Unit 8: Inorganic Chemical Reactions: Precipitation, Redox Spontaneity & Potential Diagrams

Heterogeneous Ionic Dissolution Equilibria

In aqueous inorganic chemistry, the dissolution of a sparingly soluble symmetrical or asymmetrical crystalline salt $\text{M}_p\text{X}_q(s)$ establishes a dynamic heterogeneous equilibrium between the solid phase and solvated ions:

Thermodynamic equilibrium is defined by the equality of chemical potentials:

Since the activity of a pure solid phase at standard state is unity ($a_{\text{solid}} = 1$), the thermodynamic equilibrium constant is the Solubility Product Constant ($K_{sp}^\circ$):

In dilute solutions where activity coefficients approach unity ($\gamma_\pm \approx 1$), the concentration-based solubility product is:

Molar Solubility ($S$) Formulations:

If $S$ denotes the molar solubility of $\text{M}_p\text{X}_q$ in pure water (mol/L):

• For a $1:1$ salt ($\text{AgCl}, \text{BaSO}_4$): $p=1, q=1 \implies K_{sp} = S^2 \implies S = \sqrt{K_{sp}}$.
• For a $1:2$ or $2:1$ salt ($\text{PbI}_2, \text{Ag}_2\text{CrO}_4, \text{CaF}_2$): $p=1, q=2 \implies K_{sp} = 4 S^3 \implies S = \left(\frac{K_{sp}}{4}\right)^{1/3}$.
• For a $1:3$ salt ($\text{Fe(OH)}_3, \text{Al(OH)}_3$): $p=1, q=3 \implies K_{sp} = 27 S^4 \implies S = \left(\frac{K_{sp}}{27}\right)^{1/4}$.
• For a $2:3$ salt ($\text{Bi}_2\text{S}_3, \text{Ca}_3(\text{PO}_4)_2$): $p=2, q=3 \implies K_{sp} = 108 S^5 \implies S = \left(\frac{K_{sp}}{108}\right)^{1/5}$.

The Common-Ion Effect & Le Chatelier's Principle

When an electrolyte containing an ion common to the sparingly soluble salt is added to the saturated solution, Le Chatelier's Principle dictates that the dissolution equilibrium shifts to the left, precipitating additional solid and drastically suppressing molar solubility.

Consider the dissolution of $\text{PbI}_2$ ($K_{sp} = 7.9 \times 10^{-9}$) in the presence of $0.10\text{ M }\text{KI}$:

• Iodide concentration: $[\text{I}^-] = 0.10 + 2S' \approx 0.10\text{ M}$ (since $2S' \ll 0.10$).
• Lead concentration: $[\text{Pb}^{2+}] = S'$.

Compared to its solubility in pure water ($S = \left(\frac{7.9\times 10^{-9}}{4}\right)^{1/3} = 1.25 \times 10^{-3}\text{ M}$), the presence of $0.10\text{ M}$ common ion depresses solubility by a factor of nearly $1600$-fold!

