Calculate the pH of 0.500 L of a buffer solution composed of 0.50 M formic acid (HCO₂H) and 0.70 M sodium formate (NaHCO₂) before and after adding 10.0 mL of 1.0 M HCl.

Interpretation:

The pH value is to be calculated for the formic acid/sodium formate buffer solution before and after addition of HCl.

Concept introduction:

The Henderson-Hasselbalch equation relates pH of a buffer with pKa of acid, concentration of conjugate base and concentration of acid. The expression is written as,

pH=pKa+log[conjugate base][acid] (1)

This equation shows that pH of buffer solution is controlled by two major factors. First, Strength of the acid can be expressed on terms of pKa and second, the relative concentration of acid and its conjugate base at equilibrium. It can be seen from equation (1) that pH of the buffer solution is comparable to pKa values. So this equation can be used to establish a relation between pH and pKa value of acid.

A weak acid (HA) undergoes partial dissociation it can be represented as following equilibrium.

HA(aq.)+ H2O(l)⇌H3O+(aq.) + A−1(aq.)

There is a relation between dissociation constant Ka (equilibrium constant) and the concentration of reactants and products.

  Ka=[H3O+](eq)[A−](eq)[HA](eq) (2)

Here,

• [H3O+](eq) is the equilibrium concentration of hydronium ion.
• [A−](eq) is the equilibrium concentration of conjugate base of acid.
• [HA](eq) is the equilibrium concentration of acid.

If in a solution one of the constituent of a weak acid or weak base is already present before ionization. The present ion will suppress the ionization of the weak acid/ weak base. This is called Common Ion effect. The common ion effect may come from strong acid or strong base. For example, a mixture contains strong acid HCl and  weak acid CH3COOH there will be supression for the dissociation of CH3COOH due to the common ion [H3O+] from the strong acid HCl.

The ICE table is used to give the concentration relationships between ions in presence of common ion.

EquationHA(aq)+H2O(aq)⇌H3O+(aq)+A−(aq)Initial(M)cy0Change(M)−x+x+xEquilibrium(M)c−xy+xx

The acid-dissociation constant for such cases will be written as

Ka=[H3O+](eq)[A−](eq)[HA](eq)

From ICE table

[H3O+](eq)=x+y[A−](eq)=x[HA](eq)=c−x

Substitute for Ka, (x+y) for [H3O+](eq),x for [A−](eq) and (c−x) for [HA](eq) in equation (3).

The acid-dissociation constant expression is as follows;

  Ka=(x+y)(x)(c−x) (3)

The value of pH for the given buffer solution before and after addition of HCl is calculated below;

Given:

Refer to table 16.2 for the value of Ka in the text book.

The value of Ka for formic acid is 1.8×10−4.

The pKa value is calculated as follows;

pKa=−log(Ka)

Substitute, 1.8×10−4 for Ka.

pKa=−log(1.8×10−4)=3.74

Therefore, pKa values is 3.74.

Initial concentration of HCl is 1.0 mol⋅L−1

The concentration of 10 mL, HCl(1.0 mol⋅L−1) is calculated as;

Conversion of 10.0 mL into L.

(10.0 mL)(1 L1000 mL)=0.01 L

Therefore concentration of HCl is calculated as;

concentration = (1.0)(0.01)=0.01​ mol⋅L−1

Therefore, concentration of HCl is 0.01​ mol⋅L−1.

The volume of formic acid/sodium formate buffer is 0.500 L.

Concentration of formic acid HCOOH is 0.50 mol⋅L−1.

Concentration of formate ion HCOO− is 0.70 mol⋅L−1.

The equilibrium for the given buffer can be written as given below.

HCOOH(aq.)+ H2O(l)⇌H3O+(aq.) + HCOO−(aq.)

The pH value of the buffer before addition of HCl is calculated by using equation (1).

pH=pKa+log[conjugate base][acid]

Substitute, 0.50 mol⋅L−1 for [acid], 0.70 mol⋅L−1 for [conjugate base] and 3.74 for pKa.

pH=3.74+log(0.70)(0.50)=3.74+log(1.4)=3.74+0.14=3.88

Therefore pH value of the buffer solution before addition of HCl is 3.88.

As being a strong acid HCl undergoes complete dissociation and gives H3O+ and Cl−.

HCl(aq)→H3O++Cl−(aq)

These H3O+ react from with the base formate ion and form formic acid. The reaction is given as;

HCOO−(aq)+ H3O+(aq)⇌H2O(l) + HCOOH(aq)

Table gives the relationship of the concentration for the reaction between H3O+ and HCOO−.

           H3O+(from added HCl)    HCOO−(from buffer)   HCOOH(from buffer) initial amount of acid or base(mol = concentration⋅volume)0