[10.4].1 SULPHUR DIOXIDE

Though sulphur dioxide is supposed to ionize into ions, it is a poor conductor of electricity:

2SO₂ ⇌ SO²⁺ + SO₃^{2 –}

It is not associated as it has no hydrogen atoms generally responsible for association of liquids.

[10.4].1.1 Solubility: Only thionyl halides and acetate are miscible with sulphur dioxide in all proportions, solubility of other solutes are only 0.2 – 2 %. It has only weak solvating powers for ionic substances.  Solubility decreases from iodides to fluorides. Alkali and alkaline earth metal halides have fair solubility, and alkali metal sulphates, cyanides and thiocyanates are soluble. Ammonium, mercury and thallium salts are also soluble due to covalence. It is a good solvent for covalent organic compounds and is used for the purification of certain petroleum products.

[10.4].1.2 Acid – Base Reactions: In sulphur dioxide medium, substances giving thinyl ions are acids, whereas sulphite ions are bases. The solution of potassium sulphite can be titrated against thionyl halide or acetate can be studied conductometrically:

SOX₂ + K₂SO₃ ⇌ 2KX + 2SO₂    (X = Cl, Br or OCOCH₃)

Amphoteric behavior is shown by zinc, aluminium or tin(II) salts:

ZnCl₂ + K₂SO₃ ⇌ ZnSO₃ (↓) + 2KCl
ZnSO₃ (↓) + K₂SO₃ ⇌ K₂[Zn(SO₃)₂]

2AlCl₃ + 3K₂SO₃ ⇌ Al₂(SO₃)₃ (↓) + 6KCl
Al₂(SO₃)₃ (↓) + 3K₂SO₃ ⇌ 2K₂[Al(SO₃)₃]

[10.4].1.3 Metathetical Reactions: Some examples of metathetical reactions are:

BaI₂ + Zn(CNS)₂ → Ba(CNS)₂ (↓) + ZnI₂
PbF₂ + Li₂SO₄ → PbSO₄ (↓) + 2LiF
AlCl₃ + 3NaI → 3NaCl (↓) + AlI₃
SbCl₃ + 3LiI → SbI₃ (↓) + 3LiCl

Thionyl derivatives can be easily prepared by reacting thionyl chloride through the precipitation of AgCl:

2AgOCOCH₃ + SOCl₂ → 2AgCl (↓) + SO(OCOCH₃)₂

[10.4].1.4 Solvolysis Reactions: Solvolysis reactions have been observed with covalent halides like PCl₅ or AsCl₅:

PCl₅ + SO₂ → POCl₃ + SOCl₂
AsCl₅ + SO₂ → AsOCl₃ + SOCl₂

[10.4].1.5 Sulphur Dioxide of Crystallization: Like water or ammonia of crystallization, sulphur dioxide of crystallization has also been observed. Examples include highly soluble NaI.4SO­_2­, KI.4SO₂, LiI.2SO₂, BaI₂.4SO₂, KCNS.SO₂ and AlCl₃.SO₂.

[10.4].1.6 Complex Formation: Besides dissolution of amphoteric metal salts, typical complex formation reactions include formation of halide complexes by the interaction of covalent halides and alkali metal halides:

SbCl₃ + 3NaCl ⇌ K₃[SbCl₆]

[10.4].1.7 Redox Reactions: Though gaseous sulphur dioxide shows both oxidizing as well as reducing properties, liquid sulphur dioxide does not have any pronounced oxidizing or reducing tendency and can act as a medium for redox reactions:

6KI + 3SbCl₅ → 2K₃[SbCl₆] + SbCl₃ + 3I₂

[10.4].1.8 Autoionization of Sulphur Dioxide into thionyl and sulphite ions seems attractive, it seems far stretched in a nonpolar medium. Further, SO₂ will exchange radio-sulphur (³⁵S) with ³⁵SOCl₂ or ³⁵SOBr₂, no exchange takes place between SO₂ and ³⁵SO₃^{2 –} ions. This indicates non-ionizing nature of sulphur dioxide into sulphite ions. Hence, ionization of sulphur dioxide is not so simple but proceeds through some complicated mechanism.

