Henderson-Hasselbalch equation

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In chemistry, the Henderson-Hasselbalch (frequently misspelled Henderson-Hasselbach) equation describes the derivation of pH as a measure of acidity (using pK_a, the acid dissociation constant) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions.

Two equivalent forms of the equation are

$\textrm{pH} = \textrm{pK}_{a}+ \log_{10} \frac{[\textrm{A}^-]}{[\textrm{HA}]}$

and

$pH = pK_{a}+\log_{10} \left ( \frac{[\mathrm{base}]}{[\mathrm{acid}]} \right ).$

Here, $p K a$ is $- log 10 (K a)$ where $K a$ is the acid disassociation constant, that is:

$pK_{a} = - \log_{10}(K_{a}) = - \log_{10} \left ( \frac{[\mbox{H}_{3}\mbox{O}^+][\mbox{A}^-]}{[\mbox{HA}]} \right )$ for the reaction: $\mbox{HA} + \mbox{H}_{2}\mbox{O} \rightleftharpoons \mbox{A}^- + \mbox{H}_{3}\mbox{O}^+$

In these equations, $A -$ denotes the ionic form of the relevant acid. Bracketed quantities such as [base] and [acid] denote the molar concentration of the quantity enclosed.

1 History
2 Limitations
3 See also
4 External links
5 References

[edit] History

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 [1]. Hasselbalch was using the formula to study metabolic acidosis, which results from carbonic acid in the blood.

[edit] Limitations

There are some significant approximations implicit in the Henderson-Hasselbalch equation. The most significant is the assumption that the concentration of the acid and its conjugate base at equilibrium will remain the same as the formal concentration. 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 (pKa more than a couple units away from 7), dilute solutions (1 mM or less), or heavily skewed acid/base ratios (more than 100 to 1).

[edit] See also

[edit] External links

[edit] References

Lawrence J. Henderson. Concerning the relationship between the strength of acids and their capacity to preserve neutrality. Am. J. Physiol. 1908, 21, 173-179.
Hasselbalch, K. A. Biochemische Zeitschrift 1916, 78, 112-144.
Po, Henry N.; Senozan, N. M. Henderson-Hasselbalch Equation: Its History and Limitations. J. Chem. Educ. 2001, 78, 1499-1503.
de Levie, Robert. The Henderson-Hasselbalch Equation: Its History and Limitations. J. Chem. Educ. 2003, 80, 146.