This is the sequence of steps in this laboratory determination:
 

1. Prepare buffer phosphate solutions with varying pH.
2. Use an indicator (bromothymol blue) as the weak acid whose pK_a we will determine.
3. read the pH of EACH sample.
4. read samples at the wavelengths to determine amount of ionized.
5. read samples at wavelength to determine amount of unionized.
6. graph data to determine where the concentrations are equal.

Background:
One of the most important of properties of a drug molecule is its acidity constant. For many drugs, this property can be related to physiological activity because solubility, rate of solution, extent of binding, and rate of absorption are affected by the extent of dissociation at various pH's. 

For an acidic drug, the following reaction expresses this disassociation:

HA  +H₂O <==> H₃O⁺ + A^-

The determination of an acid dissociation constant requires the estimation of the equilibrium concentration of the acid and base forms of the drug. It can be seen mathematically by using the Henderson-Hasselbach equation:

If the concentration of the acid and base forms are equivalent, the pKa of the drug will be equal to the pH of the solution in which those forms are found.

pH = pK_a + log (base/acid)

If the acid/base ratio is 1:1, then the log of that number will be zero, and 

pH = pK_a

In the following procedure, the acid dissociation constant of an acidic dye will be determined by estimating the point at which the acid and base forms are equal.  The ionized and unionized forms of the dye have different absorption in the visible portion of the electromagnetic spectra and we will use the spectrophotometer to determine these absorptions.  We will then determine the pH of the solution at which the two forms are present at equal concentrations.

A basic knowledge of spectrophotometry is beneficial to the understanding of the principles of this laboratory exercise.

Procedure: Spectrophotometric Determination of pK_a Utilizing Bromothymol Blue 

Bromothymol Blue (B) is a weak acid whose acid and base forms have different absorption spectra.

Both species of Bromothymol Blue absorb in the visible region but at different wavelengths.  We will determine the specific absorption maxima of each species under highly acidic conditions where only HB is present and highly basic conditions where only B^- is present.  Then use that data to determine the pH at the point when both species are present at equal concentration.

Using the stock solutions provided, prepare the following dilutions, each with a total of 25 ml, as described in the table. The solutions should be prepared in small beakers, or other vessel in which the pH can be conveniently measured. A portion of each sample should then be assayed spectrophotometrically, at both 450nm and 550 nm. Data should be recorded in the table. 

Plot absorbance vs. pH for each of the two wavelengths examined.

Connect the points with a smooth curve. The midpoint of the straight portion of each curve corresponds to the point at which the acid and base species are present in equal concentration.  The midpoint of each straight portion should intersect.   At  that point, the pH equals the pK_a. Determine the acid dissociation constant from this graph.