[10.4].2 BROMINE TRIFLUORIDE

The high liquid range (m.p. 289 K, b.p. 399 K), high specific conductance (0.8 Ω ^–1 m ^–1 at 298 K) and association in liquid state make bromine trifluoride a good solvent for ionic compounds. However, due to its corrosive nature and high reactivity, not many reactions have been studied in bromine trifluoride.

[10.4].2.1 Acid – Base Reactions: Its autoionization indicates that ionic fluorides like alkali metal fluorides will act as a base while acids will be species that can abstract a fluoride ion from bromine trifluoride. Typical examples are:

2BrF₃ ⇌ BrF₂⁺ + BrF₄ ^–       (autoionization)
KF + BrF₃ ⇌ K⁺ + BrF₄ ^–             (base)
AgF + BrF₃ ⇌ Ag⁺ + BrF₄ ^–         (base)
NOBr + BF₃ ⇌ NO⁺ + BrF₄ ^–        (base)

MF₅ + BrF₃ ⇌ BrF₂⁺ + MF₆ ^–     (M = P, As, Sb, Nb, Ta)        (acids)
MF₄ + 2BrF₃ ⇌ 2BrF₂⁺ + MF₆ ^–     (M = Sn, Ti, Ge)        (acids)

A typical neutralization reaction that can be studied conductometrically is

SbF₅ + AgF → Ag⁺ + [SbF₆]^–
AuF₃ + AgF → Ag⁺ + [AuF₄] ^–
SnF₄ + 2AgF → 2Ag⁺ + [SnF₆]^2–

As solvated species, these reactions can be written as:

BrF₂⁺[SbF₆] ^– + Ag⁺[BrF₄] ^– →  Ag[SbF₆] + 2BrF₃
BrF₂⁺[AuF₄] ^– + Ag⁺[BrF₄] ^– →  Ag[AuF₄] + 2BrF₃
[BrF₂⁺]₂[SnF₆] ^– + 2Ag⁺[BrF₄] ^– →  Ag₂[SnF₆] + 3BrF₃

[10.4].2.2 Fluorination Reactions: Bromine trifluoride is a powerful fluorinating agent and will readily fluorinate metal and nonmetal halides, oxides, carbonates, etc. forming fluorido complexes:

3SiO₂ + 4BrF₃ → SiF₄ + 2Br₂ + 3O₂
3GeO₂ + 4BrF₃ → GeF₄ + 2Br₂ + 3O₂
2WO₃ + 4BrF₃ → 2WF₆ + 2Br₂ + 3O₂
6Sb₂O₃ + 20BrF₃ → 12SbF₅ + 10Br₂ + 9O₂
6PCl₅ + 10BrF₃ → 6PF₅ + 5Br₂ + 15Cl₂
6NiCO₃ + 4BrF₃ → 6NiF₂ + 3O₂ + 2Br₂ +

[10.4].2.3 Redox Reactions: Metals like Nb, Ta, Ag, Au or alkali metals dissolve in bromine trifluoride with evolution of bromine:

3K + 4BrF₃ → 3KF + 2Br₂
6Nb + 16BrF₃ → 6BrF₂⁺[NbF₆] ^– + 5Br₂

[10.4].3 OTHER SOLVENTS

[10.4].3.1 Selenium Oxidochloride SeOCl₂

Selenium oxidochloride or selenyl chloride (SeOCl₂) has a good liquid range (281 – 446 K), low conductivity and a high dielectric constant. It autoionizes as

2SeOCl₂ ⇌ {[SeOCl][SeOCl₂]}⁺  + Cl^–

The ionization is similar to that of SOCl₂. Upon electrolysis of pure SeOCl₂ or of KCl solution in SeOCl₂ gives chlorine gas at anode, but a mixture of SeO₂ and Se₂Cl₂ at the cathode.

