# pKa Value Calculation

pKa value is the negative base -10 logarithm of the acid dissociation constant (Ka) of a solution. It measures how completely an acid dissociates in an aqueous solution.

It also indicates how weak or powerful an acid is in simple terms. The larger the value of Ka, the stronger the acid as acid largely dissociates into its ions and has lower pka value and the greater its ability to donate its protons.

The pKa of a strong acid is most often found less than zero. The relationship between pKa and Ka is described by the following equation:

pKa = -log[Ka]

Conversely, Ka is measurable when pKa is given:

Ka = 10^-pKa

Relationship between pH and pKa

The relationship between pKa and pH is described by the Henderson-Hasselbalch equation:

Let us consider a weak acid HA which ionizes 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]}

The Henderson–Hasselbalch equation relates the increase in the solubility to the pH of the solution relative to the pKa (acidic) or pKa (basic) of the ionizable acid or base.

PKa = −log(Ka)

Ka = acid dissociation constant

[A−] = molar concentration of the acid’s conjugate base

[HA] = molar concentration of the undissociated weak acid

Stot = total solubility of weak acid

S0 = intrinsic solubility of uncharged moiety

PKa = −log(Ka)

Ka = base dissociation constant

[B] = molar concentration of the base’s conjugate base

[BH+] = molar concentration of the dissociated base

Stot = total solubility of weak base

S0 = intrinsic solubility of uncharged moiety

The Henderson–Hasselbalch equation helps explain the increase in solubility at the first pKa, but is not useful for modeling the behavior of polyprotic acids over a pH range incorporating additional pKa values. Because ionizable molecules can differ in the number and type of ionizable groups, it is important to explore solubility across a range of pH values.

In summary, pH is a measure of the acidity of a solution, while pKa is a measure of the strength of a weak acid.

#### pKa of Some Weak & Strong Acids

• Hydrocyanic acid pKa = 9.21 (HCN, weak acid)
• Acetic acid pKa = 4.75 (CH3COOH, weak acid)
• Hydrofluoric acid pKa = 3.14 (HF, weak acid)
• Hydrochloric acid pKa = -8 (HCl, strong acid)
• Sulfuric acid pKa = –10 (H2SO4, strong acid)

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