Ionic Equilibria

Study of equilibrium processes involving ions in solution, particularly acid-base equilibria and related phenomena.

Introduction

Ionic equilibria refer to equilibrium reactions in aqueous solution or molten state that show the presence of ions. Reactions contain positively charged ions (cations) and negatively charged ions (anions). Strong acids and bases fully ionise/dissociate, while weak acids and bases only partially dissociate.

Applications include electrolytes in electrolysis and electrochemistry (e.g., NaCl dissociation in aqueous and molten states, electrolytic cells, Daniell cells).

Acid-Base Theories

Arrhenius Theory (1884)

Introduced by Svante Arrhenius (1884).

  • Acid: A substance that dissociates in water to produce an excess of hydrogen ions, H⁺(aq) [or hydronium H₃O⁺] in aqueous solution.
  • Base: A substance that dissociates in water to produce an excess of hydroxide ions, OH⁻(aq) in aqueous solution.

Acids dissolve in water in two ways:

  1. Dissociates without reacting with water molecules: $\text{HCl(aq)} \xrightarrow{\text{H}_2\text{O}} \text{H}^+\text{(aq)} + \text{Cl}^-\text{(aq)}$

  2. Dissociates when reacted with water molecules: $\text{HCl(aq)} + \text{H}_2\text{O}(\ell) \rightarrow \text{H}_3\text{O}^+\text{(aq)} + \text{Cl}^-\text{(aq)}$

Limitation: Only applicable to aqueous solutions for compounds containing H⁺ and OH⁻.

Brønsted-Lowry Theory (1923)

Proposed by Johannes Brønsted and Thomas M. Lowry (1923).

  • Acid: Proton (H⁺) donor. Becomes its conjugate base when it donates a proton.
  • Base: Proton (H⁺) acceptor. Becomes its conjugate acid when it accepts a proton.
  • Conjugate acid-base pair: HA ⇌ H⁺ + A⁻

Example: $\text{HCl} + \text{H}_2\text{O} \rightarrow \text{Cl}^- + \text{H}_3\text{O}^+$

  • HCl / Cl⁻ is a conjugate pair
  • H₂O / H₃O⁺ is also a conjugate pair

$\text{H}_2\text{O} + \text{NH}_3 \rightleftharpoons \text{OH}^- + \text{NH}_4^+$

Water as Amphoteric Solvent

H₂O is an amphoteric solvent — it acts as both a base and an acid, and undergoes auto-ionisation (self-ionisation):

$\text{H}_2\text{O} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^-$

Lewis Theory (1938)

Proposed by G. N. Lewis (1938).

  • Acid (Lewis acid): An atom, ion or molecule that accepts a pair of electrons to form a coordinate covalent bond. Also called an electrophile (usually +ve charge).
  • Base (Lewis base): An atom, ion or molecule that donates a pair of electrons to form a coordinate covalent bond. Also called a nucleophile (usually -ve charge).
  • Most general definition; includes reactions without proton transfer.

Examples:

$\text{NH}_3 + \text{BF}_3 \rightarrow \text{adduct}$

FB(F)F

N

$\text{F}^- + \text{BF}_3 \rightarrow [\text{F-BF}_3]^-$

F[B-](F)(F)F

$2\text{NH}_3 + \text{Ag}^+ \rightarrow [\text{H}_3\text{N-Ag-NH}_3]^+$

The products are called adducts.

Important: Not all Lewis Bases are Brønsted-Lowry Bases because the definition of a Lewis Base is broader than that of a Brønsted-Lowry Base.

Lewis Base vs Lewis Acid Comparison

Category Lewis Base (e⁻ donor) Lewis Acid (e⁻ acceptor)
General Complexes with Lewis Acid Complexes with Lewis Base
Lone-Pair Lone-Pair donors: :NH₃, H₂O: Lone-Pair acceptors: BF₃, AlCl₃
Brønsted relation Brønsted bases: ⁻OH, ⁻CH₃ Metal cations: Al³⁺, Fe³⁺
Nucleophile/Electrophile Nucleophiles: CH₃-S⁻ Electrophiles: CH₃CO⁺
Ligands [Fe(H₂O)₆]³⁺ The proton: H⁺
Counter ions Anionic counter ions: SO₄²⁻, NO₃⁻ Cationic spectator ions: K⁺
π systems Electron-rich π systems (benzene) Electron-poor π systems: [CH₂-CH=CH₂]⁺ 
Cl[Al](Cl)Cl