The solvent dissolves many ionic and covalent chlorides (NaCl, KCl, NH₄Cl, BaCl₂, HgCl₂, FeCl₃, etc.) to form conducting solutions:

KCl  ⇌ K⁺ + Cl^–       (Base)
2SeOCl₂ + py ⇌ {[SeOCl][SeOCl₂,py]}⁺  + Cl^–            (Base)
FeCl₃ + 2SeOCl₂ ⇌ {[SeOCl][SeOCl₂]}⁺ + [FeCl₄] ^–      (Acid)
SnCl₄ + 4SeOCl₂ ⇌ 2{[SeOCl][SeOCl₂]}⁺ + [SnCl₆] ^–      (Acid)

Alkali metal and alkaline earth metal chlorides, pyridine, quinoline, etc. form basic solutions in selenium oxidochloride, but chlorides of Sn(IV), Ge(IV), Si(IV), As(V) Sb(V) and Fe(III) give acidic solutions. Several neutralization titrations can be conducted in selenium oxidochloride medium and studied conductometrically. Some typical examples are KCl – SnCl₄, CaCl₂ – SnCl₄, py – SO₃, py – AsCl₅, etc.

KCl is a weak base, followed by py; acid strength is in the order SO₃ > FeCl₃ > SnCl₄.

 [10.4].3.2 Phosphorus Oxidochloride  POCl₃

Phosphorus oxidochloride, also called phosphoryl chloride, POCl₃, is an aprotic solvent which autoionizes as

POCl₃ ⇌ POCl₂⁺ + Cl^–                       K = 5× 10^–10

Considering solvation of ions formed,

(m + n) OPCl₃ ⇌ [OPCl₂(OPCl₃)_(m–1)]⁺  + [Cl(OPCl₃)_n] ^–

In this medium, compounds giving chloride ions are bases

KCl ⇌ K⁺ + Cl^–       (strong base)
Et₃N + OPCl₃ ⇌ [Et₃N.OPCl₂]⁺ + Cl^–     (weak base)

Molecular Lewis acids behave as acids in phosphorus oxidochloride:

FeCl₃ + OPCl₃ ⇌ OPCl₂⁺ + [FeCl₄] ^–
SbCl₅ + OPCl₃ ⇌ OPCl₂⁺ + [SbCl₆] ^–

Conductometric, potentiometric or photometric methods can be used to follow the acid – base titrations in this medium.

With phosphoric acid, diphosphoric acid is formed:

5H₃PO₄ + OPCl₃ ⇌ 3H₄P₂O₇ + 3HCl

With substances containing active hydrogen (hydronium) atoms, solvolysis takes place leaing to the formation of phosphoric acid derivatives:

OPCl₃ + 3ROH → OP(OR)₃ + 3HCl
OPCl₃ + HNR₂ → OP(NR₂)₃ + 3HCl

With transition metal halides, the solvent can form strong coordination compounds like Cl₃PO.ZrCl₄, Cl₃PO.AlCl₃, etc. These compounds are similar to hydrates from aqueous solutions.

 [10.4].3.3 Carbonyl Chloride COCl₂

Carbonyl chloride (COCl₂) has a good liquid range (155 – 281 K), low dielectric constant and is not associated. Even though it is a poor solvating agent and a poor conductor of electricity, certain covalent chlorides dissolve in carbonyl chloride to give conducting solutions.Upon electrolysis, these solution evolve CO at cathode and Cl₂ at anode:

AlCl₃ + COCl₂ ⇌ COCl⁺ + [AlCl₄] ^–

From solutions of AlCl₃ in COCl₂, active metals like Mg, Ca, K and Zn, liberate CO:

Mg + COCl⁺ → Mg²⁺ + CO + Cl ^–

Other halides, soluble in carbonyl chloride, are SnCl₄, SbCl₅, S₂Cl₂, ICl, I₂.

[10.4].4 MOLTEN SALTS 

Molten salts are also nonaqueous solvents, except that they are formed at high temperatures. The main differences in the chemistry of solutions and molten salts are the following;

1. Strongly bonded structure of melts
2. Stable nature
3. A concomitant resistance to destruction
4. High concentration of solvents in melts.

