Acids and Bases

Buffer Solutions: AP Chemistry Rundown

What is a Buffer Solution?

A buffer solution is an aqueous solution that resists changes in pH upon the addition of small amounts of acid or base. It works by containing a weak acid and its conjugate base, or a weak base and its conjugate acid. The components of the buffer neutralize added acid or base, preventing drastic pH changes.

Components of a Buffer

A buffer solution must contain two components:

• A Weak Acid and its Conjugate Base: For example, acetic acid ( $ CH_3COOH $ ) and acetate ion ( $ CH_3COO^− $ ), commonly found as sodium acetate ( $ CH_3COONa $ ).
• A Weak Base and its Conjugate Acid: For example, ammonia ( $ NH_3 $ ) and ammonium ion ( $ NH_4^+ $ ), commonly found as ammonium chloride ( $ NH_4Cl $ ).

Buffer Composition

How Buffers Work

The key to a buffer’s function is the equilibrium between the weak acid/base and its conjugate.

• Adding Acid ( $ H^+ $ ): The conjugate base reacts with the added acid, neutralizing it and shifting the equilibrium towards the weak acid form.

  $ A^- (aq) + H^+ (aq) \rightleftharpoons HA (aq) $

• Adding Base ( $ OH^- $ ): The weak acid reacts with the added base, neutralizing it and shifting the equilibrium towards the conjugate base form.

  $ HA (aq) + OH^- (aq) \rightleftharpoons A^- (aq) + H_2O (l) $

Neutralization Reactions in Buffers

The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation allows us to calculate the pH of a buffer solution:

• For a weak acid ( $ HA $ ) buffer:

  $ pH = pK_a + log \frac{[A^-]}{[HA]} $

• For a weak base ( $ B $ ) buffer:

  $ pOH = pK_b + log \frac{[BH^+]}{[B]} $

  Since $ pH + pOH = 14 $ , we can find pH from pOH.

Where:

• $ pK_a = -log(K_a) $ ( $ K_a $ is the acid dissociation constant)
• $ pK_b = -log(K_b) $ ( $ K_b $ is the base dissociation constant)
• $ [A^-] $ is the concentration of the conjugate base.
• $ [HA] $ is the concentration of the weak acid.
• $ [BH^+] $ is the concentration of the conjugate acid.
• $ [B] $ is the concentration of the weak base.

Henderson-Hasselbalch Equation Derivation

Buffer Capacity

Buffer capacity is the amount of acid or base a buffer can neutralize before the pH begins to change appreciably. A buffer is most effective when the concentrations of the weak acid/base and its conjugate are equal (or close to equal), where $ pH \approx pK_a $ . Higher concentrations of the buffer components lead to a greater buffer capacity.

Buffer Capacity Factors

Preparing a Buffer Solution

There are two main ways to prepare a buffer solution:

1. Direct Mixing: Dissolve a weak acid (or base) and its conjugate salt in water. Use the Henderson-Hasselbalch equation to determine the appropriate ratio of acid/base to achieve the desired pH.

2. Partial Neutralization: Start with a solution of a weak acid (or base) and partially neutralize it with a strong base (or acid). This creates a mixture of the weak acid/base and its conjugate. For example, add NaOH to acetic acid.

   $ CH_3COOH (aq) + NaOH (aq) \rightarrow CH_3COONa (aq) + H_2O (l) $

Buffer Preparation Methods

Buffer Range

The effective buffering range is generally considered to be $ pH = pK_a \pm 1 $ . A buffer is most effective when the desired pH is close to the $ pK_a $ of the weak acid.

Titration Curves and Buffers

Buffer regions are visible on titration curves. The region of the titration curve where the pH changes slowly corresponds to the buffering region. The midpoint of this region corresponds to the $ pK_a $ of the weak acid being titrated. At the half-equivalence point, $ [HA] = [A^-] $ , and $ pH = pK_a $ .

Titration Curve Buffer Regions

Common Mistakes

• Using Strong Acids/Bases: Buffers must contain a weak acid/base and its conjugate. Strong acids/bases completely dissociate and do not form buffers.
• Incorrect Ratio: The ratio of the weak acid/base and its conjugate significantly affects the pH. Use the Henderson-Hasselbalch equation to calculate the correct ratio.
• Exceeding Buffer Capacity: Adding too much acid or base will overwhelm the buffer, and the pH will change drastically.

Key Takeaways

• Buffers resist changes in pH.
• Buffers contain a weak acid/base and its conjugate.
• The Henderson-Hasselbalch equation is used to calculate the pH of a buffer.
• Buffer capacity is the amount of acid or base a buffer can neutralize.
• Buffers are most effective within a range of $ pH = pK_a \pm 1 $ .
• Buffer regions can be identified on titration curves.

AP Chemistry Buffer Problems