OBJECTIVES

Weak acids are frequently represented by the general formula HX where X represents the anionic portion of the molecule. The ionization of these acids can be represented by the following equation and corresponding equilibrium constant:

In this equation, [X^-] = concentration of anion, which is equal to the concentration of salt (NaX, for example) and [HX] = concentration of acid. A convenient means of following this equilibrium is to measure the hydronium ion concentration with indicators, short range pH paper or, more accurately, with a pH meter. The value of the ionization constant can be calculated if the concentrations of the acid and the anion (which is added as the salt of the acid) are varied and the resulting pH values measured. The mathematical reasoning is outlined in the following equations: Re-arrange Equation (2) to give:

Take log of both sides of Equation (3) to give:

By definition

Therefore,

or

A simple way to evaluate the data obtained is to graph the pH versus the log. If the ratio of anion to acid is 1.00, the last term in the equation is zero and

The graphical representation of the data should yield a straight line from which the pH at which the log equals zero can be determined. At this point, the value of the pH is equal to pK_a, from which we can determine K_a. Recall from earlier work that dilution problems can be solved by using the equation M_dV_d = M_cV_c. The subscripts d and c represent the dilute and concentrated solutions. (As usual M and V represent molarity and volume.) Since the concentration of the stock solutions of acid and salt are small, the volume of the dilute solution (after mixing acid and salt solutions) is assumed to the sum of the volumes of the acid and salt solutions.