Melts are generally classified as (a) alkali metal halides, and (b) covalent bonded halides (mostly mercury halides) having autoionization in molten state, and (c) molten metals (better studies in phase diagrams).

[10.4].4.1 Alkali Metal Chlorides and Halides

These are ionic melts. Coordination number decreases from 6 in solid state to about 4 in melts. Long range order of crystals breaks down and only short range localized order exits. These are good electrolytes and behave normally with respect to cryoscopy. Alkali and alkaline earth halides dissolve in molten NaCl to give ions:

BaF₂ (in NaCl) ⇌ Ba²⁺ + 2F ^–               (number of ions = 3)
CaBr₂ (in NaCl) ⇌ Ca²⁺ + 2Br ^–       (number of ions = 3)

But salts giving the ions common to melts behave anomalously as the common ion is not able to make any change in the bulk concentration of the ion:

CaCl₂ (in NaCl) ⇌ Ca²⁺ + 2Cl ^–        (number of ions = 1)
NaF (in NaCl) ⇌ Na⁺ + 2F ^–             (number of ions =1)

Alkali metal halides dissolve large quantities of alkali metals molten chloride melts. There is no satisfactory explanation for the nature of metal species in the melts. Formation of M₂⁺ is not possible for alkali metals. It is possible that the melts contain free electrons (as in ammonia solutions of alkali metals) but evidence is not conclusive.

Due to very high concentration of chloride ions (12 M in saturated aqueous solutions, 36 M in NaCl melts) and absence of any other competing ligand (e.g., water in aqueous solutions), many chloride complexes can be obtained in melts. Examples include [TiCl₆]^{3 –}, [CrCl₆]^{2 –}, etc.

As the melts are unreactive, many reactions can be done in melts which are not possible in aqueous solutions. For example, electrolysis of molten LiCl, NaCl, MgCl₂, Al₂O₃, KHF₂ gives metals. Slag formation between metal oxides and silica or between metal oxides and boron trioxide takes place only in molten state. Some reactions that take place in molten state are:

CaCO₃ + SiO₂ → CaSiO₃ + CO₂
ZnO + CoO → ZnCoO₂
Cr₂O₃ + 4Na₂CO₃ + 3O₂ → 2Na₂CrO₄ + 4CO₂
CoO + B₂O₃ → Co(BO₂)₂

[10.4].4.2 Molten Covalent Halides

Molten covalent halides ionize as aprotic solvents:

2HgCl₂ ⇌ HgCl⁺ + HgCl₃^–

In HgX₂ melts, basic solutions can be obtained by increasing the concentration of the halide ion (X ^–), whereas acidic solutions will increase the concentration of HgCl⁺ ions.

2Hg(ClO₄) + HgCl₂ ⇌ 2HgCl⁺ + 2ClO₄ ^–        (acidic solution)
KX + HgX₂ ⇌ K⁺ + HgCl₃ ^–  (Basic solution)

A neutralization reaction can be titration of KCl solutions against Hg(ClO₄)₂ solutions in HgCl₂ medium.

Molten HgCl₂ dissolves metallic mercury forming Hg₂²⁺ ions. The Hg₂²⁺ compounds are obtained by cooling the melt. Similarly, metallic cadmium dissolves in molten HgCl₂ , probably due to the formation of Cd₂²⁺ ions. The ion can be isolated as the chloride by adding aluminium trichloride to Cd + CdCl₂ melts.

[10.4].5 ORGANIC SOLVENTS

Due to low dielectric constant and low polarity, organic solvents are poor solvents for ionic compounds. This is due to the very low solvation energies due to ion – induced dipole interactions, which are insufficient to overcome the high lattice energies of ionic compounds. However, water-like solvents with higher dielectric constant and higher dipole moments like alcohols, ethers or chloroform can dissolve ionic compounds with some covalent character. Detailed characteristics of the organic solvents can be found in a text book on organic chemistry. However, only a very brief outline is presented of some common organic solvents for inorganic compounds.

