pKa Value Determination Guidance 2024

pKa Value is a number that represents, how weak acid or strong acid is. A strong acid having a “Less than zero pKa Value”. The lower the value of pKa, the stronger the acid and the greater its ability to donate its protons.

pKa Value definitions and pKa formula

The definitions and formulas of the pKa Value are given below.

Acid Dissociation Constant (K_a)

The Acid Dissociation Constant is the equilibrium constant for the reaction in which a weak acid is in equilibrium with its conjugate base in an aqueous solution. Notice that in the equilibrium expression below the concentration of water is not included. This is because water is vastly in excess and the amount changes negligibly upon equilibrium being established. K_a can be thought of as a modified equilibrium constant.

The larger the value of K_a, the stronger the acid. The value is sometimes expressed as the logarithm of its reciprocal, called pK_a.

pKa = -log K_a             [pKa+ pKb =14]

The smaller the value of pK_a the stronger the acid. K_a is a better measure of the strength of acid than pH.

Relationship between pKa and pKb

The pKa is the negative log of the Ka, the pKb is the negative log of the Kb, and the pKa plus the pKb equals fourteen. The Ka box is the same as the pH box, but substitute Ka for [H+], pKa for pH, Kb for [OH-], and pKb for pOH.

Let us consider a weak acid, symbolized HA, is one which is only slightly ionized in water, i.e., exists in equilibrium with its ions (equation 1).

                                            HA(aq)       H⁺(aq)   +   A^–(aq)       ———  (1)         

The equilibrium constant for this reaction is given by the law of mass action  :

                                                 K_a =  [H⁺] [A^–]              ———————     (2)
                                                             [HA]

where the square brackets signify that the concentrations are those existing at equilibrium. A convenient form of this equation may be derived if one first takes the common logarithm of both sides

                                        log K_a    =   log[H⁺]   +   log([A^–]/[HA])       —————  (3)

Definition: pX = -log₁₀X, where X may be a variable or a constant. The pH of a solution is thus defined to be equal to -log₁₀[H⁺]. Substituting into equation 3 now yields

                                       -pK_a   =   -pH   +   log([A^–]/[HA])           ——————— (4)

Re-arrangement of equation 4 gives the Henderson-Hasselbalch equation:

                                        pH   =   pK_a   +   log([A^–]/[HA])             —————–      (5)

pKa Value determination procedure

This equation serves as the basis for the determination of the ionization constant, K_a.

Follow any one of the suitable methods given below.

pKa by Potentiometric method

The titration of a fixed amount, of a weak acid with a standard base solution, recording the pH of the solution at intervals throughout the titration. The equivalence point is determined from the inflection point of a graph of pH vs. volume of added base. The half-equivalence point is the point at which one-half of the volume of base needed to reach the equivalence point has been added. At this point, half of the acid converts to the conjugate base, A^–, and half remains in the non-ionized form HA. The ratio [A^–]/[HA] thus equals one, and the logarithm of 1 is zero. The pH at this point then is numerically equal to the value pK_a(acid dissociation constant).

The base pKa can be determined by using the standard acid solution as a titrant.

Perform analysis with a known compound, compare the result with the reference value, and do the test sample with identical conditions.

Perform the reproducibility (% Relative standard deviation), and also with different amounts of test samples if required.

This method is applicable only in an aqueous medium and a mixture of water & any water-miscible solvent as the medium for the analyte.

This procedure is applicable only for easily ionizable compounds or high polar compounds.

The technique may be carried out on compounds with reasonable aqueous solubilities (> 0.0025 M) and that are available in amounts greater than 30 mg. The method is rapid, simple, and accurate.

However, very low pKa’s (pKa < 3) and overlapping pKa’s cannot be determined.

pKa Value by solubility method

In cases of extreme insolubility, pKa values may be measured by the solubility method. An aqueous solution of a substance is titrated in the direction of its neutral species until the free base or free acid is precipitated. pKa may then be calculated from the solubility product.

This method is not very accurate but may be used on very dilute solutions. pKa by U.V. Spectroscopy.

In cases of poor solubility or small sample amounts, pKa values are calculated from U.V. measurements. The method simply relies on the change in U.V. spectra at different pH’s.

Lower sample concentrations of up to 4mg/400ml, can determine by using UV (approx. 0.000025M).

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pKa Value by HPLC Method

The HPLC method is also used widely for the determination of the pKa Value.

The HPLC method is based on the different retention behavior of the protonated and the non-protonated form of the test material. The retention time of determined in relationship to the pH value of the mobile phase by reverse phase HPLC. The pKa value is the point of inflection in the resulting “sigmoidal” curve, which can be easily achieved.

This method of analysis has salient features to suit poor soluble materials, and the micro level of the sample is sufficient. This method is suitable for those whose titration methods are not suitable.

Procedure:  Calculate the retention time divided by the pH value and plotted the resulting ratio in a coordinate system with the pH value on the abscissa. The resulting carve had a U-Shaped form. Estimate the pKa value at the minimum of the curve.

Precautions for HPLC Method

Using a solvent system so that the retention time is as short as possible, implies the analysis time can be reduced.

Use a short-length column to reduce the analysis time.

Case Study to determine pKa

Procedure: Injected 10 µl of sample solution until two retention time values were equal and noted down the average retention time of the sample peak.

As per the chromatographic procedure difference in Rt of two adjacent pHs will give dRt and the difference in the corresponding pH will give dpH.

Then we have taken the ratio of dRt and dpH i.e; dRt/dpH pKa is nothing but the pH corresponding to a minimum value of dRt/dpH. 

pKa Table

Result: From the above table, two lower values are getting at dRT/dpH  i.e –0.682 at pH

6.0 and –1.784 at pH 8.5.

Note:  Similar way, perform the analysis for better clarity on the pKa value, with fewer increments of about 0.2 pH variation and conclude the exact pKa value.

Correlate the observed value with the available literature value.

Finalize the method, based on the outcome and justification only.      

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