4.2 Reactivity of Inorganic Compounds: Acid-Base Concepts, HSAB, and Redox Diagrams

4.2 Reactivity of Inorganic Compounds: Acid-Base Concepts, HSAB, and Redox Diagrams

Quick Answer: "Reactivities of inorganic compounds" is a 12-item TOS area. Most of it is acid-base and redox reasoning. Know the main acid-base definitions, why metal aqua ions are acidic, Pauling's rules for oxoacids, and the leveling effect of water. Apply Pearson's hard-soft acid-base (HSAB) principle to predict which compounds form, and use Latimer and Frost diagrams to calculate potentials and spot disproportionation.

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Acid-Base Definitions

Every Bronsted reaction is also a Lewis reaction, but the Lewis concept extends to metal-ligand bonding: in $[Cu(NH_3)_4]^{2+}$, $Cu^{2+}$ is the Lewis acid.

Acidity of Metal Aqua Ions

A small, highly charged metal ion polarizes coordinated water so that it releases a proton:

$[Fe(H_2O)_6]^{3+} + H_2O \rightleftharpoons [Fe(H_2O)_5(OH)]^{2+} + H_3O^+ \qquad pK_a \approx 2.2$

Acidity rises with charge and falls with radius. $Fe^{3+}$ and $Al^{3+}$ solutions are acidic, while $Na^+$ and $K^+$ barely hydrolyze. Continued hydrolysis leads to hydroxide precipitation and, for $Al^{3+}$, amphoteric redissolution as $[Al(OH)_4]^-$ in excess base.

Oxoacid Strength: Pauling's Rules

For an oxoacid $O_pE(OH)_q$, with $p$ oxygen atoms not bonded to hydrogen:

1. $pK_{a1} \approx 8 - 5p$
2. Each successive $pK_a$ rises by about 5.

Phosphorous acid fits the rule only when you recognize its P-H bond: it has two OH groups and is diprotic, not triprotic.

The Leveling Effect

In water, any acid stronger than $H_3O^+$ is converted completely to $H_3O^+$, and any base stronger than $OH^-$ to $OH^-$. Water therefore levels $HCl$, $HBr$, $HNO_3$, and $HClO_4$ to the same apparent strength. In a less basic solvent such as glacial acetic acid, they ionize to different extents and can be ranked ($HClO_4 > HBr > HCl$). The amide ion ($NH_2^-$) cannot exist in water because it deprotonates water completely.

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Pearson's Hard and Soft Acids and Bases (HSAB)

Hard species are small, highly charged, and weakly polarizable; soft species are large, low-charged, and highly polarizable. Hard acids prefer hard bases and soft acids prefer soft bases.

Applications:

• Geochemistry: Hard metals (Al, Ca, Mg, Ti) occur as oxides, silicates, and carbonates; soft metals (Cu, Ag, Hg, Cd, Pb) occur as sulfide ores (chalcopyrite, cinnabar, galena).
• Solubility: $AgF$ is water-soluble, while $AgI$ is very insoluble ($K_{sp} \approx 8.5 \times 10^{-17}$), because $Ag^+$ is soft.
• Toxicology: Soft $Hg^{2+}$, $Cd^{2+}$, and $Pb^{2+}$ bind soft thiol groups in proteins (Section 4.4).
• Coordination: Thiocyanate binds soft metals through S and hard metals through N.

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Oxidation States and Balancing Redox Equations

Assign oxidation states with the usual priorities (F is $-1$; O is usually $-2$; H is usually $+1$; the sum equals the overall charge). Balance in acid by splitting into half-reactions, balancing O with $H_2O$, H with $H^+$, and charge with electrons; in base, add $OH^-$ to neutralize $H^+$.

$MnO_4^- + 8H^+ + 5Fe^{2+} \rightarrow Mn^{2+} + 5Fe^{3+} + 4H_2O$

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Latimer, Frost, and Pourbaix Diagrams

Latimer Diagrams

A Latimer diagram lists the species of an element from highest to lowest oxidation state, with standard reduction potentials between them. For manganese in acid:

$MnO_4^- \xrightarrow{+0.56} MnO_4^{2-} \xrightarrow{+2.26} MnO_2 \xrightarrow{+0.95} Mn^{3+} \xrightarrow{+1.51} Mn^{2+} \xrightarrow{-1.18} Mn$

Potentials do not add, but free energies do. For non-adjacent couples:

$E^\circ = \frac{n_1E_1^\circ + n_2E_2^\circ}{n_1 + n_2}$

Example: $E^\circ(MnO_4^-/MnO_2) = \frac{(1)(0.56) + (2)(2.26)}{3} = \frac{5.08}{3} = +1.69\text{ V}$

Disproportionation test: a species is unstable toward disproportionation when the potential on its right is more positive than the potential on its left. $MnO_4^{2-}$ ($+2.26 > +0.56$) and $Mn^{3+}$ ($+1.51 > +0.95$) disproportionate in acid. $Mn^{2+}$ is the most stable state.

Frost Diagrams

A Frost diagram plots $nE^\circ$ (proportional to $-\Delta G^\circ$ of forming the species from the element) against oxidation state $N$:

• The lowest point is the most thermodynamically stable species ($Mn^{2+}$ in acid).
• The slope between two points equals $E^\circ$ for that couple; steep upward slopes to high oxidation states mark strong oxidants ($MnO_4^-$).
• A species lying above the line joining its neighbours tends to disproportionate. One lying below that line is favoured by comproportionation.

Pourbaix (E-pH) Diagrams

Pourbaix diagrams map which species is stable at each potential and pH. Two dashed lines bound the stability of water: below the lower line water is reduced to $H_2$, and above the upper line it is oxidized to $O_2$. For iron, $Fe^{2+}$ dominates in acidic, reducing water; $Fe(OH)_3$ precipitates as pH and potential rise; and metallic Fe lies below the water line. That is why iron corrodes in aerated water.