[10.4].5.1 ETHANOL

Ethanol has close resemblance to water as solvent. It has, however, lower dipole moment and solvation energies are low. A large number of compounds are soluble in ethanol, for example, anhydrous metal halides (CaCl₂, MgCl₂, transition metal halides, acetates of nickel, cobalt(II), silver, ammonium and copper(II), KOH, HCl, HBr, HI, KI, AgNO₃, AgNO₂, etc.

Ethanol autoionizes as

2EtOH ⇌ EtOH₂⁺ + EtO^–

Therefore, protonic acids are strong acids and ethoxide ion is strong base. This permits titration of HCl against EtOK, which can be studied conductometrically or pH-metrically (neutralization reaction):

HCl + EtOK → KCl + EtOH

Addition of CoCl₂ or NiCl₂ solutions to KI solution precipitates KCl (metathetical reaction):

CoCl₂ + 2KI → 2KCl (↓) + CoI₂

Solvolysis reactions of covalent halides in alcohols are very common and are used to prepare metal alkoxides:

TiCl₄ + 4ROH → Ti(OR)₄ + 4HCl
OPCl₃ + ROH → OPCl₂(OR) + 3HCl
OPCl₂(OR) + 2ROH or 2RONa → OP(OR)₃ + 2HCl or 2NaCl
m-C₆H₅TiCl₂ + 2NaOR → m-C₆H₅Ti(OR)₂ + 2NaCl

Similar to water of crystallization, alcohol of crystallization is also known, e.g. CaCl₂.2EtOH, FeCl₃.4EtOH or FeCl₂.6EtOH.

[10.4].5.2 DIETHYL ETHER

The oxygen atom in ethers has a lone pairs of electrons which can be used for coordination to metal ions. Therefore, ethers dissolve many ionic compounds, especially if they have s covalent character. Examples include HCl, HBr, HNO₃, FeCl₃, UO₂(NO₃)₂, etc. Solubility increases if the ionic species is attached to a hydrophobic end, e.g. metal alkoxide.

Limited solubility of metal compounds in ether makes ether a good solvent for separation of metal ions from aqueous solutions by solvent extraction method. Thus FeCl₃ can be extracted quantitatively into ether from 6M HCl solutions, whereas UO₂(NO₃)₂ can be separated quantitatively from thorium(IV) in 6 – 12 M HNO₃ as H[FeCl₄] and UO₂(NO₃)₂.2Et₂O respectively.

Ether is a good solvent for Lewis acids as forms sable etherates Et₂O.BF₃, RMgX.2Et₂O, or RZnX.2Et₂O.

As ether does not autoionize, the conventional acid – Base neutralization reactions are not possible. However, HCl or HNO₃ can be titrated against organic bases like pyridine, alkyl amines, etc. NaOH or KOH does not dissolve as ether cannot solvate OH ^– ions.

[10.4].5.3 CHLOROFORM

Though chloroform is a polar solvent, it cannot solvate ionic compounds. Yet it is a good solvent for compounds having polar covalent bonds or easily polarizable molecules. Thus it is very good solvent for the extraction of iodine (polarizable molecule) or metal chelates like salicylaldoximates, thiolates, 8-hydroxyquinolinolates, diphenylcarbazido or acetylcetonate complexes.

[10.4].6 SOLVOLYTIC REACTIONS

[10.4].6.1 Hydrolysis 

A reaction in which water reacts with a species and brings a change in its pH (pH =  – log a_H, where a_H is the activity given by c_Hγ_±, where γ_± is the mean activity coefficient of H⁺ ions;  γ_± → 1 in dilute solutions).It can be considered as the formation of a hydrated species (ion or molecule) (the aqua acid), which further ionizes or dissociates to form the products:

Al³⁺ + 6H₂O ⇌  [Al(H₂O)₆]³⁺  ⇌  [Al(H₂O)₅(OH)]²⁺ + H⁺

Hydrolysis reactions are generally much more complicated due to the formation of hydrated (or, aquated) species in solutions.