Dissolution via Coordination Complex Formation

Precipitates can be quantitatively redissolved by introducing competing Lewis base ligands that sequester the metal cation into an extraordinarily stable coordination complex with an astronomical formation constant ($\beta_n \gg 1$).

``` AgCl(s) <===========> Ag+(aq) + Cl-(aq) K_sp = 1.8 x 10^-10 ^ | + 2 NH3(aq) β_2 = 1.7 x 10^7 v [Ag(NH3)2]+(aq) ---------------------------------------------------------------------- Net: AgCl(s) + 2 NH3(aq) <===> [Ag(NH3)2]+(aq) + Cl-(aq) K_net = 3.0 x 10^-3 ```

Analytical Coupling of Equilibria:

1. Precipitation: $\text{AgCl}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Cl}^-(aq), \quad K_{sp} = 1.8 \times 10^{-10}$
2. Complexation: $\text{Ag}^+(aq) + 2\,\text{NH}_3(aq) \rightleftharpoons [\text{Ag}(\text{NH}_3)_2]^+(aq), \quad \beta_2 = 1.7 \times 10^7$
3. Overall Dissolution Reaction:

This coupled equilibrium explains why sparingly soluble silver chloride dissolves completely in excess aqueous ammonia, whereas silver iodide ($\text{AgI}$, $K_{sp} = 8.5 \times 10^{-17}$, $K_{\text{net}} \approx 1.4 \times 10^{-9}$) remains completely insoluble in aqueous ammonia.

The Formalism of Oxidation Numbers

An oxidation number (oxidation state, $OS$) is a formal bookkeeping number assigned to an atom in a chemical compound representing the hypothetical electrical charge the atom would retain if all shared covalent electron pairs were cleaved purely heterolytically, allocating both bonding electrons entirely to the more electronegative bonding partner.

Priority Rules for Assigning Oxidation States:

1. Elemental State: Atoms in uncombined pure elements have $OS = 0$ ($\text{Na}, \text{O}_2, \text{P}_4, \text{S}_8$).

2. Monatomic Ions: Oxidation state equals ionic charge ($\text{Fe}^{3+} \implies +3$, $\text{Cl}^- \implies -1$).

3. Fluorine: Almost universally $-1$ in all compounds due to highest electronegativity ($\chi = 3.98$).

4. Oxygen: Almost universally $-2$, with rigorous exceptions:

• In peroxides ($\text{H}_2\text{O}_2, \text{O}_2^{2-}$): $-1$.
• In superoxides ($\text{KO}_2, \text{O}_2^-$): $-\frac{1}{2}$.
• In oxygen difluoride ($\text{OF}_2$): $+2$ (since fluorine is more electronegative).

5. Hydrogen: $+1$ when bonded to nonmetals; $-1$ when bonded to electropositive metals (hydrides like $\text{NaH}, \text{CaH}_2$).

6. Alkali & Alkaline Earth Metals: Group 1 metals are strictly $+1$; Group 2 metals are strictly $+2$.

7. Conservation: The algebraic sum of oxidation numbers across all atoms in a neutral molecule must equal zero; in a polyatomic ion, it must equal the net charge $q$.

The Ion-Electron (Half-Reaction) Method

Balancing complex polyatomic oxidation-reduction reactions requires partitioning the process into two simultaneous half-reactions: the oxidation half-reaction (loss of electrons) and the reduction half-reaction (gain of electrons).

``` Stepwise Algorithm for Balancing Redox Equations:

1. Identify oxidized and reduced species and split into two half-reactions.
2. Balance all atoms other than Hydrogen and Oxygen.
3. Balance Oxygen atoms by adding H2O molecules.
4. Balance Hydrogen atoms:

• In ACIDIC media: add H+ ions.
• In BASIC media: add H2O to the deficient side and OH- to the opposite side.

