Chapter 17: Additional Aspects of Aqueous Equilibria – Buffers, Common Ion Effect, and Acid-Base Titrations

Common Ion Effect

Definition and Explanation

The common ion effect refers to the shift in chemical equilibrium that occurs when an ion already present in the equilibrium is added to the solution. This effect is a direct application of Le Chatelier's Principle.

• Key Point: Adding a salt that contains an ion common to the equilibrium will shift the position of equilibrium to reduce the concentration of that ion.

• Example: For the equilibrium $\mathrm{HF(aq) \rightleftharpoons H^+(aq) + F^-(aq)}$, adding $\mathrm{NaF}$ (which dissociates to $\mathrm{Na^+}$ and $\mathrm{F^-}$) increases $\mathrm{F^-}$, shifting the equilibrium to the left and decreasing $\mathrm{H^+}$ concentration.

Sample Problem: Effect on pH

Calculating pH with Common Ion

When a common ion is added, the equilibrium concentrations change, affecting the pH.

• ICE Table: Used to track changes in concentrations.

• Example: Calculate the pH of a solution containing 1.0 M HF ($K_a = 7.2 \times 10^{-4}$) and 1.0 M NaF.

Species	Initial	Change	Equilibrium
HF	1.0 M	-x	1.0-x
H+	0	+x	x
F-	1.0 M	+x	1.0+x

Set up the equilibrium expression:

$K_a = \dfrac{[H^+][F^-]}{[HF]} = \dfrac{x(1.0+x)}{1.0-x} = 7.2 \times 10^{-4}$

Assuming $x$ is small, $x \approx 7.2 \times 10^{-4}$, so $pH = -\log(7.2 \times 10^{-4}) = 3.14$ (compare with 1.0 M HF alone, $pH = 1.57$).

Buffered Solutions

Definition and Composition

A buffer is a solution that resists changes in pH when small amounts of acid or base are added. Buffers are essential in maintaining stable pH in chemical and biological systems.

• Key Point: Buffers consist of a mixture of either:

  • a weak acid and its conjugate base (e.g., $\mathrm{HC_2H_3O_2}$ and $\mathrm{C_2H_3O_2^-}$)

  • or a weak base and its conjugate acid (e.g., $\mathrm{NH_3}$ and $\mathrm{NH_4^+}$)

Buffer Example: Acetic Acid and Sodium Acetate

Consider a mixture of acetic acid ($\mathrm{HC_2H_3O_2}$) and sodium acetate ($\mathrm{NaC_2H_3O_2}$):

• $\mathrm{HC_2H_3O_2(aq) + H_2O(l) \rightleftharpoons H_3O^+ + C_2H_3O_2^-(aq)}$

• $\mathrm{NaC_2H_3O_2(aq) \rightarrow Na^+(aq) + C_2H_3O_2^-(aq)}$

• Both weak acid and conjugate base are present in excess, providing buffering action.

Buffer Action: Bar Graph Illustration

When $\mathrm{OH^-}$ is added to a buffer, it reacts with the weak acid to form water and the conjugate base. When $\mathrm{H^+}$ is added, it reacts with the conjugate base to form the weak acid. The buffer maintains nearly constant concentrations of $\mathrm{H^+}$ and $\mathrm{OH^-}$.

Buffer pH Change Example

• 1.0 L of 0.50 M $\mathrm{HC_2H_3O_2}$ + 0.50 M $\mathrm{NaC_2H_3O_2}$: $pH = 4.74$

• Adding 0.010 mol solid NaOH raises the pH to 4.76, a very minor change, demonstrating buffer action.

Buffering Capacity

Definition and Factors

Buffering capacity is the amount of acid ($\mathrm{H^+}$) or base ($\mathrm{OH^-}$) a buffer can absorb without a significant change in pH.

• Depends on the concentrations of the weak acid and its conjugate base.

• Higher concentrations provide greater buffering capacity.

• Buffer reaction: $\mathrm{HA(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + A^-(aq)}$

Henderson-Hasselbalch Equation

Derivation and Use

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentrations of the weak acid and its conjugate base.

• Starting from $[H_3O^+] = K_a \dfrac{[HA]}{[A^-]}$

• Taking $-\log$ of both sides:

$pH = pK_a + \log \left( \dfrac{[A^-]}{[HA]} \right)$

• Useful for calculating pH of buffer solutions when concentrations of acid and base are known.

• Assumes the change in concentration ($x$) is small.

Simplified Common Ion Problem Using H-H Equation

Example Calculation

• Calculate the pH of a solution containing 0.75 M lactic acid ($\mathrm{HC_3H_5O_3}$, $K_a = 1.4 \times 10^{-4}$) and 0.25 M sodium lactate ($\mathrm{NaC_3H_5O_3}$).

• Reaction: $\mathrm{HC_3H_5O_3(aq) + H_2O(l) \rightleftharpoons H_3O^+ + C_3H_5O_3^-(aq)}$

• Apply Henderson-Hasselbalch:

$pH = pK_a + \log \left( \dfrac{[C_3H_5O_3^-]}{[HC_3H_5O_3]} \right) = 3.85 + \log \left( \dfrac{0.25}{0.75} \right) = 3.85 - 0.48 = 3.37$

Summary Table: Buffer Components and Their Roles

Buffer Type	Weak Acid	Conjugate Base	Weak Base	Conjugate Acid
Acidic Buffer	HC2H3O2	C2H3O2-	—	—
Basic Buffer	—	—	NH3	NH4+

Additional info: These notes cover the foundational concepts of buffer solutions, the common ion effect, and the mathematical treatment of buffer pH using the Henderson-Hasselbalch equation, which are essential for understanding acid-base equilibria in General Chemistry.