Application to the Ionization Equilibria of Weak Acids and Bases and Their Salts JORGE GUERRA Williams Industrial Products, S. A,, Havana, Cuba
L o a m T m a c triangular charts' may be used tu advantage for plotting equations of the general form XA.YB.ZC= a constant other than zero
(1)
where the exponents A, B, and C may be any real numbers, positive or negative. Expressions of this form are frequently met with in the study of chemical reaction equilibria. The application of logarithmic tr~angularplotting to t.he ionization equilibrium of the weak acid, acetic acid, in water solution is shown in the figure. For this acid, the ionization equilibrium reaction may be written
which may he seen to haw, after a slight rearrangement, the form of equation (1). The figure shows a logarithmic triangular coordinate . network having the following property: For any point of it the values of the three point-coordinates, corre sponding to concentrations in gram-moles per liter of un-ionized acetic acid, acetate ion, and hydrogen ion, are such as always to satisfy the equilibrium equation (4). The range of this network has been restricted to those values of the coordinates likely to be met with in pract,ice. This also is the rauge in which the cunstancy of the acid constant may be expected t,ohold reasonably well. IONIZATION OF PURE ACETIC ACID SOLUTIONS
or, ignoring the hydration of the proton The expression for the ionization constant of acetic acid is usually written in the form [H+l[CnHsO'-l
=
[HC~HZO~
1.80 X 10-5 (at 25' C.)
VOLUME 34, NO. 7, JULY, 1957
(4'
I n order to determine the hydrogen ion concentration of pure acetic acid solutions, enter the chart from the bottom up, along the value of the total acid concentra, tion, on the HC2H,02scale, until the broken Pure acid line is met. From this point may be read, on the scales at the right of the figure, the hydrogen ion concentre tion, the conjugate hydroxyl ion concentration, and the pH of the solution. The acetate ion conrentration may be read on the top scale.
[HC~H,O,I
\ Pure salt line
sptemunfonid A C ~ I Ci c i d - i r r m I O ~ - H U ~ ~ O W in
Note that a small error is committed in this way, since the chart is entered in the first place a t the value of the total acid concentration of the solution, whereas the scale used in so entering it corresponds to concentrations of unionized acid remaining in the solution when equilibrium has been reached. This error is small since a weak acid is involved. So little of it ionizes that, except in the higher concentration range ( 2 1 M ) the approximation is fully warranted. This approximation generally is made in the elementary treatment accorded this topic in most general chemistry textbooks. For weaker acids than acetic the error mvolved in this approximation is still smaller. The broken Pure acid line is the locus of all points of the coordinate network for which the values of the hydrogen ion and the acetate ion concentrations are equal. Its utilization in the manner described follows from the fact that according to the equilibrium r e action (3) equal numbers are always formed, one each, of hydrogen ion and acetate ion for every molecule of acid that ionizes. Here again a harmless approximation is involved in that the hydrogen ion concentration supplied by the solvent (water) is neglected, all of the hydrogen ion in the solution being considered as originating, exclusively, from the acid. The error is negligible except a t extremely low concentrations of acid (