Practically, all metal alkyls and hydrides undergo rapid hydrolysis in solutions, whereas the hydrides and alkyls of non-metals are comparatively more stable stable towards hydrolysis. On the other hand, almost all the halides of metals are stable, whereas those of non-metals undergo rapid hydrolysis. Further, hydrolysis of metal alkyls is facilitated by lowering the pH, where that of halides of non-metals is rapis at higher pH. In either case, the hydronium ions (H⁺) goes to the more electronegative part of the compounds.

The hydrolysis reaction an be written as the acid–base equilibrium reactions:

MZ_n + nHOH ⇌ M(OH)_n + nHZ

Hydrolysis is favored if Z is the anion of a weak acid HZ and/or M is a cation of a weak base M(OH)_n. The effect of the anion can be observed by considering the hydrolytic reaction of lithium salts:

Li₂C₂  +  2H₂O → 2LiOH + C₂H₂
Li₂Y₂  +  3H₂O → 2LiOH + 2YH₃           (Y = N, P, As, Sb)
Li₂Y + 2HOH → 2LiOH + Li(YH)             (Y = O, S, Se, Te)
LiX  + aq   → [Li(aq)]⁺ + X[(aq)]^–            (X = F, Cl, Br, I)

If the cation forms an insoluble product with hydroxide ions, hydrolysis is facilitated:

Al₂Te₃  +  3H₂O → Al(OH)₃ + 3H₂Te

If the pH of the solutions is raised, even strong acids may be forced to form to form anions;

HSO₄^– + OH^– → SO₄^2– + HOH

[10.4].6.2 Electrostatic Approach to Hydrolysis Reactions

The degree of hydrolysis generally depends upon the charge density on the central atom. It decreases in a group with the increasing atomic mass:

PCl₃  +  3H₂O → H₃PO₃ + 3HCl
but         BiCl₃ + H₂O ⇌ BiOCl + 2HCl;
or,          TiCl₄ + 2HOH ⇌ TiO₂ + 4HCl
but         ZrCl₄ + H₂O ⇌ ZrO + 2HCl + 2Cl (charges omitted)

The ionization constant K_h of the metal hydroxide K_b,  can be related to the K_a of rhe cationic aqua acid by the expressions (charges on ions are omitted for clarity):

M + H₂O ⇌ M(H₂O) ⇌  H + MOH     K_h  =   [MOH][H] / [M]
MOH ⇌ M + OH                                      K_b =   [M][OH] / [MOH]
[H₂O] = 1                                                          (being liquid)

For ionization of water,

HOH ⇌ H + OH                  K_w = [H][OH]

This gives             K_h K_{b ­} =  {[H][A] / [HA]} × {[HA][)H] / [A]}
= [H][OH] = K_w

so that, pK­_h + pK_b = pK_w

Hence, the hydrolysis constant for the strong base is high and that of a weak metal is low. Consequently, the K_h for the strong base (alkalis) is low and that for weak base is high.

A high pK_b value or a lower pK_a indicates a weaker base whereas a lower pK_b or a higher pK_a means a stronger base.

For the inert gas ions (group 18), interaction with the hydroxide ions is purely electrostatic. Higher charge density on the cation leads to greater hydration and thence to higher base strength. For cations undergoing hydrolysis, the charge density on the cation is so high that it polarizes the O–H bond to the extent of bond rupture releasing one H⁺ ion from hydrated cation. Therefore, the pK_b should depend directly on z²/r, where z is the charge on the cation and r is its radius (pK_b refers to the last ionizable OH ion). For the group 1 cations, Li⁺ is most easily hydrolyzed ion and the base strength increases as LiOH (–0.7) < NaOH < KOH (–1.7).

