Aqueous Equilibria: Buffers, Titrations, and Solubility

Chapter 17: Aqueous Equilibria

Buffers

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They are essential in many biological and chemical systems to maintain a stable pH.

• Definition: A buffer is typically composed of a weak acid and its salt (conjugate base) or a weak base and its salt (conjugate acid).

• Function: Buffers work by having conjugate pairs that neutralize additions of acid or base to the system.

• Example: The blood is a classic example of a buffer system in the human body.

Calculating Buffer pH

The pH of a buffer solution can be calculated using the acid dissociation constant ($K_a$) and the Henderson-Hasselbalch equation.

• Generic Buffer System: $HA + H_2O \rightleftharpoons H_3O^+ + A^-$

• Acid Dissociation Constant: $K_a = \frac{[H_3O^+][A^-]}{[HA]}$

• Henderson-Hasselbalch Equation: $\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Note: Always use $pK_a$ for acid buffers, not $pK_b$.

Identifying Buffer Components

Correctly identifying the components of a buffer is crucial for calculations.

• Ensure initial amounts of both components of the conjugate pair are present.

• Determine which is the acid and which is the base.

• Use $pK_a$ for pH calculations.

• Relationship: For a conjugate pair, $K_w = K_a \times K_b$ and $pK_a + pK_b = 14$.

Buffer Example Calculation

Calculate the pH of an acetate buffer containing 0.10 M acetic acid and 0.10 M sodium acetate.

• Use the Henderson-Hasselbalch equation:

• $\text{pH} = \text{p}K_a + \log\left(\frac{[\text{acetate}]}{[\text{acetic acid}]}\right)$

Buffer Response to Addition of Acid or Base

Buffers resist changes from external stress by having both acid and base forms in solution simultaneously.

• Strong Base Addition (OH-): $OH^- + HA \rightarrow H_2O + A^-$

• Strong Acid Addition (H3O+): $H_3O^+ + A^- \rightarrow H_2O + HA$

• Example: Acetic acid/acetate buffer neutralizes added OH- or H+ to minimize pH change.

Calculating Changes in Buffer pH

To calculate buffer pH after addition of strong acid or base:

• Incorporate changes using the buffer equation.

• Determine initial concentrations of each conjugate pair.

• Adjust for limiting reagent (amount added).

• Apply the Henderson-Hasselbalch equation at equilibrium.

• Find the concentration of all components after mixing.

Buffer Capacity

Buffer capacity is the amount of acid or base a buffer can neutralize before the pH changes significantly.

• High concentrations of conjugate pair result in higher buffer capacity.

• Optimal buffers have approximately equal concentrations of acid and conjugate base.

• Effective buffer range is generally $\text{p}K_a \pm 1$.

• Biological Relevance: In blood, exceeding buffer capacity leads to acidosis or alkalosis, causing severe illness.

Composition of a Buffer

A buffer will not resist changes in pH if one component is less than 10% the concentration of the other.

• Weak acid + conjugate base are preferred for acidic buffers.

• Weak base + conjugate acid are preferred for basic buffers.

Example Table: Buffer System Properties

Buffer Type	Components	Effective pH Range
Acidic Buffer	Weak acid + conjugate base	$\text{p}K_a \pm 1$
Basic Buffer	Weak base + conjugate acid	$\text{p}K_b \pm 1$