Acid-Base Equilibria: Core Concepts and Calculations

Acid-Base Equilibria

Introduction to Acid-Base Equilibria

Acid-base equilibria are fundamental to understanding chemical reactions in aqueous solutions. This topic covers the identification of acids and bases, the equilibrium condition in acid-base reactions, and the quantitative relationships involving pH, pOH, and ion concentrations.

Identification of Equilibrium Condition in Acid-Base Reactions

Recognizing Acids and Bases

• Acids are substances that donate protons (H+), while bases accept protons.

• To analyze an acid-base reaction, identify the acid and base on both sides of the equation and determine which is stronger.

• The equilibrium favors the transfer of protons from the stronger acid to the weaker acid (or from the stronger base to the weaker base).

• Example: For the reaction $\mathrm{HNO_3(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + NO_3^-(aq)}$, the equilibrium lies to the right because HNO3 is a strong acid.

Autoionization of Water

Definition and Equilibrium Constant

• Autoionization (autoprotolysis) of water is the process where two water molecules react to form hydronium and hydroxide ions:

$\mathrm{2H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)}$

• The equilibrium constant for this reaction is:

$K_c = \frac{[H_3O^+][OH^-]}{[H_2O]^2}$

• In dilute solutions, the concentration of water is nearly constant, so we define the ion-product constant for water:

$K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C

• In pure water, $[H_3O^+] = [OH^-] = 1.0 \times 10^{-7}$ M

The pH Scale

Definition and Calculation

• pH is defined as the negative logarithm (base 10) of the hydronium ion concentration:

$pH = -\log [H_3O^+]$

• For pure water at 25°C, $pH = 7.00$ (neutral).

• Acidic solutions: $pH < 7.00$; Basic solutions: $pH > 7.00$.

• Example: If $pH = 4.3$, then $[H_3O^+] = 10^{-4.3}$ M.

pOH Scale and Relationship to pH

Definition and Interconversion

• pOH is defined as the negative logarithm of the hydroxide ion concentration:

$pOH = -\log [OH^-]$

• At 25°C, $pH + pOH = 14$.

• To find $[OH^-]$ from $[H_3O^+]$, use $[OH^-] = \frac{K_w}{[H_3O^+]}$.

• Example: For a solution with $[OH^-] = 6.7 \times 10^{-3}$ M, $pOH = -\log(6.7 \times 10^{-3})$, and $pH = 14 - pOH$.

Relationships Between [H+], [OH-], and pH

Summary Table at 25°C

pH	[H+]	[OH-]
<7.00 (Acidic)	>1.0 × 10-7	<1.0 × 10-7
7.00 (Neutral)	1.0 × 10-7	1.0 × 10-7
>7.00 (Basic)	<1.0 × 10-7	>1.0 × 10-7

Measuring pH

Methods

• pH meters provide accurate, electronic measurements of pH.

• Acid-base indicators change color depending on the pH, but are less precise.

Strong Acids and Strong Bases

Properties and Examples

• Strong acids completely ionize in aqueous solution: $[H^+] = [acid]_{initial}$.

• Examples: HCl, HI, H2SO4, HNO3

• Strong bases completely dissociate: $[OH^-] = [base]_{initial}$.

• Examples: NaOH, KOH, Ca(OH)2

• pH for strong acids: $pH = -\log [H^+]$

• pH for strong bases: $pH = 14 + \log [OH^-]$

Weak Acids and Weak Bases

Ionization and Equilibrium Constants

• Weak acids only partially ionize in solution. The extent is given by the acid dissociation constant ($K_a$):

$K_a = \frac{[H^+][A^-]}{[HA]}$

• The higher the $K_a$, the stronger the acid.

• Percent ionization quantifies acid strength:

Percent Ionization = $\frac{\text{Concentration of ionized acid}}{\text{Initial concentration of acid}} \times 100\%$

• Relationship between $K_a$ and pH (Henderson-Hasselbalch equation):

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

• Weak bases accept protons and are described by the base dissociation constant ($K_b$):

$K_b = \frac{[HB^+][OH^-]}{[B]}$

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

$pH = 14 - pK_b - \log \frac{[HB^+]}{[B]}$

• For conjugate acid-base pairs: $K_a \times K_b = K_w$

Polyprotic Acids

Multiple Ionizations

• Polyprotic acids can donate more than one proton, with each ionization step having its own $K_a$ value.

• First ionization is always stronger than subsequent ones ($K_{a1} > K_{a2}$).

• For example, carbonic acid ($H_2CO_3$):

First ionization: $H_2CO_3(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + HCO_3^-(aq)$ $K_{a1} = 4.3 \times 10^{-7}$, $pK_{a1} = 6.4$

Second ionization: $HCO_3^-(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + CO_3^{2-}(aq)$ $K_{a2} = 5.6 \times 10^{-11}$, $pK_{a2} = 10.3$

• When $K_{a1} / K_{a2} > 10^3$, the pH is determined mainly by the first dissociation.

Comparison of Acid Strengths

Trends in the Periodic Table

• For binary acids (HA): Acidity increases with increasing electronegativity across a period and with decreasing bond strength down a group.

• For oxyacids (Y–OH): Acidity increases with the electronegativity of the central atom Y.

Summary Table: pH, pOH, [H+], and [OH-] of Common Substances

Substance	[H+] (M)	pH	pOH	[OH-] (M)
Gastric juice	1×10-1	1.0	13.0	1×10-13
Lemon juice	1×10-2	2.0	12.0	1×10-12
Cola, vinegar	1×10-3	3.0	11.0	1×10-11
Wine	1×10-4	4.0	10.0	1×10-10
Tomatoes	1×10-4.5	4.5	9.5	1×10-9.5
Baking soda	1×10-9	9.0	5.0	1×10-5
Household ammonia	1×10-11	11.0	3.0	1×10-3
NaOH, 0.1 M	1×10-13	13.0	1.0	1×10-1

Examples of Weak Acids and Their Ka Values

Acid	Structural Formula	Conjugate Base	Ka
Chlorous (HClO2)	H–O–Cl=O	ClO2-	1.0 × 10-2
Hydrofluoric (HF)	H–F	F-	6.8 × 10-4
Nitrous (HNO2)	H–O–N=O	NO2-	4.5 × 10-4
Benzoic (C6H5COOH)	See structure	C6H5COO-	6.3 × 10-5
Acetic (CH3COOH)	H–O–C(=O)–CH3	CH3COO-	1.8 × 10-5
Hypochlorous (HOCl)	H–O–Cl	OCl-	3.0 × 10-8
Hydrocyanic (HCN)	H–C≡N	CN-	4.9 × 10-10
Phenol (HOC6H5)	See structure	C6H5O-	1.3 × 10-10

Summary

• Acid-base equilibria involve the transfer of protons and are governed by equilibrium constants ($K_a$, $K_b$, $K_w$).

• pH and pOH provide a convenient way to express the acidity or basicity of a solution.

• Strong acids and bases ionize completely, while weak acids and bases only partially ionize.

• Polyprotic acids have multiple ionization steps, each with its own $K_a$.

• Acid strength trends can be predicted based on periodic properties and molecular structure.