Henderson's Equation (pH of a buffer):

(i)  Acidic buffer:        

It consists of a mixture of weak acid and its salt (strong electrolyte). The ionisation of the weak acid, HA, can be shown by the equation

HA ↔  H+ + A-

 Applying law of mass action,

Ka =   H+A/[HA] 

It can be assumed that concentration of A- ions from complete ionisation of the saltBA is too large to be compared with concentration of A- ions from the acid HA.

BA ↔  B+ + A-

Thus, [HA] = Initial concentration of the acid as it is feebly ionised in presence of common ion

and [A-] = Initial concentration of the salt as it is completely ionised.

So [H+] = Ka . [Acid]/[Salt]                               ...... (iii)

Taking logarithm and reversing sign,

-log [H+] = -log Ka - log[Acid]/[Salt]

or     pH = log[Salt]/[Acid] - log Ka

or     pH = pKa + log[Salt]/[Acid]                        ...... (iv)

This is known as Henderson's equation.

    When [Salt]/[Acid] = 10 , then

            pH = 1 + pKa

    and when [Salt]/[Acid] , then

            pH = pKa -1

So weak acid may be used for preparing buffer solutions having pH values lying within the ranges pKa + 1 and pKa -1. The acetic acid gas a pKa of about 4.8; it may, therefore, be used for making buffer solutions with pH values lying roughly within the ranges 3.8 to 5.8.

 

(ii)   Basic offer:

It consists of a weak base and its salt with strong acid. Ionization of a weak base, BOH, can be represented by the equation.

BOH ↔  B+ + OH-

Applying law of mass action,

Kb =  [B+][OH-]/[BOH]                                   ....... (i)

or      [OH-] = Kb [BOH]/[B+]                           ...... (ii)

As the salt is completely ionized, it can be assumed that whole of B+ ion concentration comes from the salt and contribution of weak base to B+ ions can be ignored.

BA ↔ B+ + A-              (Completely ionised)

So   [OH-]= Kb[Base]/[Salt]                             .... (iii)

or    pOH = log[Salt]/[Base]  log Kb

or    pOH = pKb + log[Salt]/[Base]                   ...... (iv)

Knowing pOH, pH can be calculated by the application of the formula.

pH + pOH = 14

Related Resources
Relative Strength of Acids and Bases

Relative Strength of Acids and Bases: According to...

Salt of Strong Acid and Weak Base

Salt of a strong acid and a weak base: The...

Solubility Product

SOLUBILITY PRODUCT: If to a given amount of...

Hydrolysis of Amphiprotic Anion

Hydrolysis of Amphiprotic Anion: Let us consider...

Salt of Weak Acid and Weak Base

Salt of a weak acid and a weak base: Maximum...

Salt of Weak acid and Strong Base

Salt of a Weak Acid and a Strong Base: The...

Common ION Effect

COMMON ION EFFECT: Let AB to the weak electrolyte....

Acids and Bases

Acids and Bases: The earliest criteria for the...

Periodic Variations of Acidic and Basic Properties

Periodic variations of acidic and basic...

Salt Hydrolysis

Salt Hydrolysis: Pure water is a weak electrolyte...

Buffer Capacity

Buffer capacity: The property of buffer solution...

pH OF Weak Acids and Bases

pH OF Weak Acids and Bases: Weak acids and bases...

Buffer Solutions

BUFFER SOLUTIONS: For several purposes, we need...

Relationship-Solubility and Solubility Product

Relationship between solubility and solubility...

Types of Electrolytes

Types of Electrolytes: The compounds which give...

Ostwald s Dilution Law

Ostwald’s Dilution Law: According to...

Lewis Concept of Acids and Bases

Lewis Concept of Acids and Bases: This concept was...

Acid-Base Neutralization

ACID-BASE NEUTRALISATION-SALTS When aqueous...

Hydrogen Ion Concentration pH Scale

HYDROGEN ION CONCENTRATION-pH SCALE: It is clear...

Applications of Solubility Product

Applications of Solubility Product (i)...

Ionic Product of Water

Ionic Product of Water: Pure water is a very weak...

Theory of Indicators

Ionic Equilibrium THEORY OF INDICATORS: An...