Common Acids and Bases

Common Acids

Name Formula Occurrence/Uses
Hydrochloric acid HCl Metal cleaning; food preparation; ore refining; stomach acid
Sulfuric acid H₂SO₄ Fertilizer, explosives, dye/glue, automobile batteries
Nitric acid HNO₃ Fertilizer, explosives, dye/glue
Acetic acid CH₃COOH Plastic/rubber, food preservative, vinegar
Citric acid C₆H₈O₇ Citrus fruits, pH adjustment 
CC(=O)O

O=C(O)CC(O)(CC(=O)O)C(=O)O

O=S(=O)(O)O

O=[N+]([O-])O

Common Bases

Name Formula Occurrence/Uses
Sodium hydroxide NaOH Petroleum, soap/plastic manufacturing
Potassium hydroxide KOH Cotton, electroplating, soap, batteries
Sodium bicarbonate NaHCO₃ Antacid, baking soda, CO₂ source
Sodium carbonate Na₂CO₃ Glass/soap, cleanser, water softener
Ammonia NH₃ Detergent, fertilizer, synthetic fibers 
[K+].[OH-]

[Na+].OC(=O)[O-]

[Na+].[Na+].C(=O)([O-])[O-]

N

pH Scale

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

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

$pH + pOH = 14 \text{ (at 25°C)}$

pH [H⁺] Nature
< 7 > 10⁻⁷ M Acidic
= 7 = 10⁻⁷ M Neutral
> 7 < 10⁻⁷ M Basic

Amphoteric Species

An amphoteric species is a substance that has the ability to act either as an acid or a base depending on what other substances it is reacting with.

Examples: water, aluminium hydroxide, bicarbonate ion. Other amphoteric substances include oxides and hydroxides of beryllium, zinc, and lead. Amino acids are also amphoteric.

Water

  • With a base (e.g., NH₃), water acts as an acid (donates proton): $\text{H}_2\text{O}(l) + \text{NH}_3\text{(aq)} \rightleftharpoons \text{NH}_4^+\text{(aq)} + \text{OH}^-\text{(aq)}$
  • With an acid (e.g., HCl), water acts as a base (accepts proton): $\text{HCl(aq)} + \text{H}_2\text{O}(l) \rightarrow \text{Cl}^-\text{(aq)} + \text{H}_3\text{O}^+\text{(aq)}$

Bicarbonate Ion (HCO₃⁻)

  • With acid (H₃O⁺), HCO₃⁻ acts as a base: $\text{H}_3\text{O}^+ + \text{HCO}_3^- \rightleftharpoons \text{H}_2\text{CO}_3 + \text{H}_2\text{O}$
  • With base (OH⁻), HCO₃⁻ acts as an acid: $\text{HCO}_3^- + \text{OH}^- \rightleftharpoons \text{CO}_3^{2-} + \text{H}_2\text{O}$

Aluminum Hydroxide (Al(OH)₃)

  • With base (NaOH), acts as an acid: $\text{Al(OH)}_3 + \text{NaOH} \rightarrow \text{Na[Al(OH)}_4]$
  • With acid (HCl), acts as a base: $\text{Al(OH)}_3 + 3\text{HCl} \rightleftharpoons \text{AlCl}_3 + 3\text{H}_2\text{O}$
O[Al](O)O

Note: HSO₄⁻ is also amphoteric.

Acid and Base Dissociation Constants

Strong Acids and Bases

Strong acids dissociate completely (100% ionized, α = 1). Examples: HCl, H₂SO₄, HNO₃, HBr, HClO₄, HI. pH ≈ 1.

Cl

Br

O=Cl(=O)(=O)O

I

Strong bases dissociate completely (100% ionized, α = 1). Examples: NaOH, Mg(OH)₂, Ca(OH)₂. pH ≈ 14.

[OH-].[OH-].[Mg+2]

[OH-].[OH-].[Ca+2]

Weak Acids

Not dissociate completely (partially ionized). The system exists as an equilibrium:

$\text{HA}{\text{(aq)}} + \text{H}2\text{O}{(\ell)} \rightleftharpoons \text{A}^-{\text{(aq)}} + \text{H}3\text{O}^+{\text{(aq)}}$

At equilibrium: (1-x) M HA, x M A⁻, x M H₃O⁺

$K_a = \frac{[\text{H}_3\text{O}^+][\text{A}^-]}{[\text{HA}]}$

  • $K_a$ is the acid dissociation constant; measures acid strength.
  • Values of $K_a$ are unaffected by acid concentration (only temperature).
  • Larger $K_a$ = stronger acid. Higher $K_a$ = lower $pK_a$.
  • $pK_a = -\log K_a$

