pKa

What is pKa?

The pKa value is the negative base -10 logarithm of the acid dissociation constant (Ka) of a solution.

The quantitative behavior of acids and bases in solution can be understood only if their pKa values are known. In particular, the pH of a solution can be predicted when the analytical concentration and pKa values of all acids and bases are known; conversely, it is possible to calculate the equilibrium concentration of the acids and bases in solution when the pH is known. These calculations find application in many different areas of chemistry, biology, medicine, and geology. For example, many compounds used for medication are weak acids or bases, and a knowledge of the pKa values.

Table of Contents:

• Definition of pKa
• Calculation of pKa
• pKa and pH of buffer solution
• Relation between pK_a and pK_b
• List of pKa value of acids
• FAQs

Definition of pKa

pKa is a number that describes the acidity of a particular molecule. It measures the strength of an acid by how tightly a proton is held by a Bronsted acid. The lower the value of pKa, the stronger the acid and the greater its ability to donate its protons. describe the acidity of a particular molecule

Ka denotes the acid dissociation constant. It measures how completely an acid dissociates in an aqueous solution. The larger the value of Ka, the stronger the acid as acid largely dissociates into its ions and has lower pka value. The relationship between pKa and Ka is described by the following equation:

pKa = -log[Ka]

Acid dissociation constants, or pKa values, are essential for understanding many fundamental reactions in chemistry. These values reveal the deprotonation state of a molecule in a particular solvent. There is great interest in using theoretical methods to calculate the pKa values for many different types of molecules.

Calulation of pKa

• Let us consider a weak acid HA which ionises in the aqueous solution as:
  • HA(acid) + H2O ⇋ H3O+ (aq) + A– (aq)(conjugate base)
• The dissociation constant of acid is defined by

Ka = [H₃O⁺] [A^–] / [HA]

pKa = – log Ka = – log { [H₃O⁺] [A^–] / [HA]}

• In the case of polyprotic acid which contains more than 1 proton dissociates stepwise and produces more than one dissociation constant and more than one pKa value.
  

Examples with Phosphoric acid which contain 3 protons that produced dissociation of the first proton may be denoted as Ka1 and the constants for the dissociation of successive protons as Ka2, and Ka3.

H₃PO₄ ⇋ H₂PO₄^– + H⁺

K_a1 = [H₂PO₄^– ] [H⁺] / [H₃PO₄]

pK_a1 = – log K_a1 = – log {[H₂PO₄^– ] [H⁺] / [H₃PO₄]}

H₂PO₄^– ⇋ HPO₄^2- + H⁺

K_a2 = [HPO₄^2- ] [H⁺] / [H₂PO₄^– ]

pK_a2 = – log K_a2 = – log {[HPO₄^2- ] [H⁺] / [H₂PO₄^– ]}

HPO₄^2- ⇋ PO₄^3- + H⁺

K_a3 = [PO₄^3- ] [H⁺] / [HPO₄^2- ]

pK_a3 = – log K_a3 = – log {[PO₄^3- ] [H⁺] / [HPO₄^2- ]}

pKa and pH of buffer solution

From the Henderson equation of acidic buffer, the pH of the solution is defined as the

pH = pK_a + log { [salt] / [Acid]}

When [salt] / [Acid] = 10 then,

pH = pK_a + 1

When [salt] / [Acid] = 1/10 then,

pH = pK_a – 1

Note: So weak acid may be used for preparing buffer solutions having pH values lying within the ranges pK_a + 1 and pK_a – 1.

The acetic acid has a pK_a of about 4.8. It may therefore be used for making buffer solutions with pH values lying roughly between the range 3.8 to 5.8.

Relation between pK_a and pK_b

Let us consider a weak acid HA which ionises in the aqueous solution as:

HA + H₂O ⇋ H₃O⁺ (aq) + A^– (aq)

(acid) (conjugate base)

The dissociation constant of acid is defined by

K_a = [H₃O⁺] [A^–] / [HA] ……….. (1)

The conjugate base A- behaves as a weak base in water

A^– + H₂O ⇋ HA + OH^–

For base Kb = [HA] [ OH^–] / [A^– ] …………. (2)

Multiply equation (i) and (ii)

K_a x K_b = {[H₃O⁺] [A^–] / [HA]} x {[HA] [OH^–] / [A^– ]} = [H₃O⁺] [OH^–] = K_w

K_a x K_b = K_w

On taking negative logarithm on both side

– log K_a – log K_b = – log K_w

pKa + pKb = pKw

List of pKa value of acids

Acid ionisation constants (K_a) and pK_a values at 25℃