Henderson-Hasselbalch equation

ヘンダーソン・ハッセルバルヒの式

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1. the act of regarding as equal (同)equating
2. a mathematical statement that two expressions are equal

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1. 等式; 方程式

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/01/17 23:57:29」(JST)

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In chemistry, the Henderson–Hasselbalch equation describes the derivation of pH as a measure of acidity (using pK_a, the negative log of 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 the isoelectric point of proteins).

Two equivalent forms of the equation are

and

Here, [HA] is the molar concentration of the undissociated weak acid, [A⁻] is the molar concentration of this acid's conjugate base and is where is the acid dissociation constant, that is:

for the non-specific Brønsted acid-base reaction:

A third form of the equation, known as the Heylman Equation, expressed in terms of where is the base dissociation constant:

In these equations, 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:

Where BH⁺ denotes the conjugate acid of the corresponding base B.

Derivation

The Henderson–Hasselbalch equation is derived from the acid dissociation constant equation by the following steps:

The ratio is unitless, and as such, other ratios with other units may be used. For example, the mole ratio of the components, or the fractional concentrations where will yield the same answer. Sometimes these other units are more convenient to use.

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.

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). Also, the equation does not take into effect the dilution factor of the acid and conjugate base in water. If the proportion of acid to base is 1, then the pH of the solution will be different if the amount of water changes from 1mL to 1L.

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:

, where:

• pK_{a H2CO3} is the cologarithm of the acid dissociation constant of carbonic acid. It is equal to 6.1.
• [HCO₃^-] is the concentration of bicarbonate in the blood
• [H₂CO₃] is the concentration of carbonic acid in the blood

This is useful in arterial blood gas, but these usually state pCO₂, that is, the partial pressure of carbon dioxide, rather than H₂CO₃. However, these are related by the equation:

, where:

• [H₂CO₃] is the concentration of carbonic acid in the blood
• k_{H CO2} is the Henry's law constant for the solubility of carbon dioxide in blood. k_{H CO2} is approximately 0.03 mmol/mmHg
• pCO₂ is the partial pressure of carbon dioxide in the blood

Taken together, the following equation can be used to relate the pH of blood to the concentration of bicarbonate and the partial pressure of carbon dioxide:

, where:

• pH is the acidity in the blood
• [HCO₃^-] is the concentration of bicarbonate in the blood
• pCO₂ is the partial pressure of carbon dioxide in the blood

See also

• Acid
• Base
• Titration
• Buffer solution
• Acidosis
• Alkalosis

References

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. http://ajplegacy.physiology.org/cgi/content/abstract/21/4/465-s.
• 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.

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

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

• 1. Chapter 10A：酸と塩基 chapter 10a acids and bases
• 2. 単純性および混合性酸塩基障害 simple and mixed acid base disorders
• 3. Chapter 11C：動脈血pHが換気に及ぼす影響 chapter 11c effect of arterial ph on ventilation
• 4. Chapter 10B：バッファー chapter 10b buffers
• 5. Chapter 13B：尿浸透圧とpHの意義 chapter 13b meaning of urine osmolality and ph

English Journal

• Ammonia in breath and emitted from skin.

• Schmidt FM, Vaittinen O, Metsälä M, Lehto M, Forsblom C, Groop PH, Halonen L.SourceLaboratory of Physical Chemistry, Department of Chemistry, University of Helsinki, Finland. florian.schmidt@umu.se
• Journal of breath research.J Breath Res.2013 Mar;7(1):017109. doi: 10.1088/1752-7155/7/1/017109. Epub 2013 Feb 27.
• Ammonia concentrations in exhaled breath (eNH3) and skin gas of 20 healthy subjects were measured on-line with a commercial cavity ring-down spectrometer and compared to saliva pH and plasma ammonium ion (NH(+)4), urea and creatinine concentrations. Special attention was given to mouth, nose and ski
• PMID 23445955

• Hypothesis: the regulation of the partial pressure of oxygen by the serotonergic nervous system in hypoxia.

• Devereux D, Ikomi-Kumm J.SourceMDI, Tågarpsvägen 13, 27021 Glemmingebro, Sweden. diana.devereux@yahoo.com
• Medical hypotheses.Med Hypotheses.2013 Mar;80(3):292-6. doi: 10.1016/j.mehy.2012.12.006. Epub 2013 Jan 9.
• The regulation of the partial pressure of oxygen by the serotonergic nervous system in hypoxia is a hypothesis, which proposes an inherent operative system in homo sapiens that allows central nervous system and endocrine-mediated vascular system adaption to variables in partial pressure of oxygen, p
• PMID 23312111

• Reply from Authors re: Jonathan Bergman, Mark S. Litwin. The Henderson-Hasselbalch Equation for Urologists. Eur Urol. In press. http://dx.doi.org/10.1016/j.eururo.2012.12.021: Health-related Quality-of-life Scores from the Finnish Trial of Screening for Prostate Cancer Offer One Useful Contribution.

• Booth N, Rissanen P, Tammela TL, Määttänen L, Taari K, Auvinen A.SourceSchool of Health Sciences, University of Tampere, Tampere, Finland. Electronic address: neill.booth@uta.fi.
• European urology.Eur Urol.2013 Jan 3. pii: S0302-2838(12)01589-8. doi: 10.1016/j.eururo.2012.12.059. [Epub ahead of print]
• PMID 23312597

Japanese Journal

• The Extracellular pH Dependency of Transport Activity by Human Oligopeptide Transporter 1 (hPEPT1) Expressed Stably in Chinese Hamster Ovary (CHO) Cells : A Reason for the Bell-Shaped Activity versus pH(Biopharmacy)

• FUJISAWA Yuki,TATEOKA Ryoko,NARA Toshifumi,KAMO Naoki,TAIRA Takahiro,MIYAUCHI Seiji
• Biological & pharmaceutical bulletin 29(5), 997-1005, 2006-05-01
• … As pH increased the activity increased, and the Henderson-Hasselbalch equation with a single pKa was fitted well to the activity curve. …
• NAID 110005602229

Related Links

• Henderson-Hasselbalch equation and the pH of buffer solution

pH calculation lectures » pH of a buffer - the Henderson-Hasselbalch equation Solutions able to retain a constant pH regardless of small amounts of acids or bases added are called buffers. Classical buffer contains both a weak acid ...

• Henderson-Hasselbalch equation - The Biology Project

Henderson-Hasselbalch equation Consider the ionization of a weak acid HA which has some pK a. It is often convenient to be able to relate the pH of a solution of a weak acid to the pK a of the acid and the extent of ionization. The ...

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Henderson-Hasselbalch equation

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Henderson-Hasselbalchの式、Henderson-Hasselbalch式、ヘンダーソン・ハッセルバルヒ式

• pH＝6.10＋log([HCO₃^-]/［CO₂］)
• pH＝6.10＋log([HCO₃^-]/ (0.03 x P_aCO2 ) )

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• 式、方程式

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