This can be simplified: [H2O] remains constant and physicians are much more familiar with: PCO2:
Clinically, this simple equation provides all the information required. It is often easy to anticipate how changes in one variable will affect another: When the PCO2 is constant, then an increase in [H+] must be associated with a fall in [HCO3–], and an increase in the PCO2 will normally increase both [H+] and [HCO3–].
Sørensen and HasselbalchEdit
In 1909 Søren Peter Lauritz Sørensen introduced the pH terminology which allowed Karl Albert Hasselbalch to re-express that equation in logarithmic terms, resulting in the Henderson–Hasselbalch equation (see Acid-Base History):
A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate. The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant, Ka, and the concentrations of the species in solution. To derive the equation a number of simplifying assumptions have to be made. The mixture has the ability to resist changes in pH when a small amount of acid or base is added, which is the defining property of a buffer solution.
Assumption 1: The acid is monobasic and dissociates according to the equation
Assumption 2. The self-ionization of water can be ignored.
This assumption is not valid with pH values more than about 10. For such instances the mass-balance equation for hydrogen must be extended to take account of the self-ionization of water.
and the pH will have to be found by solving the two mass-balance equations simultaneously for the two unknowns, [H+] and [A−].
Assumption 3: The salt MA is completely dissociated in solution. For example, with sodium acetate
Assumption 4: The quotient of activity coefficients, , is a constant under the experimental conditions covered by the calculations.
The thermodynamic equilibrium constant, ,
The Henderson–Hasselbalch equation can be used to calculate the pH of a solution containing the acid and one of its salts, that is, of a buffer solution. With bases, if the value of an equilibrium constant is known in the form of a base association constant, Kb the dissociation constant of the conjugate acid may be calculated from
where Kw is the self-dissociation constant of water. pKw has a value of approximately 14 at 25 °C.
If the "free acid" concentration, [HA], can be taken to be equal to the analytical concentration of the acid, TAH (sometimes denoted as CAH) an approximation is possible, which is widely used in biochemistry; it is valid for very dilute solutions.
- Lawrence J. Henderson (1908). "Concerning the relationship between the strength of acids and their capacity to preserve neutrality". Am. J. Physiol. 21 (2): 173–179. doi:10.1152/ajplegacy.1908.21.2.173.
- Hasselbalch, K. A. (1917). "Die Berechnung der Wasserstoffzahl des Blutes aus der freien und gebundenen Kohlensäure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl". Biochemische Zeitschrift. 78: 112–144.
- For details and worked examples see, for instance, Skoog, Douglas A.; West, Donald M.; Holler, F. James; Crouch, Stanley R. (2004). Fundamentals of Analytical Chemistry (8th ed.). Belmont, Ca (USA): Brooks/Cole. pp. 251–263. ISBN 0-03035523-0.
- Po, Henry N.; Senozan, N. M. (2001). "Henderson–Hasselbalch Equation: Its History and Limitations". J. Chem. Educ. 78 (11): 1499–1503. Bibcode:2001JChEd..78.1499P. doi:10.1021/ed078p1499.