Acid-Base Equilibria & Solution Equilibria: Buffers and pH Calculations

Acid-Base Equilibria & Solution Equilibria

Introduction to Buffers

Buffers are essential solutions in chemistry and biology that resist changes in pH when small amounts of strong acid or strong base are added. They play a critical role in maintaining stable pH environments in living systems, laboratory research, and medicine.

• Definition: A buffer is a solution that minimizes pH changes upon addition of small quantities of acid or base.

• Importance:

  • Living systems (e.g., human blood buffered at pH ~7.4)

  • Lab research

  • Medicine

  • Enzymes: function within narrow pH ranges

  • Ocean water: near-surface pH ~8.1–8.3

Buffer Solutions

Buffer solutions are composed of a weak acid or base and its conjugate partner, typically in the form of a salt. This combination allows the solution to neutralize added acids or bases.

• Types of Buffer Solutions:

  • Weak acid + salt of its conjugate base (e.g., HF + NaF)

  • Weak base + salt of its conjugate acid (e.g., NH3 + NH4Cl)

• Conjugate acid-base pair: The acid and base differ by one proton.

Common Ion Effect

The common ion effect describes how the addition of an ion already present in equilibrium shifts the position of equilibrium, affecting solubility and pH.

• Example: Adding NaF to an HF solution introduces more F- ions, shifting the equilibrium and increasing the pH.

• Le Chatelier’s Principle: The system responds to added F- by reducing HF dissociation, thus raising the pH.

Equilibrium Constant and Buffer Solutions

The equilibrium constant (Ka) for a weak acid does not change when a common ion is added, as long as the temperature remains constant.

• Key Point: $K_a$ is a constant at a given temperature.

• Example: For 1.0 M HF, $K_a = 7.2 \times 10^{-4}$ at 25°C, and remains unchanged if NaF is added at the same temperature.

Calculating pH of a Buffer Solution

To determine the pH of a buffer, first identify the major species present before any reactions occur. For a solution of HF and NaF:

• Major species: HF, Na+, F-, H2O

• Minor species: H+, F- (from dissociation, but not major contributors)

There are two main methods to calculate the pH of a buffer:

1. Use an ICE (Initial, Change, Equilibrium) table to solve for [H+].

2. Apply the Henderson-Hasselbalch equation for a shortcut.

ICE Table Method

The ICE table is a systematic way to calculate equilibrium concentrations:

• Reaction: $\mathrm{HF} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}_3\mathrm{O}^+ + \mathrm{F}^-$

• Simplified: $\mathrm{HF} \rightleftharpoons \mathrm{H}^+ + \mathrm{F}^-$

• Set up initial concentrations, changes, and equilibrium values to solve for [H+].

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a quick way to calculate the pH of a buffer solution:

• Equation: $pH = pK_a + \log \left( \frac{[A^-]}{[HA]} \right)$

• Conditions: Valid only for buffer solutions where $0.1 < \frac{[A^-]}{[HA]} < 10$.

• Example: For [HF] = 1.0 M and [NaF] = 0.5 M: $pH = pK_a + \log \left( \frac{0.5}{1.0} \right)$

Effect of Adding Strong Base to Buffer

When a strong base (e.g., NaOH) is added to a buffer, the buffer neutralizes the base, minimizing the pH change.

• Major species after addition: HF, Na+, F-, OH-, H2O

• Reaction: $\mathrm{HF} + \mathrm{OH}^- \rightarrow \mathrm{F}^- + \mathrm{H}_2\mathrm{O}$

• Stoichiometry: Use a before-and-after table with moles to determine how much HF and F- remain after neutralization.

	HF	OH-	F-	H2O
Before	0.040 mol	0.002 mol	0.020 mol	XXXX
Change	-0.002 mol	-0.002 mol	+0.002 mol	XXXX
After	0.038 mol	0 mol	0.022 mol	XXXX

• All of the limiting reagent (OH-) is used up.

• After neutralization, the solution still contains both HF and F-, so it remains a buffer.

• Use the Henderson-Hasselbalch equation to calculate the new pH.

Summary: Buffers Resist Change in pH

Buffers are effective at minimizing pH changes compared to unbuffered solutions. For example, adding NaOH to deionized water causes a large pH increase, while adding the same amount to a buffer results in only a small change.

• Unbuffered solution: Large pH change (e.g., pH from 2.84 to 12.7)

• Buffered solution: Small pH change (e.g., pH from 2.84 to 2.9)

Key Equations and Concepts

• Henderson-Hasselbalch equation: $pH = pK_a + \log \left( \frac{[A^-]}{[HA]} \right)$

• ICE table: Used for equilibrium calculations in buffer and acid-base reactions.

• Stoichiometry: Used to determine changes in moles when strong acids or bases are added to buffers.

Additional info: These notes cover the foundational concepts of buffer solutions, their composition, the common ion effect, and methods for calculating pH, including the use of ICE tables and the Henderson-Hasselbalch equation. The importance of buffers in biological and chemical systems is emphasized, along with practical examples and calculations.