Buffer capacity and equation

1. 1
BUFFER CAPACITY
By Praveen Gujjula
M.Pharm,.(Ph.D)

2. 6
Buffer Capacity
A buffer counteracts the change in pH of a solution upon the
addition of a strong acid, a strong base, or other agents that tend
to alter the hydrogen ion concentration.
Buffer capacity β: buffer efficiency, buffer index or buffer value
Is the resistance of a buffer to pH changes
upon the addition of a strong acid or base.
Definition
The ratio of amount added of strong base (or acid) to small
change in pH brought about by this addition.
β = Δ B
Δ pH
ΔB = the small addition in gram equiv./liter of strong base
added to the buffer solution to produce a pH change
Δ pH = pH change

3. 7
The buffer capacity of the solution has a value of 1:
when the addition of 1 gram equiv. of strong base (or acid) to 1 liter of
the buffer solution results in a change of 1 pH unit.
Example: Acetate buffer
acetic acid & sodium acetate
0.1 mole each in 1 liter of solution.
a) 0.01 mole portions of NaOH is added
HAc +
(0.1 – 0.01)
NaOH
(0.01)
NaAc + H2O
(0.1 + 0.01)
b) The conc. of Na acetate (the [salt] in buffer equation)  by 0.01 mol/l
& the conc. of acetic acid [acid]  by 0.01 mol/l
because each addition of base converts 0.01 mole of acetic acid into
0.01 mole of sodium acetate according to the reaction.

4. Before the addition of the first portion of NaOH,
the pH of the buffer solution is:
pH = pKa + log [salt ] + [base]
[acid] - [base]
pKa = pH + log Cu [acid]
Ci [salt]
pH = pKa - log [acid]
[salt]
pH = pKa + log [salt ]
[acid]
pH = 4.76 + log (0.1) = 4.76
(0.1)
pH = pKa
The changes in concentration of the salt and the acid by the
addition of a base are represented by
pH = 4.76 + log (0.1) + 0.01
(0.1) – 0.018

5. 9
Moles of
NaOH added
pH of
solution
Buffer
Capacity, β
0 4.76 0.11
0.01 4.85 0.11
0.02 4.94 0.11
0.03 5.03 0.10
0.04 5.13 0.09
0.05 5.24 0.08
0.06 5.36 0.07

6. 10
The buffer capacity is not a fixed value for a given buffer
system, but depends on the amount of base added.
With the addition of more NaOH, the
decreases rapidly, and, when sufficient
buffer capacity
base has been
added the acid convert completely into sodium ions and
acetate ions
The buffer has it’s greatest capacity before any base is
added where [salt] / [acid] = 1, and according to equation,
pH = pKa.
The buffer capacity is influenced by an increase in the total
conc. of the buffer constituents since a greater conc. of salt
and acid provides a greater alkaline and acid reserve.

7. 11
Van Slyke developed a more exact equation for
calculation of buffer capacity β
β = 2.3 C Ka [H3O+]
(Ka +[H3O+])2
C = The total buffer concentration (the sum of the molar
concentrations of the acid and the salt).
Ka = dissociation constant
H3O+ = hydrogen ionconcentration
The equation permits the calculation of the buffer capacity at any
hydrogen ion concentration, i.e. when no acid or base has been
added to the buffer
[H+]

8. 12
Example:
If hydrogen ion concentration is 1.75 x 10-5, pH = 4.76
what is the capacity of the buffer containing 0.10 mole of
each of acetic acid and sodium acetate per liter of solution ?
The total concentration , C = [acid] + [salt], is 0.20 mol/l and
the dissociation constant Ka is 1.75 x 10-5
β = 2.3 C Ka [H3O+]
(Ka + [H3O+])2
β = 2.3 x 0.20 x (1.75x10-5) x (1.75 X 10-5) = 0.115
[(1.75x10-5) +(1.75 X 10-5)]2

9. 13
Maximum buffer capacity .
The maximum buffer capacity occurs when pH = pKa or
when (H3O+) = Ka
β max = 2.303 C (H3O+) 2 = 0.576 C
(2 H3O+) 2
β max = 0.576 C
Where C is the total buffer concentration
Example:
What is the maximum buffer capacity of an acetate buffer
with a total concentration of 0.20 mol/l?
β max = 0.576 C
= 0.01152 = 0.01

10. 14
PharmaceuticalSignificance
Buffer in biological & pharmaceutical systems
I. In vivo biological buffer systems
a) Blood
 Blood is maintained at a pH of about 7.4 by:
the 1° buffers in the plasma &
the 2° buffers in the erythrocytes.
The buffer capacity of blood = 0.039 gram equiv. per liter/pH
unit for whole blood of which: 0.031 by the cells
0.008 by the plasma
* When the pH of the blood goes below 7.0 or
above 7.8, life is in serious danger.
* The pH of the blood in diabetic coma is dropped to about
6.8

11. 15
b) Lacrimal fluid
Tears have a great degree of buffer capacity, allowing
a dilution of 1:15 with neutral distilled water before an
alteration of pH is noticed.
The pH of tears is about 7.4 with a range of 7 to 8

12. II. Pharmaceutical Buffers
Buffer solutions are used in pharmaceutical formulation
particularly in ophthalmic preparations
Gifford suggested two stock solutions of:
- boric acid and monohydrated sodium carbonate
- mixed in various proportions to yield buffer solutions
of pH values from about 5 - 9.
Sorensen proposed a mixture of the salts of:
- sodium phosphate for buffer solutions of pH 6 to 8.
The Clark-Lubs mixtures and their pH ranges
a. pH 1.2 to 2.2: HCI and KCI
b. pH 2.2 to 4.0: HCI and potassium hydrogen phthalate
c. pH 4.0 to 6.2: NaOH and potassium hydrogen phthalate
d. pH 5.8 to 8.0: NaOH and KH2PO4
e. pH 7.8 to 10 : H3BO3, NaOH and KCl
Sodium chloride is added to buffer mixture to make it isotonic with bo16
dy.

13. 17
Preparation of Pharmaceutical buffer solutions
Factors of some importance in the choice of pharmaceutical
buffer include:
 Availability and cost of chemicals
 Sterility of the final solution.
 Stability of the drug and buffer on aging.
 Freedom from toxicity.
For example, a borate buffer, because of its toxic effects,
cannot be used for a solution to be administrated orally or
parenterally.

14. 18
The following steps should be used in preparing buffer systems
a. Select a weak acid having a pKa approximately equal to the pH
wanted to insure maximum buffer capacity.
b. From the buffer equation, calculate the ratio of salt and weak
acid required to obtain the desired pH.
log Cu = pKa - pH
Ci
c. Consider the individual concentrations of the buffer salt
and acid needed to obtain a suitable buffer capacity.
β = 2.3 C Ka [H3O+]
(Ka + [H3O+])2
A concentration of 0.05 to 0.5 molar is sufficient and
a buffer capacity of 0.01 to 0.1 is sufficient.
d. Finally, determine the pH and buffer capacity of the completed
buffered solution using a pH meter.

15. 19
III. Buffer Capacity and pH on Tissue Irritation
Solutions to be applied to tissues or administered
parenterally are liable to cause irritation, if their pH is
greatly away from the normal pH of the body fluid.
 must be considered when formulating:
- ophthalmic solutions
- parenteral products
- fluids to be applied to abraded surfaces.
Factors affecting: (i &ii are of greater significance)
i) The buffer capacity of the solution
ii) The volume to be used in relation to that of body
fluid with which the buffered solution will come in
contact
iii) Actual pH of the solution
iv) The buffer capacity of the body fluid