In
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
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, a ...
, the
pH of weakly acidic
chemical solutions
can be estimated using the Henderson-Hasselbach Equation:
The equation relates the pH of the
weak acid
Acid strength is the tendency of an acid, symbolised by the chemical formula , to dissociate into a proton, , and an anion, . The dissociation or ionization of a strong acid in solution is effectively complete, except in its most concentrated s ...
to the numerical value of the
acid dissociation constant
In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative property, quantitative measure of the acid strength, strength of an acid in Solution (chemistry), solution. I ...
, ''K''
a, of the
acid
An acid is a molecule or ion capable of either donating a proton (i.e. Hydron, hydrogen cation, H+), known as a Brønsted–Lowry acid–base theory, Brønsted–Lowry acid, or forming a covalent bond with an electron pair, known as a Lewis ...
, 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 gives a proton () to a base—in other words, it is a base with a hydrogen ion added to it, as it loses a hydrogen ion in the reve ...
.
''Acid-base Equilibrium Reaction''
The Henderson-Hasselbalch equation is often used for estimating the
pH of
buffer solution
A buffer solution is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solution ...
s by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA. It is also useful for determining the
volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
s of the reagents needed before preparing buffer solutions, which prevents unncessary waste of chemical reagents that may need to be further neutralized by even more reagents before they are safe to expose.
For example, the acid may be
carbonic acid
Carbonic acid is a chemical compound with the chemical formula . The molecule rapidly converts to water and carbon dioxide in the presence of water. However, in the absence of water, it is quite stable at room temperature. The interconversion ...
:
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 organic compounds that contain carbon-nitrogen bonds. Amines are formed when one or more hydrogen atoms in ammonia are replaced by alkyl or aryl groups. The nitrogen atom in an amine possesses a lone pair of elec ...
,
:
The Henderson–Hasselbach buffer system also has many natural and biological applications, from physiological processes (e.g., metabolic acidosis) to geological phenomena.
History
The Henderson–Hasselbalch equation was developed by two scientists,
Lawrence Joseph Henderson
Lawrence Joseph Henderson (June 3, 1878 – February 10, 1942) was an American physiologist, chemist, biologist, philosopher, and sociologist. He became one of the leading biochemists of the early 20th century. His work contributed to the Hend ...
and
Karl Albert Hasselbalch.
Lawrence Joseph Henderson
Lawrence Joseph Henderson (June 3, 1878 – February 10, 1942) was an American physiologist, chemist, biologist, philosopher, and sociologist. He became one of the leading biochemists of the early 20th century. His work contributed to the Hend ...
was a biological chemist and
Karl Albert Hasselbalch was a physiologist who studied pH.
In 1908,
Lawrence Joseph Henderson
Lawrence Joseph Henderson (June 3, 1878 – February 10, 1942) was an American physiologist, chemist, biologist, philosopher, and sociologist. He became one of the leading biochemists of the early 20th century. His work contributed to the Hend ...
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 introduced the pH terminology, which allowed
Karl Albert Hasselbalch to re-express Henderson's equation in
logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
ic
terms, resulting in the Henderson–Hasselbalch equation.
Assumptions, limitations, and derivation
A simple
buffer solution
A buffer solution is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solution ...
consists of a solution of an
acid
An acid is a molecule or ion capable of either donating a proton (i.e. Hydron, hydrogen cation, H+), known as a Brønsted–Lowry acid–base theory, Brønsted–Lowry acid, or forming a covalent bond with an electron pair, known as a Lewis ...
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 gives a proton () to a base—in other words, it is a base with a hydrogen ion added to it, as it loses a hydrogen ion in the reve ...
of the acid. For example, the acid may be
acetic acid
Acetic acid , systematically named ethanoic acid , is an acidic, colourless liquid and organic compound with the chemical formula (also written as , , or ). Vinegar is at least 4% acetic acid by volume, making acetic acid the main compone ...
and the salt may be
sodium acetate
Sodium acetate, CH3COONa, also abbreviated Sodium, NaOxygen, OAcetyl, Ac, is the sodium Salt (chemistry), salt of acetic acid. This salt is colorless, deliquescent, and hygroscopy, hygroscopic.
Applications
Biotechnological
Sodium acetate is u ...
. The Henderson–Hasselbalch equation relates the
pH of a solution containing a mixture of the two components to the
acid dissociation constant
In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative property, quantitative measure of the acid strength, strength of an acid in Solution (chemistry), solution. I ...
, ''K''
a of the acid, and the concentrations of the species in solution.

To derive the equation a number of simplifying assumptions have to be made.
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 cation , also written as , the type of oxonium ion produced by protonation of water. It is often viewed as the positive ion present when an Arrhenius acid is dissolved ...
ion. K
a is an
acid dissociation constant
In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative property, quantitative measure of the acid strength, strength of an acid in Solution (chemistry), solution. I ...
.
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, ...
is such an acid.
Assumption 2. The
self-ionization of water
The self-ionization of water (also autoionization of water, autoprotolysis of water, autodissociation of water, or simply dissociation of water) is an ionization reaction in properties of water, pure water or in an aqueous solution, in which a wa ...
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, autoprotolysis of water, autodissociation of water, or simply dissociation of water) is an ionization reaction in properties of water, pure water or in an aqueous solution, in which a wa ...
. 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 Sodium, NaOxygen, OAcetyl, Ac, is the sodium Salt (chemistry), salt of acetic acid. This salt is colorless, deliquescent, and hygroscopy, hygroscopic.
Applications
Biotechnological
Sodium acetate is u ...
:
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 as
magnesium sulphate
Magnesium sulfate or magnesium sulphate 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, soluble in water but not in ethanol.
Magnesium ...
, 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 ...
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.
:
Derivation
Source:
Following these assumptions, the Henderson–Hasselbalch equation is derived in a few logarithmic steps.
Solve for
:
On both sides, take the negative logarithm:
Based on previous assumptions,