Acids, Bases, pH, and Biological Buffers: Key Concepts and Calculations

Acids and Bases

Brønsted-Lowry Theory of Acids and Bases

The Brønsted-Lowry theory defines acids and bases in terms of proton transfer. This concept is foundational for understanding acid-base reactions in organic and biological chemistry.

• Brønsted acid: A substance that donates a proton (H+) to another substance.

• Brønsted base: A substance that accepts a proton (H+) from another substance.

• Proton (H+): The hydrogen ion, which is transferred in acid-base reactions.

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

Strong vs. Weak Acids and Bases

Acids and bases are classified by their ability to donate or accept protons. The strength is determined by the extent of ionization in water.

• Strong acids: Completely ionize in water (e.g., HCl).

• Weak acids: Only partially ionize (e.g., CH3COOH).

• Strong bases: Completely accept protons or produce OH- ions (e.g., O2-).

• Weak bases: Only partially accept protons (e.g., NH3).

• Example: Magnesium reacts more vigorously with HCl (strong acid) than with CH3COOH (weak acid) due to higher hydronium ion concentration.

Conjugate Acid-Base Pairs

Every acid has a conjugate base, and every base has a conjugate acid. The strength of an acid is inversely related to the strength of its conjugate base.

• Conjugate acid: Formed when a base gains a proton.

• Conjugate base: Formed when an acid loses a proton.

• Example: Acetic acid (CH3COOH) loses a proton to become acetate (CH3COO-).

pH and pOH: Calculations and Concepts

Definition and Scale

The pH scale measures the acidity or basicity of a solution, while pOH measures the concentration of hydroxide ions. Both are logarithmic scales.

• pH: $pH = -\log[H_3O^+]$

• pOH: $pOH = -\log[OH^-]$

• Relationship: $pH + pOH = 14$ (at 25°C)

• Scale: pH < 7 is acidic, pH = 7 is neutral, pH > 7 is basic.

• Example: If pH = 1.7 (stomach acid), then pOH = 14 - 1.7 = 12.3.

Calculating Ion Concentrations

Given pH or pOH, you can calculate the concentrations of hydronium and hydroxide ions using inverse logarithms.

• Hydronium ion concentration: $[H_3O^+] = 10^{-pH}$

• Hydroxide ion concentration: $[OH^-] = 10^{-pOH}$

• Example: For pH = 1.7, $[H_3O^+] = 10^{-1.7} = 0.0199$ mol dm-3; $[OH^-] = 10^{-12.3} = 5.01 \times 10^{-13}$ mol dm-3.

Logarithmic Representation

Logarithms are used to compress large ranges of concentration values into manageable numbers for graphical and analytical purposes.

• Logarithmic scale: Converts values from $10^{-4}$ to $10^{6}$ into a range from -4 to 6.

• Negative logarithms: Correspond to concentrations between 0 and 1.

• Positive logarithms: Correspond to concentrations greater than 1.

Acidity and Basicity Constants

Acid and Base Dissociation Constants

The strength of acids and bases is quantified by their dissociation constants (Ka for acids, Kb for bases) and their logarithmic counterparts (pKa, pKb).

• Acid dissociation constant: $K_a$

• Base dissociation constant: $K_b$

• pKa: $pK_a = -\log K_a$

• pKb: $pK_b = -\log K_b$

• Relationship: $pK_a + pK_b = pK_w = 14.00$ at 25°C

Table: Acidity and Basicity Constants at 25°C

Acid	Ka	pKa	Base	Kb	pKb
Trichloroacetic acid	8.0 × 10-1	0.10	Urea	1.0 × 10-14	13.96
Acetic acid	1.8 × 10-5	4.75	Methylamine	4.4 × 10-4	3.36
Hydrofluoric acid	6.8 × 10-4	3.17	Ammonia	1.8 × 10-5	4.76
Hydrochloric acid	1.3 × 106	-6.00	Hydroxide ion	0.1	1.00
Water	1.0 × 10-14	14.00	Water	1.0 × 10-14	14.00
Additional info: See full table for more acids and bases.

Table: Conjugate Acid-Base Pairs Arranged by Strength

Acid Name	Formula	Base Formula	Name
Hydrobromic acid	HBr	Br-	Bromide ion
Acetic acid	CH3COOH	CH3COO-	Acetate ion
Water	H2O	OH-	Hydroxide ion
Ammonium ion	NH4+	NH3	Ammonia
Additional info: See full table for more pairs.

Buffer Solutions

Definition and Function

A buffer is a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid) that stabilizes the pH of a solution by neutralizing added acids or bases.

• Buffer action: Buffers resist changes in pH when small amounts of acid or base are added.

• Composition: Typically consists of a weak acid and its salt, or a weak base and its salt.

• Example: Acetic acid/acetate buffer (CH3COOH/CH3COO-).

Table: Typical Buffer Systems

Composition	pKa
CH3COOH/CH3COO-	4.74
HNO2/NO2-	3.37
HCIO2/CIO2-	2.00
NH4+/NH3	9.25
(CH3)3NH+/(CH3)3N	9.81
H2PO4-/HPO42-	7.21

Henderson-Hasselbalch Equation

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

• Equation: $pH = pK_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right)$

• Application: Used to calculate the pH of buffer solutions and to design buffers with desired pH values.

• Example: For equal concentrations of acid and base, $pH = pK_a$.

Buffer Capacity and Range

Buffers are most effective when the concentrations of acid and base are similar, typically within one pH unit of the pKa.

• Buffer range: pH lies between $pK_a \pm 1$ for a wide range of concentrations.

• Buffer capacity: The ability of a buffer to resist pH change decreases as the ratio of acid to base becomes very large or very small.

• Graphical representation: The pH changes very little as strong base or acid is added, until the buffer is overwhelmed.

Approximate pH Calculation for Weak Acids

For weak acids with small dissociation constants, the following approximation can be used:

• Equation: $pH = \frac{1}{2} pK_a - \frac{1}{2} \log C$

• Example: For acetic acid ($pK_a = 4.75$, $C = 0.1$ mol dm-3): $pH = (1/2 \times 4.75) - (1/2 \times \log 0.1) = 2.88$

• Additional info: This approximation is valid when $K_a < 1 \times 10^{-5}$.

Summary Table: Key Equations

Equation	Description
$pH = -\log[H_3O^+]$	Calculates pH from hydronium ion concentration
$pOH = -\log[OH^-]$	Calculates pOH from hydroxide ion concentration
$pH + pOH = 14$	Relationship at 25°C
$pH = pK_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right)$	Henderson-Hasselbalch equation for buffers
$pH = \frac{1}{2} pK_a - \frac{1}{2} \log C$	Approximate pH for weak acids

Key Takeaways

• Acids and bases are defined by their ability to donate or accept protons.

• pH and pOH are logarithmic measures of acidity and basicity, respectively.

• Buffer solutions stabilize pH by neutralizing added acids or bases.

• The Henderson-Hasselbalch equation is essential for buffer calculations.

• Acidity and basicity constants allow comparison and classification of acids and bases.