In
chemistry and
biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
, the Henderson–Hasselbalch equation
:
relates the
pH of a
chemical solution
In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
of a
weak acid
Acid strength is the tendency of an acid, symbolised by the chemical formula HA, to dissociate into a proton, H+, and an anion, A-. The dissociation of a strong acid in solution is effectively complete, except in its most concentrated solutions ...
to the numerical value of the
acid dissociation constant, ''K''
a, of
acid and the ratio of the concentrations,
of the acid and its
conjugate base
A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid donates a proton () to a base—in other words, it is a base with a hydrogen ion added to it, as in the reverse reaction it loses a ...
in an equilibrium.
:
For example, the acid may be
acetic acid
:
The Henderson–Hasselbalch equation can be used to estimate the
pH of a
buffer solution
A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small amount of strong acid or base is ...
by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA.
The equation can also be applied to bases by specifying the protonated form of the base as the acid. For example, with an
amine
In chemistry, amines (, ) are compounds and functional groups that contain a basic nitrogen atom with a lone pair. Amines are formally derivatives of ammonia (), wherein one or more hydrogen
Hydrogen is the chemical element wi ...
,
:
Derivation, assumptions and limitations
A simple
buffer solution
A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small amount of strong acid or base is ...
consists of a solution of an
acid and a salt of the
conjugate base
A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid donates a proton () to a base—in other words, it is a base with a hydrogen ion added to it, as in the reverse reaction it loses a ...
of the acid. For example, the acid may be
acetic acid and the salt may be
sodium acetate
Sodium acetate, CH3COONa, also abbreviated Na O Ac, is the sodium salt of acetic acid. This colorless deliquescent salt has a wide range of uses.
Applications
Biotechnological
Sodium acetate is used as the carbon source for culturing bacteria ...
.
The Henderson–Hasselbalch equation relates the
pH of a solution containing a mixture of the two components to the
acid dissociation constant, ''K''
a of the acid, and the concentrations of the species in solution.
![Buffer titration graph](https://upload.wikimedia.org/wikipedia/commons/4/40/Buffer_titration_graph.svg)
To derive the equation a number of simplifying assumptions have to be made.
pdf
Assumption 1: The acid, HA, is monobasic and dissociates according to the equations
:
:
:
C
A is the analytical concentration of the acid and C
H is the concentration the hydrogen ion that has been added to the solution. The self-dissociation of water is ignored. A quantity in square brackets,
represents the concentration of the chemical substance X. It is understood that the symbol H
+ stands for the hydrated
hydronium
In chemistry, hydronium (hydroxonium in traditional British English) is the common name for the aqueous cation , the type of oxonium ion produced by protonation of water. It is often viewed as the positive ion present when an Arrhenius acid i ...
ion. K
a is an
acid dissociation constant.
The Henderson–Hasselbalch equation can be applied to a polybasic acid only if its consecutive p''K'' values differ by at least 3.
Phosphoric acid
Phosphoric acid (orthophosphoric acid, monophosphoric acid or phosphoric(V) acid) is a colorless, odorless phosphorus-containing solid, and inorganic compound with the chemical formula . It is commonly encountered as an 85% aqueous solution, w ...
is such an acid.
Assumption 2. The
self-ionization of water
The self-ionization of water (also autoionization of water, and autodissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H2O, deprotonates (loses the nucleus of one of its hydrogen ...
can be ignored.
This assumption is not, strictly speaking, valid with pH values close to 7, half the value of pK
w, the constant for
self-ionization of water
The self-ionization of water (also autoionization of water, and autodissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H2O, deprotonates (loses the nucleus of one of its hydrogen ...
. In this case the mass-balance equation for hydrogen should be extended to take account of the self-ionization of water.
:
However, the term
can be omitted to a good approximation.
Assumption 3: The salt MA is completely dissociated in solution. For example, with
sodium acetate
Sodium acetate, CH3COONa, also abbreviated Na O Ac, is the sodium salt of acetic acid. This colorless deliquescent salt has a wide range of uses.
Applications
Biotechnological
Sodium acetate is used as the carbon source for culturing bacteria ...
