Self-ionization constant of water

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 value of Kv>, at STP is 1.0x10 ". The self-ionization constant of water, Ky, is thus just a special case of an acid dissociation constant. 

Water itself is neutral. It forms an equal number of hydronium and hydroxide ions by self-dissociation. The process is described by the equilibrium constant K, the self-ionization constant of water. At 25°C,... 

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. 

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... 

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. 

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. 

Water itself is ionized to a very small extent (equation 6.1) and the value of the self-ionization constant, (equation 6.2), shows that the equilibrium lies well to the left-hand side. The self-ionization in equation 6.1 is also called autoprotolysis. 

The resulting equilibrium constant is called the ionization constant, or dissociation constant, or self-ionization constant, or ion product of water, and is symbolized byAfw... 

These two constants are related by the self-ionization or autoprotolysis constant of water. Consider the ionization of water ... 

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. 

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