buffers

Homogeneous vs. Heterogeneous Equilibrium

• Review from Chang chapter 16, covering definitions from chapter 14.

Common Ion Effect

• Application of Le Chatelier's principle.
• Qualitative understanding.
• Example: Acetic acid solution with added sodium acetate.
  • The common ion is acetate.
  • Equilibrium system: $CH<em>3COOH \rightleftharpoons H^+ + CH</em>3COO^-$
  • Adding sodium acetate increases acetate concentration, shifting the equilibrium to the left.
  • This reduces H+ concentration, increasing pH.

Quantitative Analysis and Henderson-Hasselbalch Equation

• Used to quantify the common ion effect.
• Derivation:
  • Start with the weak acid dissociation constant: $K_a = \frac{[H^+][A^-]}{[HA]}$
  • Take the negative log of both sides: $-log(K_a) = -log(\frac{[H^+][A^-]}{[HA]})$
  • Define $pK<em>a = -log(K</em>a)$
  • Using logarithm properties:
    • $pK_a = -log[H^+] - log[A^-] + log[HA]$
    • $pK_a = pH - log[A^-] + log[HA]$
  • Rearrange to get the Henderson-Hasselbalch equation:
    • $pH = pK_a + log(\frac{[A^-]}{[HA]})$
• Assumptions:
  • Equilibrium concentrations are approximately equal to initial concentrations due to small $K_a$ values.

Buffers

• Definition: A solution that resists changes in pH upon addition of small amounts of acid or base.
• Buffers contain both an acid and a base to neutralize excess base or acid, respectively.
• Key: Use a weak acid and its conjugate base (or a weak base and its conjugate acid) to avoid neutralization.
  • Example: Acetic acid and sodium acetate.
  • If $H^+$ is neutralized by acetate, it regenerates acetic acid.
  • If acetate hydrolyzes to form hydroxide, acetic acid neutralizes it back to acetate.
• Adding excess acid (e.g., HCl) to a buffer:
  • Acetate neutralizes the acid.
  • Small pH change occurs.
• Adding excess base (e.g., NaOH) to a buffer:
  • Acetic acid neutralizes the base.
  • Slight pH change occurs.
• Demonstration in Lab:
  • Compare pH changes in buffer vs. distilled water upon adding strong acid/base.

Le Chatelier's Principle and Buffers

• Buffer solutions often contain equal amounts of weak acid and conjugate base (e.g., acetic acid and sodium acetate).
  • Adding excess hydronium shifts equilibrium left, consuming added acid and restoring pH.
  • Adding excess base removes hydronium, shifting equilibrium right to restore original concentration.
  • Equilibrium shifts until $Q = K$.
• Buffer Capacity:
  • Adding enough excess acid consumes all acetate, crashing the buffer.
  • Adding enough excess hydroxide consumes all acetic acid, also crashing the buffer.
  • Exceeding buffer capacity means the solution can no longer resist pH changes.
  • Stoichiometry matters.

Sample Test Question: Identifying Buffers

• Determine if pairs of solutions can function as a buffer by checking for a weak acid and its conjugate base or a weak base and its conjugate acid.
• Examples:
  • Nitric acid and sodium nitrate:
    • Nitric acid is a strong acid, so no buffer.
  • HF and KF:
    • HF is a weak acid, and F- is its conjugate base, so it's a buffer.
  • Ammonia and NH4Cl:
    • Ammonia is a weak base, and NH4+ is its conjugate acid, so it's a buffer.
  • Two weak acids cannot form a buffer.
  • Strong base and neutral salt cannot form a buffer.

Quantitative Analysis with Henderson-Hasselbalch Equation

• Equation: $pH = pK_a + log(\frac{[A^-]}{[HA]})$
• Where:
  • $[A^-]$ is the concentration of the conjugate base.
  • $[HA]$ is the concentration of the weak acid.
• Assumptions:
  • Initial concentrations are approximately equal to equilibrium concentrations.
• Tenfold change in the ratio of conjugate base to weak acid leads to a pH change of one unit.
• To prepare a buffer of a specific pH, choose an acid whose $pK_a$ is close to the desired pH.

Lab Buffer Calculations

• Distilled Water Control:
  • Adding HCl or NaOH results in significant pH changes.
  • Using $M<em>1V</em>1 = M<em>2V</em>2$ to calculate concentration of acid/base.
  • $pH = -log[H^+]$ or $pH = 14 + log[OH^-]$
• Buffer Calculations:
  • Using Henderson-Hasselbalch equation:
    • $pH = pK_a + log(\frac{[A^-]}{[HA]})$
  • Initial Concentrations: Calculate using stoichiometry and dilution.
  • Example with acetic acid and sodium acetate:
    • Moles of sodium acetate = grams / molecular weight.
    • Moles of acetic acid = volume * molarity.
  • $pK<em>a = -log(K</em>a) = 4.7$
  • If initial concentrations are equal, pH = pKa.
• Adding HCl to Buffer:
  • HCl neutralizes acetate.
  • Changes in moles of acetate and acetic acid.
  • Use Henderson-Hasselbalch to find new pH.
• Adding NaOH to Buffer:
  • NaOH neutralizes acetic acid.
  • Changes in moles of acetate and acetic acid.
  • Use Henderson-Hasselbalch to find new pH.

Results

• Buffers significantly reduce pH changes compared to distilled water.

Sample Problem

• Problem: Calculate pH of a buffer with KF and HF.
• Use Henderson-Hasselbalch equation: $pH = pK_a + log(\frac{[F^-]}{[HF]})$
• [F-] = [KF] because KF dissociates completely.
• Use grams of KF and its molecular weight to find moles of KF, and then concentration of F-.
• Use $M<em>1V</em>1 = M<em>2V</em>2$ to find [HF] after dilution.
• Plug in values to get pH.

Other Topics in Chapter 16

• Acid-base titrations.
• Acid-base indicators: Chemicals that change color depending on pH.