Self-ionization constant

The activity of the solvent molecule HS in a single-component solvent is constant and is included in Kus. The concentration of ions is mostly quite low. For example, self-ionization occurs in water according to the equation 2H20— H30+ + OH". The conductivity of pure water at 18°C is only 3.8 X 10"8 Q"1 cm-1, yielding a degree of self-ionization of 1.4xl0"19. Thus, one H30+ or OH" ion is present for every 7.2 x 108 molecules of water. Some values of Kus are listed in Table 1.5 and the temperature dependence of the ion product of water Kw is given in Table 1.6. 

Table 1.5 Self-ionization constants of solvents. (According to B. Tremillon)... 

Kv is the self-ionization constant for water (Table 3.2) and equation (3.18) reflects the not surprising inverse relation between Ka and Kh. It is only when Ka and Kv for a compound are of different magnitudes that it may be classified as an acid or a base. An example which is difficult to classify is hypoiodous acid (HOI) where K = 2.5 x lO11 mol dm 3 andKh = 3.2 x 10 10 mol dm3. Although Kb has been widely used in the past, it is a quantity which is largely redundant, for Ka (or pKa) may be used to express the strength of bases as well as acids, see Table 3.3. 

The self-ionization constant for pure formic acid, K = [HCOOHJ] [HCOO ], has been estimated as 10 6 at room temperature. What percentage of formic acid molecules in pure formic acid, HCOOH, are converted to formate ion The density of formic acid is 1.22g/mL. 

Using the equilibrium expression that you reviewed in Chapter 13, the equilibrium constant for the self-ionization of water can be expressed as ... 

The second variation is to determine either the pH or the hydrogen ion concentration of a solution when given the hydroxide ion concentration, [OH-], for the solution. To solve these problems you need to utilize the equilibrium constant expression for the self-ionization of water (Kw). This expression will allow you to convert from the hydroxide ion concentration, [OH-], to the hydrogen ion concentration, [H+], The [H+] can then be used to calculate pH if necessary. One of the free-response questions on the 1999 test required this calculation. 

Perhaps you recognize this equation from the beginning of the chapter. If you don t, it is the equation for the self-ionization of water, from which Kw was derived. What you ve now seen are three equations. The first is an equation that would be used to calculate the Ka of acetic acid. The second is the equation used to calculate Kh for the conjugate base. The third, which is derived from these two, is the formula for calculating Kw. There is a very clear relationship between Ka, Ku, and Kw. The three constants are all related in Equation 14.9, shown below ... 

Autoprotolysis constant — The ion-product calculated from the ion activities of the conjugate acidic and basic species of an -> amphiprotic solvent (SH). The chemical equation of such self-ionization reactions can be schematized as 2HS H2S+ + S , where H2S+ is the conjugate cation, S the conjugate anion. The autoprotolysis constant can be formulated as JCauto = [H2S+] ... 

Ion product — A temperature-dependent constant related to pure substances that can dissociate forming ions and remain in equilibrium with them. It is the product of the ion activities raised to the stoichiometric coefficients of such ionic species in former pure substance. Since the concentration of the pure substance is practically a constant, it is not included in this equilibrium expression. Common pure substances characterized by an ion-product constant are -> amphiprotic solvents, and those salts that are partially dissolved in a given solvent. In the latter case, the ion product is synonymous with solubility product. The following table (Table 1) summarizes self-ionization ionic products and - autoprotolysis constants of some - amphiprotic solvents [i]. 

The pure liquid (bp -10°C) is a useful nonaqueous solvent despite its low dielectric constant (—15), and lack of any self-ionization. It is particularly useful as a solvent for superacid systems. 

Some ionizing solvents are of major importance in analytical chemistry whilst others are of peripheral interest. A useful subdivision is into protonic solvents such as water and the common acids, or non-protonic solvents which do not have protons available. Typical of the latter subgroup would be sulphur dioxide and bromine trifluoride. Non-protonic ionizing solvents have little application in chemical analysis and subsequent discussions will be restricted to protonic solvents. Ionizing solvents have one property in common, self-ionization, which reflects their ability to produce ionization of a solute some typical examples are given in table 3.2. Equilibrium constants for these reactions are known as self-ionization constants. 

Km is the self ionization constant for water (table 3.2) and equation (3. f8) reflects the not surprising inverse relation between Kt and Kh. It is only when AT, and Kh for a compound are of different magnitudes that it may be classified as an acid or base. An example which is difficult to classify is... 

Spontaneous ionization requires both good leaving groups and that the resulting carbenium ions are sufficiently stable. For example, although primary triflates are very stable covalent species which do not self-ionize, secondary triflates with phenyl substitents are very reactive and spontaneously ionize. The ionization equilibrium of styryl triflate could not be established because of side reactions such as Friedel-Crafts alkylation [56], On the other hand, methoxymethylium triflate is partially ionized with equilibrium constants Kj = 5-10 4 at 10° C and Kt = 210 4 at -70° C in S02 [57]. In this system, ionization is endothermic. Secondary triflates with alkoxy substituents, such as those in polymerizations of vinyl ethers, are apparently more strongly ionized than their primary counterparts [58,59],... 

Little is known about the thermodynamics of self-ionization equilibria. It appears that the extent of self-ionization is primarily related to the strength of the bridge bonds. For example, self-ionization constants for HF, HgO, and NHg are decreasing in the order HF K X > HgO K X 10 ) NHg (K x 10 ) which cor-... 

The equililibrium constant of the self-ionization of DMSO is 5 x 10 (25°C) the conjugate base (CH3SOCH2) , which is formed when DMSO acts as a proton donor during a reduction, is a rather strong base and a fairly good nucleophile, which may attack electrophilic centers or radicals [389]. 

Recall that an equilibrium-constant expression relates the concentrations of species involved in an equilibrium. The relationship for the water equilibrium is simply [H30" ][0H ] = K q. This equilibrium constant, called the self-ionization constant of water, is so important that it has a special symbol, Its value can be found from the known concentrations of the hydronium and hydroxide ions in pure water, as follows ... 

The result is a special equilibrium constant expression that applies only to the self-ionization of water. The constant, K, is called the ion product constant for water. The ion product constant for water is the value of the equilibrium constant expression for the self-ionization of water. Experiments show that in pure water at 298 K, [H+] and [OH ] are both equal to 1.0 X 10 M. Therefore, at 298 K, the value of K is 1.0 X 10 ... 

This convention is valid for most environmental situations because the concentration of water is essentially constant at 55.4 M, negligibly affected by the mass of chemicals dissolved in it or by its self-ionization. 

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