As the ionic radius of the group 2 cations is about 30 pm less than those of corresponding group 1 ions, and the charge is twice as much, the group 2 cations are more hydrolyzed that the group 1 (alkali metal) cations, the pK_b values decreasing from 1.5 for Mg²⁺ to 0.65 for Ba²⁺ ions for the reaction

M(aq)²⁺ + H₂O ⇌ M(OH)⁺ + H⁺

Be²⁺ is so strongly hydrolyzed that it forms polynuclear species in aqueous solutions.

Extending the electrostatic approach to beyond group 2 (alkaline earths), gives unsatisfactory results. For example, we expect a decreasing extent of hydrolysis from Mg²+ to Zn²⁺ to Cd²⁺ and to Hg² ions due to regular increase in ionic size, the reverse is actually the case. This inversion may be due to increasing electronegativity of the ions (Mg²⁺ = 1.35, Hg²⁺ = 2.0), which leads to greater covalence of the M–O bonds.

Actual evaluation of hydrolysis constants for metal cations is made practically useless due to (a) formation of polynuclear species, (b) precipitation of hydroxides and/or hydrated metal oxides, and (c) change in coordination numbers of cations due to their large size or use of d orbitals).

Hg²⁺(aq) ⇌ Hg(OH)⁺ (aq) + H⁺                                      ( pK_a = 3.70)
Hg(OH)⁺ (aq) ⇌ Hg(OH)₂ + H⁺                                      (pK_a = 2.60)

Successive Base Ionization Constants The pK_b values decrease much less than the expected 5 units for almost all the cations (e.g., 0.22, 0.62, 1.03 and 1.17 for Zr⁴⁺ ions). This indicates that the charge on the metal ion is not much affected by the successive loss of hydronium ions (H⁺).from the coordinated water molecules. This may be compared with the values for Fe²⁺ (9.5) and Fe³⁺ (3.65) ions.

A study of hydrolysis for metal ions is essentially a study of heterogeneous systems containing metal hydroxides or hydrated oxides, and is based upon the following assumptions:

1. The solution contains only the metal ions and hydroxide ions.
2. Concentration of unionized metal hydroxide in solution, which is in equilibrium with the precipitate, is negligible, and the only equilibrium reaction is

M(OH)_n(s) ⇌ M(OH)_n(aq)

3. No polynuclear species exist in aqueous solutions.
4. The concentration of the unionized metal hydroxide is same for all the metal ions.

[10.4].6.3 Hydrolysis of Covalent Compounds 

The acid–base approach is not satisfactory for the covalent compounds. For example, boron trifluoride is not easily hydrolyzed in water, whereas boron trichloride is rapidly and completely hydrolyzed, though fluoride ion is more basic than the chloride ion. In these reactions, it seems better to consider the following:

1. Energy changes involved in the bond breaking and bond making processes,
2. Activation of water on energy for the reaction,
3. Mechanism of hydrolysis reactions, and
4. Extent of bond formation, or hydrolysis.

Some examples are given below.

1. Hydrolysis of Boron Trihalides: Hydrolysis of boron trihalides is through the nucleophilic attack of water on the electron deficient boron atom, followed by the elimination of HX from H of water and X of boron halide:

H₂O + BCl₃   [ H^δ+₂O ^δ– — B^δ–Cl₃ ]    H–O–BCl₂(Cl^δ––H^δ+)

In case of boron trifluoride, the elimination of HF does not take place, so that the hydrolysis is extremely slow in aqueous solutions.

2.  Hydrolysis of Hexafluorides of sulphur and tellurium: Thermodynamically, hydrolysis of both is favorable, SF₆ is inert whereas TeF₆ is rapidly hydrolyzed to Te(OH)₆. This is because for both the cases, the hydrolysis requires a 7-coordinated transition state complex [MF₆(OH₂)]. This requires very high activation energy for sulphur compound, but not for tellurium which can easily expand its coordination number to more than 6 using its d orbitals due to its larger size (and very small energy differences amongst 5d orbitals). The hydrolysis is, however, slow. Tellurium can form stable adducts like [(R₃N)₂TeF₆]. In case of UF₆ the activation energy is so low that it is violently hydrolyzed in water.