Henderson-Hasselbalch equation: Difference between revisions
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==Overview== | ==Overview== | ||
In [[chemistry]], the | In [[chemistry]], the Henderson-Hasselbalch (frequently misspelled Henderson-Hasselbach) equation describes the derivation of [[pH]] as a measure of acidity (using pK<sub>a</sub>, 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 [[Chemical equilibrium|equilibrium]] pH in [[acid-base reaction theories|acid-base reactions]] (it is widely used to calculate [[isoelectric point]] of the proteins). | ||
==Historical Perspective== | |||
[[Lawrence Joseph Henderson]] wrote an equation, in 1908, describing the use of [[carbonic acid]] as a [[buffer solution]].<ref>[[Karl Albert Hasselbalch]] later re-expressed that formula in [[logarithm]]ic terms, resulting in the Henderson-Hasselbalch equation [http://www.acid-base.com/history.php]</ref> Hasselbalch was using the formula to study [[metabolic acidosis]], which results from carbonic acid in the [[blood]]. | |||
==Henderson-Hasselbalch equation== | ==Henderson-Hasselbalch equation== | ||
Two equivalent forms of the equation are | Two equivalent forms of the equation are | ||
pH = pK<sub>a</sub> + log([A<sup>-</sup>]/[HA]) | pH = pK<sub>a</sub> + log ([A<sup>-</sup>]/[HA]) | ||
and | and | ||
pH = pK<sub>a</sub> + log([Base]/[Acid]) | pH = pK<sub>a</sub> + log ([Base]/[Acid]) | ||
Here, pK<sub>a</sub> is -log K<sub>a</sub> where K<sub>a</sub> is the acid dissociation constant, that is: | |||
pK<sub>a</sub> = -log K<sub>a</sub> = -log ([H<sub>3</sub>O<sup>+</sup>][A<sup>-</sup>]/[HA]) for the non-specific Brønsted acid-base reaction: HA + H<sub>2</sub>O ↔ A<sup>-</sup> + H<sub>3</sub>O<sup>+</sup> | |||
In these equations, A<sup>-</sup> denotes the ionic form of the relevant acid. Bracketed quantities such as [Base] and [Acid] denote the molar concentration of the quantity enclosed. | |||
In these equations, < | |||
In analogy to the above equations, the following equation is valid: | In analogy to the above equations, the following equation is valid: | ||
pOH = pK<sub>b</sub> + log ([BH+]/[B]) | |||
where B+ denotes the salt of the corresponding base B. | |||
==Derivation== | |||
==Limitations== | ==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 or very concentrated solutions (less than 1 mM or greater than 1M), or heavily skewed acid/base ratios (more than 100 to 1). | 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 or very concentrated solutions (less than 1 mM or greater than 1M), or heavily skewed acid/base ratios (more than 100 to 1). | ||
==References== | |||
{{Reflist|2}} | |||
==See also== | ==See also== | ||
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*[http://isoelectric.ovh.org True example of using Henderson-Hasselbalch equation for calculation net charge of proteins] | *[http://isoelectric.ovh.org True example of using Henderson-Hasselbalch equation for calculation net charge of proteins] | ||
== | ==Further reading== | ||
{{ | * {{Cite journal| author = Lawrence J. Henderson | title = Concerning the relationship between the strength of acids and their capacity to preserve neutrality | journal = [[Am. J. Physiol.]] | date=1 May 1908| volume = 21 | pages = 173–179 | url = http://ajplegacy.physiology.org/cgi/content/abstract/21/4/465-s | format = Abstract | issue = 4 }} | ||
* {{Cite journal| author = Hasselbalch, K. A. | title = Die Berechnung der Wasserstoffzahl des Blutes aus der freien und gebundenen Kohlensäure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl | journal = [[Biochemische Zeitschrift]] | year = 1917 | volume = 78 | pages = 112–144}} | |||
* {{Cite journal| author = Po, Henry N.; Senozan, N. M. | title = Henderson–Hasselbalch Equation: Its History and Limitations | journal = [[J. Chem. Educ.]] | year = 2001 | volume = 78 | pages = 1499–1503 | doi = 10.1021/ed078p1499| issue = 11|bibcode = 2001JChEd..78.1499P }} | |||
* {{Cite journal| author = de Levie, Robert. | title = The Henderson–Hasselbalch Equation: Its History and Limitations | journal = [[J. Chem. Educ.]] | year = 2003 | volume = 80 | pages = 146 | doi = 10.1021/ed080p146| issue = 2|bibcode = 2003JChEd..80..146D }} | |||
* {{Cite journal| author = de Levie, Robert | journal = [[The Chemical Educator]] | year = 2002 | volume = 7 | pages = 132–135 | doi = 10.1007/s00897020562a | title = The Henderson Approximation and the Mass Action Law of Guldberg and Waage| issue = 3}} | |||
[[Category:Acid-base chemistry]] | [[Category:Acid-base chemistry]] | ||
Revision as of 19:52, 4 August 2013
Editor-In-Chief: C. Michael Gibson, M.S., M.D. [2]
Overview
In chemistry, the Henderson-Hasselbalch (frequently misspelled Henderson-Hasselbach) equation describes the derivation of pH as a measure of acidity (using pKa, 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 (it is widely used to calculate isoelectric point of the proteins).
Historical Perspective
Lawrence Joseph Henderson wrote an equation, in 1908, describing the use of carbonic acid as a buffer solution.[1] Hasselbalch was using the formula to study metabolic acidosis, which results from carbonic acid in the blood.
Henderson-Hasselbalch equation
Two equivalent forms of the equation are
pH = pKa + log ([A-]/[HA])
and
pH = pKa + log ([Base]/[Acid])
Here, pKa is -log Ka where Ka is the acid dissociation constant, that is:
pKa = -log Ka = -log ([H3O+][A-]/[HA]) for the non-specific Brønsted acid-base reaction: HA + H2O ↔ A- + H3O+
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.
In analogy to the above equations, the following equation is valid:
pOH = pKb + log ([BH+]/[B])
where B+ denotes the salt of the corresponding base B.
Derivation
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 or very concentrated solutions (less than 1 mM or greater than 1M), or heavily skewed acid/base ratios (more than 100 to 1).
References
- ↑ Karl Albert Hasselbalch later re-expressed that formula in logarithmic terms, resulting in the Henderson-Hasselbalch equation [1]
See also
External links
- Henderson-Hasselbalch Calculator
- Derivation and detailed discussion of Henderson-Hasselbalch equation
- True example of using Henderson-Hasselbalch equation for calculation net charge of proteins
Further reading
- Lawrence J. Henderson (1 May 1908). "Concerning the relationship between the strength of acids and their capacity to preserve neutrality" (Abstract). Am. J. Physiol. 21 (4): 173–179.
- 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.
- 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.
- de Levie, Robert. (2003). "The Henderson–Hasselbalch Equation: Its History and Limitations". J. Chem. Educ. 80 (2): 146. Bibcode:2003JChEd..80..146D. doi:10.1021/ed080p146.
- de Levie, Robert (2002). "The Henderson Approximation and the Mass Action Law of Guldberg and Waage". The Chemical Educator. 7 (3): 132–135. doi:10.1007/s00897020562a.