1. Balance electrical charges by adding electrons (e-).
2. Multiply half-reactions by integers to equate electrons transferred.
3. Add half-reactions, cancel identical spectator species, and verify conservation.

```

Detailed Example: Permanganate Oxidation of Nitrite in Acidic Solution

1. Reduction Half-Reaction ($\text{Mn}^{+7} \rightarrow \text{Mn}^{+2}$):

• Balance Mn: $\text{MnO}_4^- \rightarrow \text{Mn}^{2+}$.
• Balance Oxygen by adding $4\,\text{H}_2\text{O}$ to product side: $\text{MnO}_4^- \rightarrow \text{Mn}^{2+} + 4\,\text{H}_2\text{O}$.
• Balance Hydrogen by adding $8\,\text{H}^+$ to reactant side: $\text{MnO}_4^- + 8\,\text{H}^+ \rightarrow \text{Mn}^{2+} + 4\,\text{H}_2\text{O}$.
• Balance charge ($+7$ on left, $+2$ on right $\implies$ add $5e^-$ to left):

2. Oxidation Half-Reaction ($\text{N}^{+3} \rightarrow \text{N}^{+5}$):

• Balance N: $\text{NO}_2^- \rightarrow \text{NO}_3^-$.
• Balance Oxygen by adding $1\,\text{H}_2\text{O}$ to reactant side: $\text{NO}_2^- + \text{H}_2\text{O} \rightarrow \text{NO}_3^-$.
• Balance Hydrogen by adding $2\,\text{H}^+$ to product side: $\text{NO}_2^- + \text{H}_2\text{O} \rightarrow \text{NO}_3^- + 2\,\text{H}^+$.
• Balance charge ($-1$ on left, $+1$ on right $\implies$ add $2e^-$ to right):

3. Electron Harmonization and Net Equation:

Multiply reduction by 2 ($10e^-$) and oxidation by 5 ($10e^-$):

Canceling $10e^-$, $10\,\text{H}^+$, and $5\,\text{H}_2\text{O}$:

• Mass check: $2\text{ Mn}, 23\text{ O}, 5\text{ N}, 6\text{ H}$ on both sides.
• Charge check: $2(-1) + 5(-1) + 6(+1) = -1$ on both sides! Verified.

Thermodynamics of Reversible Electrochemical Cells

The fundamental link uniting thermodynamics and electrochemistry is that the maximum non-expansion electrical work ($w_{\text{elec}}$) obtainable from a reversible electrochemical reaction under isothermal, isobaric conditions equals the decrease in Gibbs Free Energy ($\Delta G$):

For an electrochemical process transferring $n$ moles of electrons across a potential difference of cell electromotive force $E_{\text{cell}}$:

where $F = N_A e = 96485.33\text{ C}\cdot\text{mol}^{-1}$ is the Faraday Constant. Therefore:

Thermodynamic Spontaneity Criteria at Constant $T$ and $P$:

• If $E_{\text{cell}} > 0 \implies \Delta G < 0$: The forward redox reaction is thermodynamically spontaneous.
• If $E_{\text{cell}} < 0 \implies \Delta G > 0$: The reaction is non-spontaneous in the forward direction.
• If $E_{\text{cell}} = 0 \implies \Delta G = 0$: The electrochemical system is at dynamic equilibrium.

Derivation of the Nernst Equation

From classical chemical thermodynamics, the Gibbs free energy change of a chemical mixture is related to the reaction quotient $Q$ by:

Substituting $\Delta G = -n F E_{\text{cell}}$ and $\Delta G^\circ = -n F E_{\text{cell}}^\circ$:

Dividing through by $-n F$ yields the Nernst Equation:

At standard temperature $T = 298.15\text{ K}$ ($25.0^\circ\text{C}$), evaluating the numerical constant:

Thus, the practical operational form of the Nernst equation is:

Equilibrium Constant and Electrochemical Potential

At dynamic electrochemical equilibrium, the cell potential vanishes ($E = 0$) and the reaction quotient equals the equilibrium constant ($Q = K$):

Temperature Dependence of EMF:

Differentiating $\Delta G^\circ = -n F E^\circ$ with respect to temperature:

By measuring the temperature coefficient of cell EMF $\left(\frac{\partial E^\circ}{\partial T}\right)_P$, the standard enthalpy and entropy of reaction can be directly determined without calorimetric measurements!

Principles of Latimer Potential Diagrams

A Latimer Diagram (introduced by Wendell M. Latimer in 1938) provides a concise, quantitative graphical representation of the standard reduction potentials connecting consecutive oxidation states of a chemical element.

In a Latimer diagram:

• Chemical species are arranged horizontally from left to right in order of decreasing oxidation state.
• Numerical standard reduction potentials ($E^\circ$, in Volts) are written above the connecting arrows.
• Potential diagrams are strongly $pH$-dependent and are reported either for standard acidic solution ($pH = 0$, $[H^+] = 1.0\text{ M}$) or standard basic solution ($pH = 14$, $[OH^-] = 1.0\text{ M}$).

``` Archetype Latimer Diagram for Chlorine in Acidic Solution (pH = 0):

+7 +5 +3 +1 0 -1 ClO4- --+1.20--> ClO3- --+1.18--> HClO2 --+1.67--> HClO --+1.63--> Cl2 --+1.36--> Cl- \ / \----------------------------- +1.39 V ---------------------------------/ ```

The Fundamental Rule for Non-Adjacent Redox Steps

CRITICAL PRINCIPLE: Electrochemical potentials are intensive variables and CANNOT be added directly! ($E^\circ_{\text{net}} \neq E^\circ_1 + E^\circ_2$). Standard Gibbs free energies, however, are extensive state functions and must add algebraically:

Substituting $\Delta G^\circ = -n F E^\circ$:

Canceling $-F$ yields the Latimer Potential Rule:

Thermodynamic Criteria for Disproportionation and Comproportionation

1. Disproportionation:

Disproportionation is a redox reaction in which an intermediate chemical species in oxidation state $N$ simultaneously undergoes self-oxidation to $N+x$ and self-reduction to $N-y$:

Consider the sequence in a Latimer diagram:

For species $B$ to disproportionate into $A$ and $C$:

• Reduction half-reaction: $B + n_R e^- \rightarrow C, \quad E_{\text{red}}^\circ = E_{\text{right}}^\circ$
• Oxidation half-reaction: $B \rightarrow A + n_L e^-, \quad E_{\text{ox}}^\circ = -E_{\text{left}}^\circ$
• Net Cell Potential:

For the reaction to be thermodynamically spontaneous ($\Delta G^\circ < 0 \iff E_{\text{cell}}^\circ > 0$):

The Disproportionation Rule: In a Latimer diagram, an intermediate oxidation state is thermodynamically unstable toward disproportionation if the standard reduction potential to its right is GREATER than the reduction potential to its left!

