Page 258 - Modern Analytical Chemistry

1400-CH08 9/9/99 2:17 PM Page 241

Chapter 8 Gravimetric Methods of Analysis 241

A solute’s relative supersaturation, RSS, can be expressed as
relative supersaturation
Q - S A measure of the extent to which a
RSS = 8.12 solution, or a localized region of
S solution, contains more dissolved solute
where Q is the solute’s actual concentration, S is the solute’s expected concentra- than that expected at equilibrium (RSS).
tion at equilibrium, and Q – S is a measure of the solute’s supersaturation when
3
precipitation begins. A large, positive value of RSS indicates that a solution is
highly supersaturated. Such solutions are unstable and show high rates of nucle-
ation, producing a precipitate consisting of numerous small particles. When
RSS is small, precipitation is more likely to occur by particle growth than by
nucleation.
Examining equation 8.12 shows that we can minimize RSS by either decreasing
the solute’s concentration or increasing the precipitate’s solubility. A precipitate’s
solubility usually increases at higher temperatures, and adjusting pH may affect a
precipitate’s solubility if it contains an acidic or basic anion. Temperature and pH,
therefore, are useful ways to increase the value of S. Conducting the precipitation in
a dilute solution of analyte, or adding the precipitant slowly and with vigorous stir-
ring are ways to decrease the value of Q.
There are, however, practical limitations to minimizing RSS. Precipitates that
are extremely insoluble, such as Fe(OH) 3 and PbS, have such small solubilities that
a large RSS cannot be avoided. Such solutes inevitably form small particles. In addi-
tion, conditions that yield a small RSS may lead to a relatively stable supersaturated
solution that requires a long time to fully precipitate. For example, almost a month
is required to form a visible precipitate of BaSO 4 under conditions in which the ini-
tial RSS is 5. 4
An increase in the time required to form a visible precipitate under conditions
of low RSS is a consequence of both a slow rate of nucleation and a steady decrease
in RSS as the precipitate forms. One solution to the latter problem is to chemically
generate the precipitant in solution as the product of a slow chemical reaction. This
maintains the RSS at an effectively constant level. The precipitate initially forms
under conditions of low RSS, leading to the nucleation of a limited number of parti-
cles. As additional precipitant is created, nucleation is eventually superseded by par-
ticle growth. This process is called homogeneous precipitation. 5 homogeneous precipitation
Two general methods are used for homogeneous precipitation. If the precipi- A precipitation in which the precipitant
tate’s solubility is pH-dependent, then the analyte and precipitant can be mixed is generated in situ by a chemical
reaction.
under conditions in which precipitation does not occur. The pH is then raised or
–
+
lowered as needed by chemically generating OH or H 3O . For example, the hydrol-
–
ysis of urea can be used as a source of OH .
CO(NH 2 ) 2 (aq)+H 2 O(l) t CO 2 (g) + 2NH 3 (aq)
+
–
NH 3 (aq)+H 2 O(l) t NH 4 (aq)+OH (aq)
The hydrolysis of urea is strongly temperature-dependent, with the rate being negli- Color Plate 5 shows the difference
gible at room temperature. The rate of hydrolysis, and thus the rate of precipitate between a precipitate formed by direct
formation, can be controlled by adjusting the solution’s temperature. Precipitates of precipitation and a precipitate formed
by a homogeneous precipitation.
BaCrO 4 , for example, have been produced in this manner.
In the second method of homogeneous precipitation, the precipitant itself is
generated by a chemical reaction. For example, Ba 2+ can be homogeneously precipi-
2–
tated as BaSO 4 by hydrolyzing sulphamic acid to produce SO 4 .
+
+
2–
NH 2 SO 3 H(aq)+2H 2 O(l) t NH 4 (aq)+H 3 O (aq)+SO 4 (aq)