General Chemistry

Buffer Solutions: Henderson’s Equation

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What is Buffer: The solutions, which resist the change in their pH, when a small amount of acid or a base is added to them, are called buffer solutions.

pH of Buffer

The pH of buffer solution remains constant, and does not change even on dilution and keeping for long time.

Preparation of Buffer Solutions

Preparation of buffer solutions of pH lesser than 7: (Acidic buffer solutions)

Such solutions can be prepared by mixing weak acids and their salts with strong bases.

Mixture of acetic acid and sodium acetate is an example of such buffer solution.

H3CCOOH (aq) + H2O (l)                                ⇆            CH3COO- (aq) + H3O+ (aq)

H3COONa (s)                                     ⇆            CH3COO- (aq) + Na+ (aq)            

The increase in concentration of CH3COO- ions in solution will shift the equilibrium towards left and hence the pH of solution will remain intact.

Preparation of buffer solutions of pH greater than 7: (Basic buffer solutions)

Such solutions can be prepared by mixing weak bases and their salts with strong acids.

Mixture of ammonium hydroxide and ammonium chloride is an example of such buffer solution.

NH4OH (aq)                        ⇆            NH4+ (aq) + OH- (aq)

NH4Cl (s)                             ⇆            NH4+ (aq) + Cl- (aq)

The increase in concentration of NH4+ ions in solution will shift the equilibrium towards left and hence the pH of solution will remain intact.

Need for Buffer Solution

  • The pH of the human blood is maintained at 7.35, a person may die if pH of his blood changes to 7.00 or 8.00…
  • Buffers are important in many areas of chemistry and allied sciences like molecular biology, microbiology, cell biology, soil sciences, nutrition and clinical analysis.
  • In laboratory, many inorganic and organic reactions are performed in buffered solution to minimize any adverse effect caused by acids or bases that might be consumed or produced during reaction.

Action of Buffer

Buffer of different pH can be prepared by changing the concentration of CH3COONa and CH3COOH

Mix CH3COOH and CH3COONa to prepare a buffer solution. Both CH3COOH and CH3COONa will dissociate as follows:

H3CCOOH (aq) + H2O (l)                 ⇆            CH3COO- (aq) + H3O+ (aq)          (i)

H3COONa (s)                                     ⇆            CH3COO- (aq) + Na+ (aq)             (ii)

Presence of CH3COONa in the solution causes to increase the concentration of CH3COO-ion (common ion) which shifts the equilibrium of equation (i) toward the backward direction. This decreases the ionization of CH3COOH.

Addition of more and more CH3COONa decreases the ionization of CH3COOH, which causes to increase the pH of the buffer.

Addition of a strong acid/base to the buffer does not change the pH significantly.

(i) When a strong acid such as HCI is added to the buffer, following reaction takes place.

CH3COONa + HCl              ⇆            CH3COOH + NaCI

According to above equation, NaCl being neutral and CH3COOH being weak acid do not change pH significantly.

(ii) When a strong base such as NaOH is added to the buffer, following reaction takes place.

CH3COOH + NaOH           ⇆            CH3COONa + H20

H2O being neutral and CH3COONa being weak basic salt do not change pH significantly.

Calculating the pH of a buffer: Henderson’s Equation

Let us try to learn, how a buffer of definite pH can be prepared. Consider a weak acid HA and its salt NaA with a strong base say NaOH. The reversible reactions for dissociation of HA are as follows:

HA          ⇆            H+ + A-

NaA       ⇆            Na+ + A-

The dissociation constant of a weak acid HA is given by:

Ka = [H+] [A-] / [HA]

Rearranging the equation,

[H+] = Ka [HA] / [A-]

The concentration of A in the reaction mixture is predominantly being supplied by NaA which is a stronger electrolyte than HA, and the ionization of HA is being suppressed by common ion effect.

(A- is the common ion in this buffer solution).

Taking log of this equation.

log [H+] = log Ka [HA] / [A-]

log [H+] =log (Ka) + log [HA] / [A-]

Multiplying with (-1) on both sides

-log [H+] = -log (Ka) – log [HA] / [A-]

Since,

-log [H+] = pH &

-log (Ka) = pKa

So,

pH = pKa – log [HA] / [A-]

[A-] refers to the concentration of the salt. Actually, NaA gives maximum possible concentrate of A-, being a strong electrolyte

So,

pH = pKa – log [acid] / [salt]

Interchanging the numerator and denominator the sign of log changes,

pH = pKa + log [salt] / [acid]

This relationship is called Henderson’s equation. This equation shows that two factors evidently govern the pH of a buffer solution. First, is the pKa of the acid used and second is the ratio of the concentrations of the salt and the acid. The best buffer is prepared by taking equal concentration of salt and acid.

Just like acidic buffers, the basic buffer have their own Henderson equation.

For this purpose,

Let us use the mixture of NH4OH and NH4Cl.

 NH4OH is a solution of NH3 in water and it can be represented as follows:

NH3 (aq)              ⇆            NH4+ (aq) + OH- (aq)

Kb = [NH4+] [OH-] / [NH3]

Taking the log, multiplying with negative sign and rearranging, we get:

pOH = pKb + log [salt] / [Base]

Using this relationship, we can prepare a basic buffer of the required pOH or pH by suitably selecting a base and adjusting the ratio of [salt] / [base].

Buffer Capacity:

The buffer capacity of a solution is the capability of a buffer to resist the change of pH. It can be measured quantitatively that how much extra acid or base, the solution can absorb before the buffer is essentially destroyed.

Buffer capacity of a buffer solution is determined by the sizes of actual molarities of its components. So, a chemist must decide before making the buffer solution, what outer limits of change in its pH can be tolerated?

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