James Richard Fromm
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 silver ion to one chloride ion, we know that the amount of silver ion used to the equivalence point equals the amount of chloride ion originally present. Since by the definition of molarity n = cV, the number of moles of either silver ion or chloride ion can be calculated from the number of moles of the other, and the molar concentration or the volume of added 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 pX = -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 solutions.
The molar concentration of either chloride ion or silver ion will change over several orders of magnitude during the course of a 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.
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 can be 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 a solution or precipitate of 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 molar in such a solution, a precipitate of Ag2CrO4 will form. If the concentration is below this, no silver chromate precipitate will form.
When we have a solution of, say, 0.01 molar chloride ion and add silver ion 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 silver nitrate solution is added after the equivalence point has been reached, there is no more chloride ion 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.