Acid Dissociation Constant - Experimental Determination

Experimental Determination

The experimental determination of pK_a values is commonly performed by means of titrations, in a medium of high ionic strength and at constant temperature. A typical procedure would be as follows. A solution of the compound in the medium is acidified with a strong acid to the point where the compound is fully protonated. The solution is then titrated with a strong base until all the protons have been removed. At each point in the titration pH is measured using a glass electrode and a pH meter. The equilibrium constants are found by fitting calculated pH values to the observed values, using the method of least squares.

The total volume of added strong base should be small compared to the initial volume of titrand solution in order to keep the ionic strength nearly constant. This will ensure that pK_a remains invariant during the titration.

A calculated titration curve for oxalic acid is shown at the right. Oxalic acid has pK_a values of 1.27 and 4.27. Therefore the buffer regions will be centered at about pH 1.3 and pH 4.3. The buffer regions carry the information necessary to get the pK_a values as the concentrations of acid and conjugate base change along a buffer region.

Between the two buffer regions there is an end-point, or equivalence point, where the pH rises by about two units. This end-point is not sharp and is typical of a diprotic acid whose buffer regions overlap by a small amount: pK_a2 − pK_a1 is about three in this example. (If the difference in pK values were about two or less, the end-point would not be noticeable.) The second end-point begins at about pH 6.3 and is sharp. This indicates that all the protons have been removed. When this is so, the solution is not buffered and the pH rises steeply on addition of a small amount of strong base. However, the pH does not continue to rise indefinitely. A new buffer region begins at about pH 11 (pK_w − 3), which is where self-ionization of water becomes important.

It is very difficult to measure pH values of less than two in aqueous solution with a glass electrode, because the Nernst equation breaks down at such low pH values. To determine pK values of less than about 2 or more than about 11 spectrophotometric or NMR measurements may be used instead of, or combined with, pH measurements.

When the glass electrode cannot be employed, as with non-aqueous solutions, spectrophotometric methods are frequently used. These may involve absorbance or fluorescence measurements. In both cases the measured quantity is assumed to be proportional to the sum of contributions from each photo-active species; with absorbance measurements the Beer-Lambert law is assumed to apply.

Aqueous solutions with normal water cannot be used for 1H NMR measurements but heavy water, D₂O, must be used instead. 13C NMR data, however, can be used with normal water and 1H NMR spectra can be used with non-aqueous media. The quantities measured with NMR are time-averaged chemical shifts, as proton exchange is fast on the NMR time-scale. Other chemical shifts, such as those of 31P can be measured.