Physical Chemistry of Milk

Module 8. Acids and bases

Lesson 19
DISSOCIATION CONSTANTS OF ACIDS AND BASES

19.1 Introduction

The dissociation constant quantifies the tendency of a compound or an ion to dissociate. Dissociation is the process by which the compound or ion is split into two components that are also ions and or compounds. In chemical language the acids and bases are the frequent terms used as such it is necessary to know their definition and their behavior under various conditions especially when they are dissociated.

19.2 Dissociation Constant

A general example is the dissociation of the compound AB into A+B which can be written as

Observing the above figure it could be noticed that when a solution is prepared by adding AB, it is possible to calculate from the dissociation how much of the material added is in the form of AB, A and B which are constant. . However, before calculation it is important to know that dissociation of AB into A and B is a reversible process. A and B can assemble back to AB. The dissociation constant can be written as

Ka = {[A] x [B]}/ [AB]

If the dissociation constant of this process is e.g 10-7, l mol of AB dissolved in to a solution of water will result in a concentration of both A and B of approximately 0.000316 moles and a concentration of AB of 0.999684. This gives us an idea that AB is not very soluble. This equation does not give much information unless we take into consideration the concentration. We have to set a second degree equation to understand this aspect of the equation. The process is as follows

10-7, = { [A} x [B]}/ [AB]
When AB dissolves x concentration is lost from AB and x concentration of A and B. So the equation is rewritten to
10-7 = (x X x) /1- x this could be rewritten as
10-7 x (1- x) = (x . x )
10-7 - 10-7. . x = x2
10-7 = x2 + 10-7. x
0 = x2 + 10-7. x - 10-7

The result obtained after calculating using this second order reaction is approximately 0.000362 which is x or [a] and [b]. The concentration of AB is 1-x or 1- 0.000362. More complicated cases are calculated using the same method and in most cases the problem is more complicated. The above equation is actually a simplification of a general equation. The general equation is written as follows.

In this case the dissociation constant is written as: Ka = ([A]x . [B]y) / [AxBy]

19.3 Definition for Acids and Bases

Arrhenius has proposed that acids are the substances that produce protons H+ in aqueous solutions while bases are the substances which produce OH+ But the behaviour of some acids and bases in aqueous solutions was different. The definition given by Bronsted and Lowry for acids was that the compounds which are capable of donating protons. Similarly bases are the substance which accepts protons. This definition being independent of the solvent explains the behavior of most acids and bases

19.4 Dissociation Constant for an Acid

The dissociation constant of an acid is used to study the dissociation of weak or strong acids. Dissociation constants are often denoted as Ka-values.

A simple example on how to use Ka-values is given here:
Consider ammonium (NH4+) dissociating reversibly into ammonia (NH3)

19.5 Reaction of Acid and Bases with Water

In the equations showing the reaction of acids and bases, we show the arrows in both the directions indicating that they are in equilibrium process. The proportion of the reagents and products at equilibrium are described by equilibrium constant. (Fig. 19.1), (Fig. 19.2)

For the reaction of an acid HA with water is shown as

We can observe in the above equation that water is the reactant and belongs in the equilibrium constant. Its value is 55.5M in aqueous solution. This is very large when compared with the change in water concentration at equilibrium. So it is assumed that the value of [H2O] with this assumption we will define the dissociation constant Ka as follows

From this equation we can see that the acids which dissociate to a greater extent will have larger value of Ka are stronger acids while those which have a smaller values of Ka are weaker acids. The dissociation constants for acids (Ka) range from 10-12 to 1013 this shows that the weakest acid is having the lowest equilibrium constant while the strongest acid will have the highest value of equilibrium constant. Further by deriving the equilibrium constant for any acid we will be in a position to know whether a given acid is a strong or a weak acid.

Similarly equilibrium constant for bases Kb with the following equation

Higher equilibrium constant of a base indicates that it is a strong base while the smaller value a weak base. These values range from 10-11 to 103.