HH equation

Biochemistry

1. HENDERSON HASSELBALCH EQUATION By  Mrs Sanchita Choubey (M.Sc., PGDCR, Pursuing Ph. D) Assistant Professor  of Microbiology Dr. D Y Patil Arts Commerce and Science College Pimpri , Pune

2. The Henderson–Hasselbalch Equation  Describes the derivation of pH as a measure of acidity in biological and chemical systems.  The equation is also useful for estimating the pH of a buffer solution.  it is widely used to calculate the isoelectric point of proteins( point at which protein neither accept nor yield proton) .

3. The Henderson hasselbalch equation for acid is :- pH = pK a + log [ Aˉ ] [HA] Here, pK a = -log(K a ) where K a is the acid dissociation constant, that is pK a = -log [H 3 O + ][A - ] [HA] for the non-specific Brønsted acid-base reaction: A - HA + H 2 + H 3 O + ( Acid ) ( Conjugate base )

4. The Henderson Hasselbalch Equation for base is : pOH = pK b + log [ BH + ] [B] where BH + denotes the conjugate acid of the corresponding base B. B + H 2 O + BH + OH - (Base ) (Conjugate acid)

5. H i s to y Lawrence Joseph Henderson wrote an equation, in 1908, describing the use of carbonic acid as a buffer solution. Karl Albert Hasselbalch later re-expressed that formula in logarithmic terms, resulting in the Henderson–Hasselbalch equation . Hasselbalch was using the formula to study metabolic acidosis.

6. Henderson-Hasselbalch Equation Derivation: - According to the Brønsted-Lowry theory of acids and bases, an acid (HA) is capable of donating a proton (H + ) and a base (B) is capable of accepting a proton. -After the acid (HA) has lost its proton, it is said to exist as the conjugate base (A - ). -Similarly, a protonated base is said to exist as the conjugate acid (BH + ).

7. The dissociation of an acid can be described by an equilibrium expression: HA + H 2 H 3 O + + A - Consider the case of acetic acid (CH 3 COOH) and acetate anion (CH 3 COO - ): CH 3 COOH + H 2 O CH 3 COO - + H 3 O +

8. Acetate is the conjugate base of acetic acid. Acetic acid and acetate are a conjugate acid/base pair. We can describe this relationship with an equilibrium constant: Ka = [H 3 O + ][A - ] [HA] Taking the negative log of both sides of the equation gives -logK a = -log [H 3 O + ][A - ] [HA] or, -logK a = -log [H 3 O + ] + (-log [A - ] ) [ H A ]

9. By definition, pK a = -logK a and pH = -log[H 3 O + ], so pk a =pH – log [A - ] [HA] This equation can then be rearranged to give the Henderson-Hasselbalch equation: pH = pK a + log [A - ] [ H A ] = pK a + log [conjugate base] [acid]

10. Estimating blood pH A modified version of the Henderson–Hasselbalch equation can be used to relate the pH of blood to constituents of the bicarbonate buffering system. pH = pK aH 2 CO 3 + log [HCO 3 - ] [H 2 CO 3 ] , where: -pK a H 2 CO 3 is the acid dissociation constant of carbonic acid. It is equal to 6.1. [HCO 3 - ] is the concentration of bicarbonate in the blood [H 2 CO 3 ] is the concentration of carbonic acid in the blood

11. Limitation : -The most significant is the assumption that the concentration of the acid and its conjugate base at equilibrium will remain the same. -This neglects the dissociation of the acid and the hydrolysis of the base. -The dissociation of water itself is neglected as well. -These approximations will fail when dealing with: relatively strong acids or bases dilute or very concentrated solutions (less than 1mM or greater than1M),