Henderson–Hasselbalch equation
[1] The Henderson–Hasselbalch equation can be used to estimate the pH of a buffer solution by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA.
The Henderson–Hasselbalch equation was developed by two scientists, Lawrence Joseph Henderson and Karl Albert Hasselbalch.
[2] Lawrence Joseph Henderson was a biological chemist and Karl Albert Hasselbalch was a physiologist who studied pH.
[2][3] In 1908, Lawrence Joseph Henderson[4] derived an equation to calculate the hydrogen ion concentration of a bicarbonate buffer solution, which rearranged looks like this: In 1909 Søren Peter Lauritz Sørensen introduced the pH terminology, which allowed Karl Albert Hasselbalch to re-express Henderson's equation in logarithmic terms,[5] resulting in the Henderson–Hasselbalch equation.
The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant, Ka of the acid, and the concentrations of the species in solution.
[6] To derive the equation a number of simplifying assumptions have to be made.
[7] Assumption 1: The acid, HA, is monobasic and dissociates according to the equations CA is the analytical concentration of the acid and CH is the concentration the hydrogen ion that has been added to the solution.
A quantity in square brackets, [X], represents the concentration of the chemical substance X.
It is understood that the symbol H+ stands for the hydrated hydronium ion.
The Henderson–Hasselbalch equation can be applied to a polybasic acid only if its consecutive pK values differ by at least 3.
In this case the mass-balance equation for hydrogen should be extended to take account of the self-ionization of water.
[7] Assumption 3: The salt MA is completely dissociated in solution.
In these expressions, the quantities in square brackets signify the concentration of the undissociated acid, HA, of the hydrogen ion H+, and of the anion A−; the quantities
If the quotient of activity coefficients can be assumed to be a constant which is independent of concentrations and pH, the dissociation constant, Ka can be expressed as a quotient of concentrations.
Source:[8] Following these assumptions, the Henderson–Hasselbalch equation is derived in a few logarithmic steps.
With homeostasis the pH of a biological solution is maintained at a constant value by adjusting the position of the equilibria where
is a mixed equilibrium constant relating to both chemical and solubility equilibria.
It can be expressed as where [HCO−3] is the molar concentration of bicarbonate in the blood plasma and PCO2 is the partial pressure of carbon dioxide in the supernatant gas.
[10] This is effective near physiological pH of 7.4 as carboxylic acid is in equilibrium with
[9] As blood travels through the body, it gains and loses H+ from different processes including lactic acid fermentation and by NH3 protonation from protein catabolism.
[9] For example, a decreased blood pH will trigger the brain stem to perform more frequent respiration.
It is important to maintain this pH of 7.4 to ensure enzymes are able to work optimally.
[10] Life threatening Acidosis (a low blood pH resulting in nausea, headaches, and even coma, and convulsions) is due to a lack of functioning of enzymes at a low pH.
[10] As modelled by the Henderson–Hasselbalch equation, in severe cases this can be reversed by administering intravenous bicarbonate solution.
does not change, this addition of bicarbonate solution will raise the blood pH.
The ocean contains a natural buffer system to maintain a pH between 8.1 and 8.3.
[12] The carbonate buffer reaction helps maintain a constant H+ concentration in the ocean because it consumes hydrogen ions,[13] and thereby maintains a constant pH.
[12] Ocean acidification affects marine life that have shells that are made up of carbonate.
In a more acidic environment it is harder organisms to grow and maintain the carbonate shells.
[12] The increase of ocean acidity can cause carbonate shell organisms to experience reduced growth and reproduction.
