The Charlot equation, named after
Gaston Charlot, is used in
analytical chemistry
Analytical chemistry studies and uses instruments and methods to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separati ...
to relate the
hydrogen ion
A hydrogen ion is created when a hydrogen atom loses or gains an electron. A positively charged hydrogen ion (or proton) can readily combine with other particles and therefore is only seen isolated when it is in a gaseous state or a nearly particle ...
concentration, and therefore the
pH, with the formal
analytical concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
of an
acid
In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a sequ ...
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 ...
. It can be used for computing the pH of
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 ...
s when the approximations of the
Henderson–Hasselbalch equation
In chemistry and biochemistry, the Henderson–Hasselbalch equation
:\ce = \ceK_\ce + \log_ \left( \frac \right)
relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant, ''K''a, of acid and ...
break down. The Henderson–Hasselbalch equation assumes that the
autoionization of water is negligible and that the dissociation or hydrolysis of the acid and the base in solution are negligible (in other words, that the formal concentration is the same as the equilibrium concentration).
For an acid-base equilibrium such as HA H
+ + A
−, the Charlot equation may be written as
:
where
+">+is the equilibrium concentration of H
+, ''K''
a is the
acid dissociation constant
In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction
:HA ...
, ''C''
a and ''C''
b are the analytical concentrations of the acid and its conjugate base, respectively, and Δ =
+">+−
−">H− The equation can be solved for
+">+by using the
autoionization constant for water, ''K''
w, to introduce
−">H−= ''K''
w/
+">+ This results in the following
cubic equation
In algebra, a cubic equation in one variable is an equation of the form
:ax^3+bx^2+cx+d=0
in which is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the ...
for
+">+ which can be solved either numerically or analytically:
:
Derivation
Considering the dissociation of the weak acid HA (e.g.,
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 component ...
):
HA H
+ + A
−
Starting from the definition of the
equilibrium constant
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
:
one can solve for
+">+as follows:
:
The main issue is how to determine the equilibrium concentrations
Aand
−">−from the initial, or analytical concentrations ''C''
a and ''C''
b. This can be achieved by considering the electroneutrality and mass balance constraints on the system. The first constraint is that the total concentration of cations needs to equal the total concentration of anions, because the system has to be electrically neutral:
:
Here M
+ is the
counterion
160px, Polystyrene sulfonate, a cation-exchange resin, is typically supplied with as the counterion.">cation-exchange_resin.html" ;"title="Polystyrene sulfonate, a cation-exchange resin">Polystyrene sulfonate, a cation-exchange resin, is typical ...
that comes with the conjugate base,
−">− that is added to the solution. For example, if HA is
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 component ...
, A
− would be
acetate
An acetate is a salt (chemistry), salt formed by the combination of acetic acid with a base (e.g. Alkali metal, alkaline, Alkaline earth metal, earthy, Transition metal, metallic, nonmetallic or radical Radical (chemistry), base). "Acetate" als ...
, which could be added to the solution in the form of
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 ...
. In this case, M
+ would be the sodium cation. The equilibrium concentration
+">+is constant and equal to the analytical concentration of the base, ''C''
b. Therefore,
:
Because of mass balance, the sum of the equilibrium concentrations of the acid and its conjugate base has to remain equal to the sum of their analytical concentrations. (HA may convert into A
− and vice versa, but what is lost of HA is gained of A
−, keeping the sum constant.)
:
Substituting
−">−and solving for
A
:
Introducing the equations for
Aand
−">−into the equation for
+">+yields the Charlot equation.
See also
*
Bjerrum plot
A Bjerrum plot (named after Niels Bjerrum; sometimes also known as a Sillén diagram or a Hägg diagram) is a graph of the concentrations of the different species of a polyprotic acid in a solution, as a function of pH, when the solution is at ...
References
*
* {{cite journal , author = de Levie, Robert , author-link = Robert de Levie , journal =
The Chemical Educator
''The Chemical Educator'' is a peer-reviewed journal in chemical education. It was published by Springer-Verlag from 1996 to 2002, and has been published online independently since 2003. The journal publishes six issues per volume and one volume pe ...
, 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
Acid–base chemistry