Table: Values of $K_a$ for common acids

Name Formula $K_a$
Hydrochloric acid HCl ∞
Nitric acid HNO₃ ∞
Hydrofluoric acid HF 7.1 × 10⁻⁴
Nitrous acid HNO₂ 4.5 × 10⁻⁴
Formic acid HCOOH 1.7 × 10⁻⁴
Aspirin C₉H₈O₄ 3.0 × 10⁻⁴
Ascorbic acid (Vitamin C) C₆H₈O₆ 8.0 × 10⁻⁵
Benzoic acid C₆H₅COOH 6.5 × 10⁻⁵
Acetic acid CH₃COOH 1.8 × 10⁻⁵
Hypochlorous acid HOCl 3.0 × 10⁻⁸
Hydrocyanic acid HCN 4.9 × 10⁻¹⁰
Phenol C₆H₅OH 1.3 × 10⁻¹⁰ 
O=NO

CC(=O)Oc1ccccc1C(=O)O

O=C1C(O)=C(O)[C@@H](O)[C@H]1CO

O=C(O)c1ccccc1

ClO

C#N

Oc1ccccc1

Weak Bases

Not dissociate completely (partially ionized). The system exists as an equilibrium:

$\text{NH}_3\text{(aq)} + \text{H}_2\text{O}(\ell) \rightleftharpoons \text{NH}_4^+\text{(aq)} + \text{OH}^-\text{(aq)}$

At equilibrium: (1-x) M NH₃, x M NH₄⁺, x M OH⁻

$K_b = \frac{[\text{NH}_4^+][\text{OH}^-]}{[\text{NH}_3]}$

  • $K_b$ is the base dissociation constant; measures base strength.
  • Larger $K_b$ = stronger base. Higher $K_b$ = lower $pK_b$.
  • $pK_b = -\log K_b$
  • pH typically between 8 to 10

Table: Values of $K_b$ for common bases

Name Formula $K_b$
Ethylamine CH₃CH₂NH₂ 5.6 × 10⁻⁴
Methylamine CH₃NH₂ 4.4 × 10⁻⁴
Caffeine C₈H₁₀N₄O₂ 4.1 × 10⁻⁴
Carbonate ion CO₃²⁻ 1.8 × 10⁻⁴
Ammonia NH₃ 1.8 × 10⁻⁵
Pyridine C₅H₅N 1.7 × 10⁻⁹
Aniline C₆H₅NH₂ 3.8 × 10⁻¹⁰
Urea N₂H₄CO 1.5 × 10⁻¹⁴ 
CCN

CN1C=NC2=C1C(=O)N(C(=O)N2C)C

c1ccncc1

Nc1ccccc1

NC(=O)N

Relationship Between Ka and Kb

For a conjugate acid-base pair, multiplying the acid dissociation expression by the conjugate base hydrolysis expression yields:

$$K_a \times K_b = K_w = 1.0 \times 10^{-14} \text{ (at 25°C)}$$

Derivation:

  • Acid dissociation: $\text{CH}_3\text{COOH} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{CH}_3\text{COO}^-$ $$K_a = \frac{[\text{H}_3\text{O}^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]}$$
  • Conjugate base hydrolysis: $\text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{OH}^- + \text{CH}_3\text{COOH}$ $$K_b = \frac{[\text{OH}^-][\text{CH}_3\text{COOH}]}{[\text{CH}_3\text{COO}^-]}$$

Multiplying the two expressions: $K_a K_b = [\text{H}_3\text{O}^+][\text{OH}^-] = K_w$.

$$pK_a + pK_b = pK_w = 14$$

Buffer Solutions

A solution that maintains its pH when a small amount of an acid or a base is added to it. Buffer solutions resist pH change by consuming added acid or base through equilibrium shifts (Le Chatelier's principle).

Composition

  • Acidic buffer (pH < 7): Weak acid + its conjugate base (salt)
  • Basic buffer (pH > 7): Weak base + its conjugate acid (salt)

Common buffer systems from lecture:

CC(=O)O

CC(=O)[O-]

N

[NH4+]

O=CO

O=C[O-]

F

[F-]

CN

C[NH3+]

S

[SH-]

C(=O)([O-])[O-]

O=C(O)[O-]

O=P([O-])(O)O

O=P([O-])([O-])O

Buffer Action

Acidic buffer (e.g., CH₃COOH / CH₃COO⁻):

  • Acid added: $H^+ + CH_3COO^- \rightarrow CH_3COOH$ (conjugate base neutralises added acid)
  • Base added: $OH^- + CH_3COOH \rightarrow CH_3COO^- + H_2O$ (weak acid neutralises added base)

Basic buffer (e.g., NH₃ / NH₄⁺):

  • Acid added: $H^+ + NH_3 \rightarrow NH_4^+$ (weak base neutralises added acid)
  • Base added: $OH^- + NH_4^+ \rightarrow NH_4OH$ (conjugate acid neutralises added base)

Henderson-Hasselbalch Equation

Derived from the acid dissociation constant by taking negative logarithms.