2. Comproportionation (Synproportionation):

The reverse of disproportionation: two different species containing the same element in distinct oxidation states react spontaneously to generate a single intermediate oxidation state:

Comproportionation is thermodynamically spontaneous when:

Frost Diagrams (Arthur Frost, 1951)

While a Latimer diagram encodes numerical potentials, a Frost Diagram (also called an oxidation state diagram) provides an intuitive, comprehensive visual plot of the thermodynamic stability landscape of an entire element across all its oxidation states.

• Abscissa ($x$-axis): Formal oxidation state ($N$).
• Ordinate ($y$-axis): Standard free energy parameter $-n F E^\circ / F$ relative to the zero-valent element, plotted as:

``` Frost Diagram Anatomy:

ΔG° / F (Volts) ^ | Oxidizing Agent (Top Left) | * | / \ | / * <-- Convex Peak (Thermodynamically unstable to DISPROPORTIONATION!) | / \ | 0 --- -------------------------- (Zero-valent element N = 0) | \ / | \ * <-- Concave Well (Thermodynamically STABLE species!) | \ / | * <-- Thermodynamic Sink (Most stable state in system) +-------------------------------------------> Oxidation State N ```

Fundamental Graphical Theorems of Frost Diagrams:

1. Slope Represents Standard Potential: The slope of the line segment connecting two species in oxidation states $N_1$ and $N_2$ equals the standard reduction potential $E^\circ$ of the couple connecting them:

• Steeper positive slope $\implies$ more powerful oxidizing couple.
• Steeper negative slope $\implies$ more powerful reducing couple.

2. Concave Wells (Valleys) are Thermodynamically Stable: If a species lies in a concave trough below the chord connecting its flanking neighbors, it is thermodynamically immune to disproportionation, and the flanking species will spontaneously comproportionate into it.

3. Convex Peaks (Humps) Undergo Disproportionation: If a species lies above the straight line connecting two adjacent states, it is thermodynamically unstable and will spontaneously disproportionate into those states.

4. Thermodynamic Sink: The lowest point on the entire diagram is the most thermodynamically stable oxidation state of that element in the specified medium.

Pourbaix ($pH$-Potential) Phase Diagrams (Marcel Pourbaix, 1945)

A Pourbaix Diagram maps out the predominant, thermodynamically stable chemical forms of an element in aqueous solution as a function of both Electrochemical Potential ($E$) (oxidizing/reducing driving force) and Solution Acidity ($pH$).

The Three Structural Types of Phase Boundaries:

1. Horizontal Boundaries (Pure Electron Transfer, pH-Independent):

Involve redox reactions with zero proton participation:

The boundary is a strictly horizontal line independent of $pH$.

2. Vertical Boundaries (Pure Acid-Base Transfer, Potential-Independent):

Involve non-redox acid-base precipitation equilibria with zero electron transfer:

Equilibrium depends purely on $[\text{H}^+]$ ($pH$), forming a strictly vertical line.

3. Slanted Boundaries (Simultaneous Redox and Proton Transfer):

Involve both electrons and protons:

By the Nernst equation:

The boundary is a slanted line with slope $-0.1775\text{ V}/pH$.

The Thermodynamic Stability Limits of Water

Liquid water decomposes at extreme potentials, defining the upper and lower thermodynamic stability envelope of all aqueous chemistry:

• Upper Limit (Water Oxidation to Oxygen):

Any oxidant with potential above line (b) can spontaneously oxidize water to $\text{O}_2(g)$.

• Lower Limit (Water Reduction to Hydrogen):

Any reductant with potential below line (a) can spontaneously reduce water to $\text{H}_2(g)$.

The Three Operational Corrosion Domains:

• Immunity Zone: The metal exists as the elemental solid $\text{M}^0$; thermodynamically immune to corrosion.
• Corrosion Zone: The metal dissolves into soluble aquo-cations ($\text{M}^{2+}, \text{M}^{3+}$); active corrosion.
• Passivation Zone: The metal forms an insoluble, dense, adherent oxide or hydroxide surface film ($\text{Fe}_2\text{O}_3, \text{TiO}_2, \text{Al}_2\text{O}_3$) that kinetically shields the underlying bulk metal from further chemical attack.

Multi-Element Pourbaix Diagrams in Metallurgy & Materials Science

In practical metallurgical engineering, aqueous corrosion rarely involves isolated elemental iron; rather, structural alloys (such as austenitic stainless steels, marine bronze, and titanium aerospace alloys) operate in multi-component aqueous electrolytes containing chloride, sulfate, and alloyed transition metals ($\text{Cr, Ni, Mo, Ti}$).

The Mechanism of Stainless Steel Passivation: The Iron-Chromium System

Chromium is the pivotal alloying element in stainless steels (typically $\ge 12\text{ wt}\%\text{ Cr}$). Consider the Pourbaix diagram of pure Chromium in water:

• Corrosion species: $\text{Cr}^{2+}(aq)$ at low potentials; $\text{Cr}^{3+}(aq)$ in acidic media ($pH < 4$); soluble chromate $[\text{CrO}_4]^{2-}$ and dichromate $[\text{Cr}_2\text{O}_7]^{2-}$ at extreme oxidizing potentials ($E > +1.3\text{ V}$).
• Passivating oxide: Chromium(III) oxide ($\text{Cr}_2\text{O}_3$ or hydrated $\text{Cr(OH)}_3$):

