Acids, Bases, and Buffers: Principles and Calculations

Acids, Bases, and Buffers

Introduction

This study guide covers the fundamental concepts of acids, bases, and buffers, focusing on their definitions, properties, and calculations of pH in aqueous solutions. These topics are essential for understanding chemical equilibria and biological systems in organic chemistry.

Brønsted Definition of Acids & Bases

Key Concepts

• Acid: A species that donates a proton (H+).

• Base: A species that accepts a proton.

• Example: When HCl dissolves in water, it donates a proton to H2O, forming Cl- and H3O+.

Strong Acids in Water	Strong Bases in Water
HBr	NaOH
HCl	KOH
HI	LiOH
HNO3	Ca(OH)2
HClO4	NaNH2
H2SO4 (1st ionization)

Strong Acids & Bases

Dissociation and pH Calculations

• Strong acids and bases completely dissociate in aqueous solutions.

• For strong acids: $\text{pH} = -\log[\text{H}^+]$

• For strong bases: $\text{pOH} = -\log[\text{OH}^-]$

• The product of [H+] and [OH-] in water is a constant: $K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$ at 25°C.

• $\text{p}K_w = -\log K_w = 14$

• $\text{pH} + \text{pOH} = 14$

The pH Scale

Understanding pH and pOH

• pH measures the acidity of a solution; neutrality is at pH 7.

• pH < 7: Acidic solution; pH > 7: Basic solution.

• pOH is the analogous scale for bases.

• Most biological systems maintain pH between 7.35 and 7.45.

Solution	Typical pH
Stomach acid	1-2
Urine	6
Blood	7.4
Ammonia solution	11

Logarithmic Scales

Application in Chemistry

• Logarithmic scales compress large ranges of values into manageable numbers.

• Negative logarithms correspond to concentrations less than 1 M.

• Positive logarithms correspond to concentrations greater than 1 M.

pH Metres

Measurement of pH

• A pH meter measures the potential difference between two electrodes in a solution.

• Directly displays pH; lower pH indicates higher [H3O+].

• Example: Orange juice (pH ~3.8) vs. lemon juice (pH ~2.6).

Calculating the pH of Solutions of Strong Acids & Bases

Worked Examples

• Calculate the pH by determining the molarity of H+ or OH- after dissociation.

• Example: Adding 10 g NaOH to 600 mL water—calculate moles, molarity, then pOH and pH.

• Example: Mixing Mg(OH)2 and HCl—calculate net [H+] or [OH-] after neutralization.

Weak Acids & Bases

Equilibrium and Dissociation

• Weak acids and bases do not fully dissociate in aqueous solutions.

• Equilibrium is described by the acid dissociation constant $K_a$ or base dissociation constant $K_b$.

• For water: $K_w = [\text{H}^+][\text{OH}^-]$

• For a weak acid: $K_a = \frac{[\text{H}_3\text{O}^+][\text{A}^-]}{[\text{HA}]}$

• The higher the $K_a$, the stronger the acid; the lower the $pK_a$, the stronger the acid.

Calculating pH of Weak Acid Solutions

• Case 1: If $[\text{HA}]_0 \gg 10^{-3}$ M and $K_a \ll 10^{-1}$, use the approximation:

$K_a = \frac{x^2}{[\text{HA}]_0}$, where $x = [\text{H}_3\text{O}^+]$

$[\text{H}_3\text{O}^+] = \sqrt{K_a [\text{HA}]_0}$

$\text{pH} = -\log [\text{H}_3\text{O}^+]$

• Case 2: If $[\text{HA}]_0 < 10^{-3}$ M or $K_a > 10^{-1}$, solve the quadratic equation:

$[\text{H}_3\text{O}^+]^2 + K_a [\text{H}_3\text{O}^+] - K_a [\text{HA}]_0 = 0$

$[\text{H}_3\text{O}^+] = \frac{-K_a + \sqrt{K_a^2 + 4K_a [\text{HA}]_0}}{2}$

Calculating pOH of Weak Base Solutions

• Analogous to acids, use $K_b$ and initial base concentration.

• For $[\text{B}]_0 \gg 10^{-3}$ M and $K_b \ll 10^{-1}$:

$K_b = \frac{x^2}{[\text{B}]_0}$, where $x = [\text{OH}^-]$

$[\text{OH}^-] = \sqrt{K_b [\text{B}]_0}$

$\text{pOH} = -\log [\text{OH}^-]$

Acidity and Basicity Constants Table

The following table lists common acids and bases with their $K_a$, $K_b$, $pK_a$, and $pK_b$ values at 25°C.

Acid	pKa	Base	pKb
Trichloroacetic acid	0.70	Ammonia	4.75
Acetic acid	4.76	Methylamine	3.36
Formic acid	3.75	Urea	0.18
Hydrochloric acid	-6.3	Chloride ion	20.7
Water	15.7	Hydroxide ion	-0.2
Additional info: See full table in textbook for more entries.

Conjugate Acid-Base Pairs

• The stronger the acid, the weaker its conjugate base.

• The stronger the base, the weaker its conjugate acid.

• Sum of $pK_a$ (acid) and $pK_b$ (conjugate base) is constant: $pK_a + pK_b = 14$ at 25°C.

Strong Acid	Conjugate Base
HCl	Cl-
HNO3	NO3-
Acetic acid	Acetate ion

Buffers

Definition and Mechanism

• A buffer is a solution that resists changes in pH upon addition of small amounts of acid or base.

• Formed by mixing a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Buffer action depends on equilibrium between acid/base and their conjugates.

Henderson-Hasselbalch Equation

• Relates pH to the ratio of conjugate base to acid:

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

$\text{pOH} = pK_b + \log \left( \frac{[BH^+]}{[B]} \right)$

Calculating the pH of Buffer Solutions

• Use the Henderson-Hasselbalch equation to calculate pH before and after addition of acid/base.

• Example: Mixing NaOH and sodium bicarbonate, use $pK_a$ of bicarbonate and concentrations to find pH.

Properties of Buffers

Buffer Capacity and Range

• Buffers are most effective within ±1 pH unit of the $pK_a$ of the acid.

• When [A-] = [HA], $\text{pH} = pK_a$.

• Choose buffer systems with $pK_a$ close to desired pH for maximum effectiveness.

Buffer System	pKa
CH3COOH/CH3COO-	4.76
H2CO3/HCO3-	6.37
H2PO4-/HPO42-	7.21

Recommended Reading

• Chemistry for the Biosciences – The essential concepts

• Chapter 16: Acids, bases, and the aqueous environment: the medium of life.

Additional info: These notes expand on the lecture slides by providing definitions, equations, and tables for reference. For more detailed examples and problem-solving strategies, consult the recommended textbook chapter.