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

For basic buffers: $$pOH = pK_b + \log\frac{[BH^+]}{[B]}$$

$$pH + pOH = 14 \text{ (at 25°C)}$$

[!important] Validity The Henderson-Hasselbalch equation is valid when the change $x$ is negligible compared to the initial concentrations of the weak acid/base and its conjugate. This assumption typically holds for buffer solutions where both components are present in appreciable amounts.

Buffer Capacity

  • Definition: The amount of acid or base a buffer can neutralise before significant pH change occurs
  • Maximum when pH = pKa (i.e., when $[A^-] = [HA]$)
  • Effective range: pKa ± 1
  • Higher concentrations of buffer components give greater buffer capacity

Biological Applications

  • Blood pH (~7.4) is maintained by the carbonic acid–bicarbonate buffer system
  • Amino acids act as buffers depending on their pKa values
  • Enzyme activity depends on maintaining optimal pH via buffer systems

Salt Hydrolysis

Hydrolysis is the reaction of a cation or an anion (or both) with water. The reaction is reversible.

Salt Type Example Hydrolysis pH
Strong acid + Strong base NaCl None 7
Strong acid + Weak base NH₄Cl Cation hydrolyzes < 7
Weak acid + Strong base CH₃COONa Anion hydrolyzes > 7
Weak acid + Weak base CH₃COONH₄ Both hydrolyze Depends on $K_a$ and $K_b$

Neutral Salts (SA-SB)

Formed from strong acid + strong base. Neither cation nor anion reacts with water (both are spectator ions). pH = 7.

$$\text{NaCl}{(aq)} \rightarrow \text{Na}^+{(aq)} + \text{Cl}^-_{(aq)}$$

[Na+].[Cl-]

Acidic Salts (SA-WB)

Formed from strong acid + weak base. The cation undergoes hydrolysis, donating a proton to water to produce H₃O⁺. pH < 7.

$$\text{NH}4\text{Cl}{(aq)} \rightarrow \text{NH}4^+{(aq)} + \text{Cl}^-_{(aq)}$$

$$\text{NH}4^+{(aq)} + \text{H}2\text{O}{(l)} \rightleftharpoons \text{NH}_{3(aq)} + \text{H}3\text{O}^+{(aq)}$$

[NH4+].[Cl-]

Calculation approach: Treat the conjugate acid as a weak acid. Use $K_a = K_w/K_b$ and solve via ICE table.

Worked example: 0.20 M NH₄Cl with $K_b(\text{NH}_3) = 1.8 \times 10^{-5}$:

  • $K_a = 5.6 \times 10^{-10}$
  • $[\text{H}_3\text{O}^+] = \sqrt{K_a \times C} = 1.05 \times 10^{-5}$ M
  • $pH = 4.98$

Basic Salts (SB-WA)

Formed from weak acid + strong base. The anion undergoes hydrolysis, accepting a proton from water to produce OH⁻. pH > 7.

$$\text{CH}3\text{COONa}{(aq)} \rightarrow \text{Na}^+_{(aq)} + \text{CH}3\text{COO}^-{(aq)}$$

$$\text{CH}3\text{COO}^-{(aq)} + \text{H}2\text{O}{(l)} \rightleftharpoons \text{CH}3\text{COOH}{(aq)} + \text{OH}^-_{(aq)}$$

CC(=O)[O-].[Na+]

Calculation approach: Treat the conjugate base as a weak base. Use $K_b = K_w/K_a$ and solve via ICE table.

