Water self-ionization constant

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. 

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 ... 

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... 

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 ... 

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... 

We take the activity of pure water as 1 and obtain the conventional ion product constant for the self-ionization of water. 

Self-Ionization of Water The self-ionization of water occurs because aqueous solutions always contain some FF30 and some OtF. In a neutral solution, the concentrations of these are equal (1.0 x 10 M). When an acid is added to water, [HsO ] increases and [OFF"] decreases. When a base is added to water, the opposite Fiappens. The ion product constant, however, still equals 1.0 x lO-, allowing us to calculate [H30 ] given [OH ] and vice versa. 

You can see the slight extent to which the self-ionization of water occurs by noting the small value of its equilibrium constant Kc. 

Although you normally ignore the self-ionization of water in calculating the HsO concentration in a solution of a strong acid, the self-ionization equilibrium still exists and is responsible for a small concentration of OH ion. You can use the ion-product constant for water to calculate this concentration. As an example, calculate the concentration of OH ion in 0.10 M HCl. You substitute [H30 ] = 0.10 M into the equilibrium equation for (for 25°C). 

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