Introductory University Chemistry I
Solubility of Ionic Salts in Water
A titration is an analytical procedure in which a
reagent called a titrant is slowly
added to another substance. A rapid stoichiometric reaction takes place as
the titrant is added, and both the addition and the reaction continue
until one of the reactants is
exhausted. Some process, device, or change in the solution indicates that
this endpoint has been reached. The purpose of a titration is to determine
the amount, or the concentration, of one of the reactants, which can be
done if the amount, or concentration and volume, of the other reactant
required to reach the endpoint of the titration is known.
In a precipitation titration, the stoichiometric reaction is a reaction
which produces in solution a slightly soluble salt that precipitates out. To
determine the concentration of chloride ion in a particular solution, one could
titrate this solution with a solution of a silver salt, say silver nitrate, whose
concentration is known. The chemical reaction occurring is Ag+(aq) + Cl-(aq) --> AgCl(s)
A white precipitate of AgCl is deposited on the bottom of the flask during the
course of the titration. Since the chemical reaction is one Ag+ to one Cl-, we
know that the amount of Ag+ used to the equivalence point equals the amount
of Cl- originally present. Since n = cV, the number of moles of either Ag+ or Cl-
can be calculated from the number of moles of the other, and the molar
concentration or the volume ofadded solution can be calculated for either ion
if the other is known.
Example. In a precipitation titration of 46.00 mL of a chloride
solution of unknown concentration, 31.00 mL of 0.6973 molar AgNO3 were
required to reach the equivalence point. The molar concentration of the
unknown solution is calculated as follows:
31.00 mL x 0.6973 molar = 21.62 mmol Ag+ = 21.62 mmol Cl-
21.62 mmol Cl-/46.00 mL Cl- = 0.4700 molar Cl-
The substance to be titrated is generally measured into the titration
vessel either directly, its mass (or density and volume) having been determined,
or by pipet if it is in the form of a solution. The titrant solution is generally
delivered from a buret. The volume added can be measured from the buret
scale as soon as the endpoint of the titration is reached. The precision of
measurement of burettes and pipettes are given in an earlier section.
It is inconvenient to the point of being impractical to plot, or even to
compare,the changes in ionic concentrations which take place over the course
of a precipitation titration because the values of the concentrations cover so
many orders of magnitude in range. Chemists have therefore introduced p
notation, in which the negative logarithm of a concentration or activity is used
rather than the concentration or activity itself; that is, pX = -log c(X) or -log a(X).
The logarithmic p notation is commonly used not only in titrations but for the
general expression of solution concentrations. In other sections this
notation, in the form of pH, is extensively used to express the acidity of
In the following Figure, pCl is used on the vertical axis to show how the
concentration of chloride ion changes over the course of the titration. The
molar concentration of either chloride ion or silver ion will change over several
orders of magnitude during the course of this titration, as the concentration of
chloride ion is first slowly reduced by the precipitation of AgCl as a
consequence of the continuous addition of silver ion. As the supply of chloride
ion is reduced to very low values, the equivalence point of the titration is
reached--the point at which the stoichiometric precipitation is complete and the
amount of silver ion that has been added is equivalent to the amount of chloride
ion originally present. The term "equivalent" is used rather than "equal"
because in some reactions, such as the precipitation of Ag2SO4, the amounts will
differ by a stoichiometric factor of two or three. Beyond the equivalence point,
addition of more silver ion will continue to reduce the concentration of chloride
ion through the common ion effect.
Figure is not available.
In any titration, it is necessary to have some method of detecting when
just enough of the titrant has been added -- a procedure known as detecting the
endpoint of the titration. The endpoint of this titration canbe detected if the
rapid change in either the concentration of silver ion or the the concentration
of chloride ion which occurs at the endpoint can be made apparent to an
observer. Either instrumental methods or equilibrium methods can be used.
The equilibrium methods are fairly straightforward. In this case we can use
Ag2CrO4, because a solution of CrO42- is yellow while Ag2CrO4 is blood-red.
Suppose [CrO42-] in the solution is 0.001 molar. Then Ksp = 1.12 x 10-12 =
[Ag+]2[CrO42-]. Since [CrO42-] = 10-3 molar, [Ag+]2 = 1.12 x 10-10, and [Ag+] = 3.35
x 10-5. At any concentration of silver ion greater than 3.35 x 10-5 in such a
solution, a precipitate of Ag2CrO4 will form; if the concentration is below this,
it will not.
When we have a solution of, say, 0.01 molar Cl- and add Ag+ to it, the
solubility product is Ksp = 1.76 x 10-10 = [Ag+][Cl-], so at the start of the titration
[Ag+] = 1.76 x 10-10/1 x 10-2 = 1.76 x 10-8 and no precipitate of Ag2CrO4 can form.
At the equivalence point, [Ag+] = [Cl-] and [Ag+]2 = Ksp = 1.76 x 10-1,
[Ag+] = 1.33 x 10-5 and no precipitate will form. But when a drop or two more
of Ag+ solution is added after the equivalence point has been reached, there is
no more Cl- to react with it. The concentration of silver ion may go up to say 10-
3 molar. The solubility product of silver chromate will then be exceeded and a
red precipitate of Ag2CrO4 will designate the end of the titration. This is known
as the Mohr method of chloride determination.
[NEXT: Ionic Interactions in Aqueous Solutions]
[PREVIOUS: The Diverse Ion Effect]
Copyright 1995 James A. Plambeck (Jim.Plambeck@ualberta.ca).
Updated November 6, 1995 jp.