Henderson-Hasselbalch equation
Encyclopedia
In chemistry
, the Henderson–Hasselbalch 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 the isoelectric point
of proteins).
Two equivalent forms of the equation are
and
Here,
is 
where 
is the acid dissociation constant
, that is:
for the non-specific Brønsted acid-base reaction: 
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.
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.
wrote an equation, in 1908, describing the use of carbonic acid
as a buffer solution
. 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. Hasselbalch was using the formula to study metabolic acidosis
.
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.
to constituents of the bicarbonate buffering system
:
, where:
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:
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:
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, the Henderson–Hasselbalch equation describes the derivation of pH
PH
In chemistry, pH is a measure of the acidity or basicity of an aqueous solution. Pure water is said to be neutral, with a pH close to 7.0 at . Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline...
as a measure of acidity (using pKa, the acid dissociation constant
Acid dissociation constant
An acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid-base reactions...
) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution
Buffer solution
A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. It has the property that the pH of the solution changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a...
and finding the equilibrium
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...
pH in acid-base reactions
Acid-base reaction theories
An acid–base reaction is a chemical reaction that occurs between an acid and a base. Several concepts that provide alternative definitions for the reaction mechanisms involved and their application in solving related problems exist...
(it is widely used to calculate the isoelectric point
Isoelectric point
The isoelectric point , sometimes abbreviated to IEP, is the pH at which a particular molecule or surface carries no net electrical charge....
of proteins).
Two equivalent forms of the equation are
and
Here,
is where is the acid dissociation constantAcid dissociation constant
An acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid-base reactions...
, that is:
for the non-specific Brønsted acid-base reaction: 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 constantAcid dissociation constant
An acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid-base reactions...
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 HendersonLawrence Joseph Henderson
Lawrence Joseph Henderson was a physiologist, chemist, biologist, philosopher, and sociologist. He became one of the leading biochemists of the first decades of the 20th century.Lawrence Henderson graduated from Harvard College in 1898 and from Harvard Medical School in 1902, receiving the M. D...
wrote an equation, in 1908, describing the use of carbonic acid
Carbonic acid
Carbonic acid is the inorganic compound with the formula H2CO3 . It is also a name sometimes given to solutions of carbon dioxide in water, because such solutions contain small amounts of H2CO3. Carbonic acid forms two kinds of salts, the carbonates and the bicarbonates...
as a buffer solution
Buffer solution
A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. It has the property that the pH of the solution changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a...
. Karl Albert Hasselbalch
Karl Albert Hasselbalch
Karl Albert Hasselbalch was a physician and chemist. He was a pioneer in the use of pH measurement in medicine , and he described how the affinity of blood for oxygen was dependent on the concentration of carbon dioxide. He was also first to determine the pH of blood...
later re-expressed that formula in logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
ic terms, resulting in the Henderson–Hasselbalch equation http://www.acid-base.com/history.php. Hasselbalch was using the formula to study metabolic acidosis
Metabolic acidosis
In medicine, metabolic acidosis is a condition that occurs when the body produces too much acid or when the kidneys are not removing enough acid from the body. If unchecked, metabolic acidosis leads to acidemia, i.e., blood pH is low due to increased production of hydrogen by the body or the...
.
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 bloodBlood
Blood is a specialized bodily fluid in animals that delivers necessary substances such as nutrients and oxygen to the cells and transports metabolic waste products away from those same cells....
to constituents of the bicarbonate buffering system
Bicarbonate buffering system
The bicarbonate buffering system is an important buffer system in the acid-base homeostasis of living things, including humans. As a buffer, it tends to maintain a relatively constant plasma pH and counteract any force that would alter it....
:
, where:
- pKa H2CO3 is the acid dissociation constantAcid dissociation constantAn acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid-base reactions...
of carbonic acidCarbonic acidCarbonic acid is the inorganic compound with the formula H2CO3 . It is also a name sometimes given to solutions of carbon dioxide in water, because such solutions contain small amounts of H2CO3. Carbonic acid forms two kinds of salts, the carbonates and the bicarbonates...
. It is equal to 6.1. - [HCO3-] is the concentration of bicarbonateBicarbonateIn inorganic chemistry, bicarbonate is an intermediate form in the deprotonation of carbonic acid...
in the blood - [H2CO3] is the concentration of carbonic acid in the blood
This is useful in arterial blood gas
Arterial blood gas
An arterial blood gas is a blood test that is performed using blood from an artery. It involves puncturing an artery with a thin needle and syringe and drawing a small volume of blood. The most common puncture site is the radial artery at the wrist, but sometimes the femoral artery in the groin or...
, but these usually state pCO2, that is, the partial pressure
Partial pressure
In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
of carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...
, rather than H2CO3. However, these are related by the equation:
, where:
- [H2CO3] is the concentration of carbonic acid in the blood
- kH CO2 is a constant including the solubilitySolubilitySolubility is the property of a solid, liquid, or gaseous chemical substance called solute to dissolve in a solid, liquid, or gaseous solvent to form a homogeneous solution of the solute in the solvent. The solubility of a substance fundamentally depends on the used solvent as well as on...
of carbon dioxide in blood. kH CO2 is approximately 0.03 mmol/mmHg - pCO2 is the partial pressurePartial pressureIn a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
of carbon dioxideCarbon dioxideCarbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...
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