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              240    Modern Analytical Chemistry


                                                  Both of the above-mentioned approaches are illustrated in Fresenius’s analyti-
                                                                                                2+
                                                                                                     2+
                                              cal method for determining Ni and Co in ores containing Pb , Cu , and Fe 3+  as
                                              potential interfering ions (see Figure 1.1 in Chapter 1). The ore is dissolved in a so-
                                              lution containing H 2 SO 4 , selectively precipitating Pb 2+  as PbSO 4 . After filtering, the
                                              supernatant solution is treated with H 2 S. Because the solution is strongly acidic,
                                              however, only CuS precipitates. After removing the CuS by filtration, the solution is
                                              made basic with ammonia until Fe(OH) 3 precipitates. Cobalt and nickel, which
                                              form soluble amine complexes, remain in solution.
                                                  In some situations the rate at which a precipitate forms can be used to separate
                                              an analyte from a potential interferent. For example, due to similarities in their
                                              chemistry, a gravimetric analysis for Ca 2+  may be adversely affected by the presence
                                                   2+
                                              of Mg . Precipitates of Ca(OH) 2 , however, form more rapidly than precipitates of
                                              Mg(OH) 2 . If Ca(OH) 2 is filtered before Mg(OH) 2 begins to precipitate, then a
                                                                    2+
                                              quantitative analysis for Ca is feasible.
                                                  Finally, in some cases it is easier to isolate and weigh both the analyte and the
                                              interferent. After recording its weight, the mixed precipitate is treated to convert at
                                              least one of the two precipitates to a new chemical form. This new mixed precipitate
                                              is also isolated and weighed. For example, a mixture containing Ca 2+  and Mg 2+  can
                                              be analyzed for both cations by first isolating a mixed precipitate of CaCO 3 and
                                              MgCO 3 . After weighing, the mixed precipitate is heated, converting it to a mixture
                                              of CaO and MgO. Thus
                                                      Grams of mixed precipitate 1 = grams CaCO 3 + grams MgCO 3

                                                        Grams of mixed precipitate 2 = grams CaO + grams MgO
                                              Although these equations contain four unknowns (grams CaCO 3 , grams MgCO 3 ,
                                              grams CaO, and grams MgO), the stoichiometric relationships between CaCO 3 and
                                              CaO
                                                                     Moles CaCO 3 = moles CaO

                                              and between MgCO 3 and MgO
                                                                    Moles MgCO 3 = moles MgO
                                              provide enough additional information to determine the amounts of both Ca 2+  and
                                                 2+
                                              Mg in the sample.*

                                              Controlling Particle Size  Following precipitation and digestion, the precipitate
                                              must be separated from the supernatant solution and freed of any remaining impu-
                                              rities, including residual solvent. These tasks are accomplished by filtering, rinsing,
                                              and drying the precipitate. The size of the precipitate’s particles determines the ease
                                              and success of filtration. Smaller, colloidal particles are difficult to filter because
                                              they may readily pass through the pores of the filtering device. Large, crystalline
                                              particles, however, are easily filtered.
                                                  By carefully controlling the precipitation reaction we can significantly increase
                                              a precipitate’s average particle size. Precipitation consists of two distinct events: nu-
                                              cleation, or the initial formation of smaller stable particles of precipitate, and the
                                              subsequent growth of these particles. Larger particles form when the rate of particle
                                              growth exceeds the rate of nucleation.


                                              *Example 8.2 shows how to solve this type of problem.
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