``` Chromium Pourbaix Diagram Topology:

Potential E (V) +1.5 | Cr2O7^2- (Acid) / CrO4^2- (Base) | ------------------------------------- (Transpassive dissolution) +1.0 | | PASSIVATION ZONE +0.5 | (Cr2O3 / Cr(OH)3) | Cr^3+ Adherent, self-healing, 0.0 | (Acidic) nanometer-thin oxide film | / -0.5 | / Cr^2+ | / -1.0 | ------------------------------------------------- | IMMUNITY ZONE (Metallic Cr) +---------------------------------------------------> pH 0 4 7 10 14 ```

Why Chromium Passivates Far More Effectively Than Iron:

1. Broader Passivation Window: The insoluble oxide $\text{Cr}_2\text{O}_3$ is thermodynamically stable over a vast $pH$ range ($3.8 \le pH \le 12.5$) and over a wide potential window ($-0.6\text{ V}$ to $+1.3\text{ V}$).

2. Defect-Free Nanoscale Film: In stainless steel, chromium atoms selectively diffuse to the alloy surface and react with dissolved oxygen to form a continuous, amorphous, pinhole-free layer of $\text{Cr}_2\text{O}_3$ just $1\text{–}3\text{ nm}$ thick.

3. Pilling-Bedworth Ratio (PBR): The ratio of the molar volume of the oxide to the molar volume of the metal:

• For Chromium: $\text{PBR} = 2.07$. The oxide is dense and in mild compression, adhering tenaciously to the metal substrate without cracking or spalling.
• For Iron: In moist air, iron forms porous, non-adherent rust ($\text{FeOOH} \cdot x\text{H}_2\text{O}$) that flakes off continuously, exposing fresh metal to catastrophic ongoing corrosion.