Worked example: 0.5 M C₆H₅COONa with $K_a(\text{C}_6\text{H}_5\text{COOH}) = 6.5 \times 10^{-5}$:

  • $K_b = 1.54 \times 10^{-10}$
  • $[\text{OH}^-] = \sqrt{K_b \times C} = 8.77 \times 10^{-6}$ M
  • $pOH = 5.06$, $pH = 8.94$
O=C([O-])c1ccccc1.[Na+]

Salts of Weak Acid & Weak Base

When both cation and anion hydrolyze, the nature of the solution depends on the relative magnitudes of $K_a$ and $K_b$:

Condition Salt Type Dominant Mechanism
$K_a \approx K_b$ Neutral Cation and anion hydrolysis equally extensive
$K_a > K_b$ Acidic Cation hydrolysis dominates
$K_a < K_b$ Basic Anion hydrolysis dominates

Example: Ammonium benzoate (C₆H₅COONH₄) is acidic because $K_a(\text{C}_6\text{H}_5\text{COOH}) = 6.5 \times 10^{-5} > K_b(\text{NH}_3) = 1.8 \times 10^{-5}$.

O=C([O-])c1ccccc1.[NH4+]

Example: Ammonium ethanoate (CH₃COONH₄) is neutral because $K_a(\text{CH}_3\text{COOH}) = K_b(\text{NH}_3) = 1.8 \times 10^{-5}$.

CC(=O)[O-].[NH4+]

Acid-Base Titrations

A titration is a process in which a solution containing a known concentration of base is slowly added to an acid (or vice versa). A plot of pH vs volume of titrant is called a titration curve.

Equivalence Point vs End Point

  • Equivalence point: stage where amounts of acid and base are stoichiometrically equivalent ([H⁺] = [OH⁻])
  • End point: point at which an indicator changes colour (meant to approximate equivalence point)

Four Stages in Titrations

  1. Initial stage — before titrant is added
  2. Before equivalence point — any point between initial and equivalence; midpoint where mole of titrant is half that of equivalence
  3. At the equivalence point
  4. After the equivalence point

Common Acid-Base Indicators

Indicator Colour in Acid Colour in Base pH range
Thymol blue Red Yellow 1.2 – 2.8
Bromophenol blue Yellow Purple 3.0 – 4.6
Methyl orange Orange Yellow 3.1 – 4.4
Methyl red Red Yellow 4.2 – 6.3
Chlorophenol blue Yellow Red 4.8 – 6.4
Bromothymol blue Yellow Blue 6.0 – 7.6
Cresol red Yellow Red 7.2 – 8.8
Phenolphthalein Colourless Pink 8.3 – 10.0 
O=C1OC(C2=CC=CC=C2)(C2=CC=CC=C2)C2=CC=C(O)C=C12

O=C1OC(C2=CC=CC=C2)(C2=CC=CC=C2)C2=CC=C([O-])C=C12

Titration Types Summary

Titration Type Equivalence Point pH Salt Type Suitable Indicator
Strong Acid – Strong Base 7.0 Neutral Bromothymol blue, Phenolphthalein
Weak Acid – Strong Base > 7 (basic) Basic salt Phenolphthalein
Weak Base – Strong Acid < 7 (acidic) Acidic salt Methyl red

Strong Acid – Strong Base Titration

Reaction: $$NaOH(aq) + HCl(aq) \rightarrow NaCl(aq) + H_2O(l)$$

[Na+].[OH-]

Cl

[Na+].[Cl-]

O
  • Equivalence point: pH = 7.0 (neutral salt, neither Na⁺ nor Cl⁻ hydrolyzes)
  • Steep pH change around equivalence
  • Calculation approach: determine limiting reactant, calculate excess [H⁺] or [OH⁻], then pH

Weak Acid – Strong Base Titration

Reaction: $$CH_3COOH(aq) + NaOH(aq) \rightarrow CH_3COONa(aq) + H_2O(l)$$

CC(=O)O

CC(=O)[O-].[Na+]
  • Equivalence point: pH > 7 (basic salt — acetate anion hydrolyzes)
  • Buffer zone before equivalence: mixture of weak acid and conjugate base
  • Half-equivalence point: pH = pKa (e.g., pKa = 4.76 for acetic acid)
  • At equivalence: calculate pH from hydrolysis of conjugate base using Kb = Kw/Ka

Weak Base – Strong Acid Titration

Reaction: $$NH_3(aq) + HCl(aq) \rightarrow NH_4Cl(aq)$$

N

[Cl-].[NH4+]
  • Equivalence point: pH < 7 (acidic salt — ammonium cation hydrolyzes)
  • Buffer zone before equivalence: mixture of weak base and conjugate acid
  • At equivalence: calculate pH from hydrolysis of conjugate acid using Ka = Kw/Kb
  • pKa of NH₄⁺ = 9.25; pKb of NH₃ = 4.745

[!important] Assumption Validity For hydrolysis calculations at equivalence, check that % ionisation < 10% to validate the assumption that $x \ll C_0$.

Related Topics

Sources