TITRATION CURVE OF A WEAK ACID AND ITS pKa

(Titration, titration curve, titration curve of acetic acid and its significance)

What is Titration?

Titration is a method to determine the concentration of a dissolved substance (analyte or titrand)

in a known volume by reacting it with another substance of known concentration and volume

(titrant). The volume of thr reactants plays a crucial role in the titration and thus the titration is

better called “volumentric analysis”.

There are different types of titrations. The acid-base titration is the most common. The acid-base

titration is used to determine the amount (concentration) of an acid in a given solution. In an

acid-base titration, a known volume of acid (0f unknown concentration) is titrated against a

solution of strong base (usually NaOH) of known concentration in the presence of an indicator.

After the titration, the concentration of the acid in the sample is calculated using the concept

N1V1 = N2V2

Where:

N1 = normality of the unknown acid

N2 = normality of the known base

V1 = volume of the unknown acid

V2 = volume of the known base

What is Titration curve?

The titration curve is a graphical representation of titration in which the volume of the titrant is

plotted on the X axis (as the independent variable) and the pH of the solution is plotted on the Y

axis (as the dependent variable).

In simple terms, the titration curve is the plot of pH of the analyte (titrand) versus the volume of

the titrant added as the titration progresses.

For the preparation of a titration curve of an acid-base titration, the base is added in small

increments as the pH of the acid in each step is determined with a pH meter. A titration curve can

be prepared for a itration of strong acid versus strong base, weak acid versus strong base, strong

acid versus weak base and weak acid versus weak base. In this note, the titration curve of a weak

acid versus strong base will be discussed.

Such a titration reveals the pKa of the weak acid and explains the buffr action of the weak base

pair.

The titration curve reveals the pKa of a weak acid

Here, as an example, we have selected acetic acid (CH3COOH) as the weak acid and it is titrated

against a strong base NaOH. The NaOH is added as small increments of equal volume and at

each step, the pH of the solution measured and a titration curve is prepared.

As in the picture below, the titration curve of a weak acid has a characteristic shape. It also

reveals the pKa (the negative logarithm of Ka) of the acid. The pKa is the pH at which the

system consists of an equimolar concentration of the weak acid (CH3COOH) and its conjugate

base (CH3COO–). The relationship between pKa and pH and buffer action can be determined

from the Handerson-Hasselbalch equation.

Let’s study the titration curve of acetic acid (CH3COOH) and its characteristic shape in details:

Points to note:

i. Since CH3COOH is a weak acid, well before the addition of NaOH, a few molecules

of the acid will be ionized

ii. The degree of the ionization can be calculated from the dissociation constant (Ka) of

the acetic acid (the Ka of acetic acid = 1.74 × 105M).

iii. As the NaOH is gradually added, the OH– ions present in it will combine with the free

H+ ions in the medium to form H2O.

iv. As the titration proceeds, the free H+ ions are removed by the addition of OH–, more

and more acetic acid molecules will dissociate to satisfy its own equilibrium constant.

v. At the midpoint of titration, one half of the original acetic acid has undergone

dissociation and the rest will be intact.

vi. At this point, the concentration of the weak acid ([CH3COOH]) and the concentration

of the conjugate base ([CH3COO–]) will be equal.

vii. At this midpoint of titration, the pH of the equimolar solution of acetic acid and the

acetate ions will be exactly equal to the pKa of acetic acid.

viii. The pKa of acetic acid is 4.76 as given in the picture\as the titration is continued by

adding more NaOH increments, the remaining non-dissociated acetic acid molecules

are gradually converted into acetate ions.

ix. The the end of titration, all the acetic acid molecules in the solution will be converted

into acetate ions

x. The titration curve of other weak acids such as phosphoric acid and ammonium also

shows similar shape

Significance of titration curve of a weak acid

1. The titration curve of a weak acid reveals its pKa

2. pKa is a pH at which the concentration of weak acid and its conjugate base will be

equimolar concentrations. This equimolar concentration of a weak acid and its conjugate

base can act as a buffer (Buffer is a solution which resist the change in pH).

3. Thus titration curve also reveals the buffer action of weak acid and its conjugate base.

DERIVATION AND USES OF HANDERSON – HASSELBALCH EQUATION

1. Derivation of Handerson – Hasselbalch equation:

Henderson – Hasselbalch equation is a simple expression which relates the pH, pKa and the

buffer action of a weak acid and its conjugate base. The equation also describes the characteristic

shape of the titration curve of any weak acid such as acetic acid, phosphoric acid and any amino

acid. The titration curve of a weak acid helps to determine the buffering capacity and buffering

pH which is exhibited around the pKa of that acid

For example, in the case of acetate buffer, the pKa is 4.76. This is the best buffering pH of acetic

acid. Besides, at this pH the acetic acid (CH3COOH) and acetate ions (conjugate base of acetic

acid: CH3COO–) will be at equimolar concentration in the solution. This equimolar solution of a

weak acid and its conjugate base will resisrt the change in pH by donating of taking up the

hydrogen ions (H+).

NB: pH is the negative logarithm of hydrogen ion concentration in a medium. The pKa is the

negative logarithm of Ka. The Ka is the dissociation constant (similar to the equilibrium

constant) for the inonization reaction of an acid.

A weak acid undergoes partial ionization in water, hence the equilibrium between the acid and its

conjugate base which is represented below

HA H+ + A– ------------ (eqn 1)

Where HA is the acid, H+ is the hydrogen ion and A– is the conjugate base of the acid HA

The dissociation constant Ka of the above reaction will be:

Ka = concentration of the productsconcentrationof the reactant

Ka = ¿¿ ---------- (eqn 2)

The dissociation constant (Ka) is the ratio of the concentration of the products divide by the

concentration of the reactants. The square boxes in the equation above denote ‘concentration’

Make [H+] in eqn 2 the subject of the formula

[H+] = Ka [ H A ][ A – ]

---------- (eqn 3)

Take the negative logarithm of both sides:

–log [H+] = –log Ka –log [ H A ][A – ]

---------- (eqn 4)

Substitute: pH = –log [H+] into eqn 4

pKa = –log Ka

pH = pKa –log [ H A ][ A – ]

---------- (eqn 5)

Now invert the –log [ H A ][ A – ]

, which involves changing its sign to obtain the Handerson –

Hasselbalch equation as it is written below:

pH = pKa + log [ A – ][ H A ] ---------- (eqn 6)

[A–] is the concentration of the conjugate base

[HA] is the concentration of the acid

So the Handerson – Hasselbalch equation can be rewritten as follows:

pH = pKa + log [C onjugate base ]

[ Acid ]

2. Uses of Handerson – Hasselbalch equation

It is mainly used for calculating the pH or pKa of a solution containing known quantities of a

weak acid and its conjugate base.

At the midpoint of the titration curve of a weak acid, the concentration of HA (acid) equals the

concentration of A– (the conjugate base of the acid HA). We have already stated that for a buffer,

the best buffering is at its pKa. Also remember, the buffer is a mixture of equimolar

concentration of weak acid and its conjugate base.

Since the concentration of the conjugate base; [A–] and the weak acid; [HA] is uniform in the

midpoint of titration, the ratio of the concentration of the conjugate base to the concentration of

the weak acid becomes 1.

So let’s put it in the Handerson – Hasselbalch equation

pH = pKa + log [C onjugate base ]

[ Acid ]

Thus the equation becomes:

pH = pKa + log1

log1 = 0

Thus pH = pKa + 0

pH = pKa

This also proved that for a buffer, the best buffering activity is obtained at the pH value

equal to its pKa value.