Comparative Frost Diagrams of First-Row Transition Metals

A side-by-side comparison of Frost oxidation state diagrams across the $3d$ series ($\text{Ti, V, Cr, Mn, Fe, Co, Ni, Cu}$) in standard acidic aqueous solution ($pH = 0$) reveals fundamental periodic redox trends:

``` Frost Diagram Landscape for First-Row Transition Metals (pH = 0):

ΔG° / F (V) +4 | Co^3+ +3 | Mn^3+ +2 | Cr^6+ (Cr2O7^2-) +1 | V^5+ (VO2+) 0 | -- Ti -- V -- Cr --------- Mn ------------ Fe --- Co --- Ni --- Cu -- (M^0 = 0) -1 | \ \ \ \ \ \ \ / -2 | \ \ \ \ \ \ *-- Cu^2+ -3 | \ \ -- Cr^3+ \ -- Fe^2+ -4 | \ -- V^3+ -- Mn^2+ (Thermodynamic Sink!) -5 | *-- Ti^3+ -6 | \ -7 | *-- Ti^4+ (TiO^2+) ```

Key Thermodynamic Discoveries from Frost Analysis:

1. The Extreme Stability of Manganese(II) ($\text{Mn}^{2+}$):

The Frost curve for Manganese displays a profound, deep minimum at $\text{Mn}^{2+}$ ($\Delta G^\circ/F \approx -1.18\text{ V}$).

• Reason: $\text{Mn}^{2+}$ possesses a high-spin $3d^5$ electron configuration with a half-filled subshell. The exchange stabilization energy is maximal ($10 K_{\text{ex}}$) and the crystal field stabilization is zero.
• Consequence: All higher oxidation states ($\text{Mn}^{3+}, \text{MnO}_2, \text{MnO}_4^{2-}, \text{MnO}_4^-$) sit high on steep positive slopes. Consequently, Permanganate ($\text{MnO}_4^-$) is a ferocious thermodynamic oxidant, reduced precipitously to $\text{Mn}^{2+}$.

2. The Convex Disproportionation Peaks of $\text{Mn}^{3+}$ and $\text{MnO}_4^{2-}$:

Both $\text{Mn}^{3+}$ and manganate ($\text{MnO}_4^{2-}$, $\text{Mn}^{+6}$) lie above the chord connecting their flanking neighbors; hence, both species spontaneously disproportionate in acidic media:

3. The Ascending Stability of Divalent Ions from Left to Right:

Early transition metals ($\text{Ti, V}$) have thermodynamic sinks in high oxidation states ($\text{Ti}^{4+}, \text{V}^{5+}$), acting as powerful reducing agents. Late transition metals ($\text{Fe, Co, Ni, Cu}$) have thermodynamic sinks in the $+2$ state ($\text{Fe}^{2+}, \text{Co}^{2+}, \text{Ni}^{2+}, \text{Cu}^{2+}$), and their high oxidation states ($\text{Co}^{3+}, \text{Ni}^{4+}$) are virtually unreachable or violently oxidizing.

Systematic Latimer Sequences Across Key Redox-Active Elements

To master inorganic redox reactivity, one must analyze the complete Latimer potential sequences for multi-valent elements in both acidic ($pH = 0$) and basic ($pH = 14$) standard solutions.

1. The Complete Latimer Diagram for Manganese

Manganese exhibits eight distinct oxidation states spanning from $+7$ to $0$:

In Acidic Solution ($pH = 0$):

Quantitative Disproportionation Analyses:

1. Manganate(VI) ($\text{MnO}_4^{2-}$):

• Potential to right ($+2.26\text{ V}$) is vastly greater than potential to left ($+0.56\text{ V}$).
• Net cell EMF: $E_{\text{cell}}^\circ = +2.26 - 0.56 = \mathbf{+1.70\text{ V}} \gg 0$.
• Conclusion: Manganate(VI) undergoes violent, spontaneous disproportionation in acid:

2. Manganese(III) ($\text{Mn}^{3+}$):

• Potential to right ($+1.51\text{ V}$) is greater than potential to left ($+0.95\text{ V}$).
• Net cell EMF: $E_{\text{cell}}^\circ = +1.51 - 0.95 = \mathbf{+0.56\text{ V}} > 0$.
• Conclusion: Uncomplexed $\text{Mn}^{3+}$ aquo ions are thermodynamically unstable and spontaneously disproportionate into $\text{Mn}^{2+}$ and insoluble $\text{MnO}_2$:

2. The Complete Latimer Diagram for Nitrogen in Acidic Solution ($pH = 0$)

Nitrogen encompasses an astonishing nine oxidation states spanning from $+5$ to $-3$:

Fundamental Discoveries:

1. Dinitrogen ($\text{N}_2$) as the Ultimate Thermodynamic Sink:

Notice the massive reduction potential forming $\text{N}_2$ from $\text{N}_2\text{O}$ ($+1.77\text{ V}$) contrasted with the deeply negative potential converting $\text{N}_2$ to hydrazinium ($-1.87\text{ V}$). On the Frost diagram, $\text{N}_2$ sits at the absolute deepest global minimum ($\Delta G^\circ = 0$).

• This colossal thermodynamic sink provides the overwhelming exothermic driving force for high explosives (such as TNT, RDX, and ammonium nitrate), which decompose instantaneously to liberate elemental $\text{N}_2$ gas!

2. Nitrous Acid ($\text{HNO}_2$) Disproportionation:

In the Latimer sequence: $\text{N}_2\text{O}_4 \xrightarrow{+1.07\text{ V}} \text{HNO}_2 \xrightarrow{+0.99\text{ V}} \text{NO}$. For disproportionation into nitrate and nitric oxide:

Aqueous nitrous acid decomposes spontaneously at room temperature, releasing brown fumes of nitrogen dioxide ($\text{NO}_2$, formed via oxidation of $\text{NO}$ in air).