Ionic Equilibrium

Introduction 

Chemical reactions in solutions, especially aqueous solutions play a very important role in Chemistry. Aqueous solutions of ionic compounds such as NaCl or CuSO₄ are good conductors of electricity. However, all chemical compounds do not behave this way. For example, an aqueous solution of sugar is non-conducting. It is not difficult to understand why aqueous solutions of some solutes conduct electricity while others do not. 

For an electrical condition to take place, there must be electrical charges that can move. If an ionic compound is dissolved in water, the closely packed ions in solid get separated; that’s called as the compounds dissociate. 

As the ions enter the solution, they get surrounded by water molecules. This process is called hydration. The hydrated ions move freely in solution and their ability to move is responsible for the electrical conductivity of the solution. 

However, when a molecule solid like sugar dissolves in water, the molecule gets dispersed throughout the solution, but they stay intact when they dissolve. They simply intermingle with water molecules when their solutions get formed. There are no charged particles in solution. Consequently, the solution does not conduct electricity. Thus, we have two types of substances:   

1. Electrolytes: These are the substances which in their molten state or aqueous solutions contain ions and therefore, conduct electricity. Generally, electrolytes are either ionic compounds such as sodium chloride or polar covalent compounds such as hydrochloric acid. 

2. Non-electrolytes: some substances do not conduct electricity either in solution or in a molten state. These are generally nonpolar covalent compounds such as sugar and naphthalene.    

Factors on Which the Degree of Dissociation Depends

The degree of dissociation of an electrolyte depends on the following factors:

1. Nature of Solute: Some substances like mineral acids, alkalies, and most of the salts ionize almost completely in aqueous solutions. These are called strong electrolytes. On the other hand, compounds like organic acids and bases, some inorganic acids like HCN and inorganic bases like NH₄OH ionizes only to a small extent. These are called weak electrolytes. 

2. Nature of Solvent: Substances like water which have a high dielectric constant (i.e., insulating power) cause greater ionization than those like alcohol which have low dielectric constant. For example, an aqueous solution of hydrochloric acid conducts electricity readily while its solution in toluene (an organic solvent) hardly allows any electricity to pass through because in the latter case a few or no ions are formed. 

3. Dilution: Larger the quantity of solvent used, larger is the amount of ionization caused by it. Thus the degree of ionization in dilute solutions is greater than in concentrated ones.

4. Temperature: Ionization increases with the rise of temperature.

5. Nature of Other Substances Present in Solution: The degree of ionization of an electrolyte is affected by the presence of other electrolytes having the common ion. For example, ionization of ammonium hydroxide is suppressed by the presence of some ammonium chloride in solution. The suppression of the degree of ionization of an electrolyte on adding another electrolyte having a common ion is called the common ion effect.

Ostwald’s Dilution Law        

According to the Arrhenius theory of ionization, there is a dynamic equilibrium between the ions of an electrolyte in solution and the undissociated electrolyte molecule. For example, for a binary electrolyte AB, we have

AB ⇔ A⁺ + B⁻                                                           

Ostwald, in 1988, pointed out that the principles of chemical equilibrium can also be applied to ionic equilibria. 

Let the initial concentration of undissociated ‘AB’ = c moles/litres. Degree of dissociation of ‘AB’ at equilibrium = α. Thus, the concentration of different species at equilibrium will be as shown in the following equation:

Initial concentration                 c          0          0

                                                    AB ⇔ A⁺   +   B⁻

Concentration at equilibrium c(1 - α)   cα        cα

Applying the laws of equilibrium, we have 

K = \[\frac{[A^{+}][B^{-}]}{[AB]}\] = \[\frac{c \alpha \times c \alpha }{c(1 - \alpha)}\] = \[\frac{c^{2} \alpha^{2}}{c(1 - \alpha)}\] = \[\frac{c \alpha^{2}}{1 - \alpha}\]   (i)

Where K is known as dissociation or ionization constant and the expression is the mathematical form of Ostwald dilution law. 

For electrolytes in which ‘α’ is extremely small as compared to unity, ‘α’ can be neglected in the denominator. For such cases, 1 - α=1.

Hence K = cα\[^{2}\]                          (K = \[\frac{c \alpha^{2}}{1 - \alpha}\] = \[\frac{c \alpha^{2}}{1}\] =  cα\[^{2}\])  

Or         α\[^{2}\] = \[\frac{K}{c}\]             Or    α = \[\sqrt{\frac{K}{C}}\]    (ii)

Equation (ii) is another form of Ostwald dilution law and can be expressed in words as follows:

For a weak binary electrolyte, with a small degree of dissociation, the degree of dissociation is inversely proportional to the square root of the initial concentration. 

Thus, for weak acids, α = \[\sqrt{\frac{K_{a}}{C}}\]

Where  K\[_{a}\] is the dissociation constant of the weak acid. 

In the case of weak bases, α = \[\sqrt{\frac{K_{b}}{C}}\]

Where K\[_{b}\]  is the dissociation constant of the weak base.

Since c is the concentration in moles/litre, therefore, the volume (V) of the solution containing 1 mole of the electrolyte will be equal to 1/c litres. Substituting 1/c = V, the equations (i) and (ii) can be written as:

K = \[\frac{\alpha^{2}}{(1 - \alpha)V}\]  and  α = \[\sqrt{KV}\]   (iii)

Hence, Ostwald’s dilution law can also be expressed in words as: 

Thus, for weak acid, α = \[\sqrt{K_{a}V}\]

Similarly, for a weak base, α = \[\sqrt{K_{b}V}\]