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Arrehenius Theory of Dissociation

The total conducting ability of 1 molar aqueous solution of electrolytes is found to increase with dilution. Based on this observation, Arrhenius postulated that a chemical equilibrium exists between the undissociated electrolyte molecule and the ions that result from dissociation. For example, in case of acetic acid we have
On dilution, more of the acetic acid dissociates to give acetate and hydronium ions, which accounts for the increasing conducting ability. In dilute solutions it is known today that the above equilibrium is valid only for weak electrolytes. Strong electrolytes are already present in the form of ions in the solid state.

The chemical equilibrium written above is, like any other equilibrium, dynamic in nature, i.e. the ionization of acetic acid to produce ions and the combination of these ions to produce acetic acid take place continuously. The rates of these two processes are equal to equilibrium. Like any other equilibrium, the above equilibrium can be characterized by its equilibrium constant defined as
Water is present in larger amounts and whatever it has consumed in the above poor ionization is negligibly small and can be ignored. Hence, the concentration of water may be taken to remain constant. This constant may be combined with the equilibrium constant to give a new constant which is known as the ionization constant or dissociation constant of acetic acid.
Thus, we have
The value of the ionization constant is a characteristic of the weak electrolyte and depends only on the temperature. It is independent of the individual concentrations of the species involved in the equilibrium.

Degree of Dissociation of a Weak Electrolyte

The extent of dissociation of a substance can be expressed in terms of degree of dissociation, which is, by definition, equal to the fraction of the total substance that is present in the form of ions. If α is the degree of dissociation, it means that the amount α out of 1 mole of the substance is present in the form of ions and thus the remaining fraction of the undissociated species will be 1 - α . If c is the concentration of the solute then the concentrations of dissociated and undissociated electrolytes will be cα and c(1 - α ), respectively. Taking the example of acetic acid, we have

Reaction: CH3COOH + H2O CH3COO- + H3O+
Concentrations: c(1 - α ) cα cα

Ostwald Dilution law
The degree of dissociation is usually a very small quantity (unless Kioniz has a large value) and thus can be neglected in comparison to unity, i.e. 1 - α 1. Thus, the above expression becomes

From the above expression it follows that as c decreases (dilution), α increases. In the limit when c 0 (infinite dilution), α will approach 1, i.e. at infinite dilution, all of the weak electrolyte gets ionized. This is the Ostwald dilution law.

Calculate the degree of dissociation and [H3O+] of a 0.1 mol dm-3 solution of acetic acid.

Given: Ka(CH3COOH) = 1.8 × 10-5 mol dm-3.
Let α be the degree of dissociation. The concentrations of various species involved in the equilibrium as follows.
c(1 - α ) cα cα

Ignoring α in comparison to 1, and rearranging we get

Substituting the values, we get
α = (1.8 × 10-5 mol dm-3/0.1 mol dm-3)1/2
   = 1.34 × 10-2
Now [H3O+] = cα = (0.1 mol dm-3) (1.34 × 10-2)
                 = 1.34 × 10-3 mol dm-3

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