:
the concentration of the sodium ion,
+">a+can be ignored. This is a good approximation for 1:1 electrolytes, but not for salts of ions that have a higher charge such with
magnesium sulphate
Magnesium sulfate or magnesium sulphate (in English-speaking countries other than the US) is a chemical compound, a salt with the formula , consisting of magnesium cations (20.19% by mass) and sulfate anions . It is a white crystalline solid, s ...
, MgSO
4, that form
ion pair
In chemistry, ion association is a chemical reaction whereby ions of opposite electric charge come together in solution to form a distinct chemical entity. Ion associates are classified, according to the number of ions that associate with each o ...
s.
Assumption 4: The quotient of activity coefficients,
, is a constant under the experimental conditions covered by the calculations.
The thermodynamic equilibrium constant,
,
:
is a product of a quotient of concentrations
and a quotient,
, of activity coefficients
.
In these expressions, the quantities in square brackets signify the concentration of the undissociated acid, HA, of the hydrogen ion H
+, and of the anion A
−; the quantities
are the corresponding
activity coefficient
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same ( ...
s. If the quotient of activity coefficients can be assumed to be a constant which is independent of concentrations and pH, the dissociation constant, ''K''
a can be expressed as a quotient of concentrations.
:
Rearrangement of this expression and taking logarithms provides the Henderson–Hasselbalch equation
Application to bases
The equilibrium constant for the protonation of a base, B,
: + H
+
is an association constant, ''K''
b, which is simply related to the dissociation constant of the conjugate acid, BH
+.
:
The value of
is ca. 14 at 25°C. This approximation can be used when the correct value is not known. Thus, the Henderson–Hasselbalch equation can be used, without modification, for bases.
Biological applications
With
homeostasis
In biology, homeostasis (British also homoeostasis) (/hɒmɪə(ʊ)ˈsteɪsɪs/) is the state of steady internal, physical, and chemical conditions maintained by living systems. This is the condition of optimal functioning for the organism and ...
the pH of a biological solution is maintained at a constant value by adjusting the position of the equilibria
:
where
is the
bicarbonate
In inorganic chemistry, bicarbonate (IUPAC-recommended nomenclature: hydrogencarbonate) is an intermediate form in the deprotonation of carbonic acid. It is a polyatomic anion with the chemical formula .
Bicarbonate serves a crucial biochem ...
ion and
is
carbonic acid.
However, the solubility of carbonic acid in water may be exceeded. When this happens carbon dioxide gas is liberated and the following equation may be used instead.
:
represents the carbon dioxide liberated as gas. In this equation, which is widely used in biochemistry,
is a mixed equilibrium constant relating to both chemical and solubility equilibria. It can be expressed as
:
where is the molar concentration of bicarbonate in the blood plasma and is the
partial pressure of
carbon dioxide
Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is trans ...
in the supernatant gas.
History
In 1908,
Lawrence Joseph Henderson
Lawrence Joseph Henderson (June 3, 1878, Lynn, Massachusetts – February 10, 1942, Cambridge, Massachusetts) was a physiologist, chemist, biologist, philosopher, and sociologist. He became one of the leading biochemists of the early 20th ce ...
derived an equation to calculate the hydrogen ion concentration of a
bicarbonate buffer solution, which rearranged looks like this:
In 1909
Søren Peter Lauritz Sørensen
Søren (, ) or Sören (, ) is a Scandinavian given name that is sometimes Anglicized as Soren. The name is derived from that of the 4th-century Christian saint Severin of Cologne,Portal Rheinische Geschichte"Severin (circa 330-400), Heiliger und B ...
introduced the pH terminology, which allowed
Karl Albert Hasselbalch
Karl Albert Hasselbalch (; 1 November 1874 – 19 September 1962) was a Danish physician and chemist known for his work on the Henderson–Hasselbalch equation.
Early life and education
Hasselbalch was born in Åstrup, near Hjørring, Denmar ...
to re-express Henderson's equation in
logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...
ic terms,
resulting in the Henderson–Hasselbalch equation.
See also
*
Davenport diagram
In acid base physiology, the Davenport diagram is a graphical tool, developed by Horace W. Davenport, that allows a clinician or investigator to describe blood bicarbonate concentrations and blood pH following a respiratory and/or metabolic acid-ba ...
Further reading
References
{{DEFAULTSORT:Henderson-Hasselbalch Equation
Acid–base chemistry
Equilibrium chemistry
Mathematics in medicine