GRAVIMETRIC METHODS OF ANALYSIS

Gravimetric Methods of Analysis

Gravimetry based on measurement of weight of an analysed species or a compound containing the analysed species. Measuring mass is the most fundamental of all analytical measurements, and gravimetry is unquestionably the oldest analytical technique.

Using Mass as a Signal

There are two ways to use mass as an analytical signal. We can, of course, measure an analyte’s mass directly by placing it on a balance and recording its mass. For example, determination of the total suspended solids in water released from a sewage-treatment facility. Suspended solids are just that; solid matter that has yet to settle out of its solution matrix. The analysis is easy. A sample collects and passes it through a preweighed filter that retains the suspended solids. After drying to remove any residual moisture, the filter weighs. The difference between the filter’s original mass and final mass gives the mass of suspended solids. It is a direct analysis because the analyte itself is the object being weighed.

If the analyte is an aqueous ion, such as Pb²⁺, we cannot isolate the analyte by filtration because the Pb²⁺ is dissolved in the solution’s matrix. We can still measure the analyte’s mass, however, by chemically converting it to a solid form. If we suspend a pair of Pt electrodes in our solution and apply a sufficiently positive potential between them for a long enough time, we can force the reaction

Pb²⁺ + 4H₂O « PbO₂ + H₂ + 2H₃O⁺

to go to completion. The Pb²⁺ ion in solution oxidizes to PbO₂ and deposits on the Pt electrode serving as the anode. If we weigh the Pt anode before and after applying the potential, the difference in the two measurements gives the mass of PbO₂ and, from the reaction’s stoichiometry, the mass of Pb²⁺. This also is a direct analysis because the material being weighed contains the analyte.

Sometimes it is easier to remove the analyte and use a change in mass as the analytical signal. For example, determine a food’s moisture content by a direct analysis. One possibility is to heat a sample of the food to a temperature at which the water in the sample vaporizes. If we capture the vapor in a preweighed absorbent trap, then the change in the absorbent’s mass provides a direct determination of the amount of water in the sample. An easier approach, however, is to weigh the sample of food before and after heating, using the change in its mass as an indication of the amount of water originally present. This technique calls an indirect analysis since we determine the analyte by a signal representing its disappearance.

The indirect determination of moisture content in foods is done by difference. The sample’s initial mass includes the water, whereas the final mass is measured after removing the water. We can also determine an analyte indirectly without its ever being weighed. Again, as with the determination of Pb²⁺ as PbO₂, we take advantage of the analyte’s chemistry. For example, phosphite, PO₃^3–, reduces Hg²⁺ to Hg₂²⁺. In the presence of Cl^– a solid precipitate of Hg₂Cl₂ forms.

2HgCl₂ + PO₃^3– + 3H₂O « Hg₂Cl₂ + 2H₃O⁺ + 2Cl^– + PO₄^3–

If HgCl₂ is added in excess, each mole of PO₃^3– produces one mole of Hg₂Cl₂. The precipitate’s mass, therefore, provides an indirect measurement of the mass of PO₃^3– present in the original sample.

 

Types of Gravimetric Methods

Described above examples illustrate the four gravimetric methods of analysis. If the signal is the mass of a precipitate, the method calls precipitation gravimetry. The indirect determination of PO₃^3– by precipitating Hg₂Cl₂ is a representative example, as is the direct determination of Cl^– by precipitating AgCl.

In electrogravimetry the analyte is deposited as a solid film on one electrode in an electrochemical cell. The oxidation of Pb²⁺, and its deposition as PbO₂ on a Pt anode is one example of electrogravimetry. Reduction also may be used in electrogravimetry. The electrodeposition of Cu on a Pt cathode, for example, provides a direct analysis for Cu²⁺.

If thermal or chemical energy is used to remove a volatile species, the method calls volatilization gravimetry. In determining the moisture content of food, thermal energy vaporizes the H₂O. The amount of carbon in an organic compound may be determined by using the chemical energy of combustion to convert C to CO₂.

In particulate gravimetry (isolation method) the analyte is determined following its removal from the sample matrix by filtration or extraction. The determination of suspended solids is one example of particulate gravimetry.

 

Calculations in Gravimetry

         An accurate gravimetric analysis requires that the mass of analyte present in a sample be proportional to the mass or change in mass serving as the analytical signal. For all gravimetric methods this proportionality involves a conservation of mass. For gravimetric methods involving a chemical reaction, the analyte should participate in only one set of reactions, the stoichiometry of which indicates how the precipitate’s mass relates to the analyte’s mass. Thus, for the analysis of Pb²⁺ and PO₃^3– described earlier, we can write the following conservation equations

Moles Pb²⁺ = moles PbO₂

Moles PO₃^3– = moles Hg₂Cl₂

Removing the analyte from its matrix by filtration or extraction must be complete. When true, the analyte’s mass can always be found from the analytical signal; thus, for the determination of suspended solids we know that

Filter’s final mass – filter’s initial mass = g suspended solid

whereas for the determination of the moisture content we have

Sample’s initial mass – sample’s final mass = g H₂O

 

Conservation of Mass

Gravimetric calculations are simply an extension of stoichiometric calculations. Our stoichiometric factor is most often based on the amount (in moles) of our analysed species in the material actually weighed.

GF =

GF – gravimetric factor.

FW – formula weight.

 

Precipitation Gravimetry

Precipitation gravimetry is based on the formation of an insoluble compound following the addition of a precipitating reagent, or precipitant, to a solution of the analyte. In most methods the precipitate is the product of a simple metathesis reaction between the analyte and precipitant; however, any reaction generating a precipitate can potentially serve as a gravimetric method. Most precipitation gravimetric methods were developed in the nineteenth century as a means for analyzing ores. Many of these methods continue to serve as standard methods of analysis.

A precipitation gravimetric analysis must have several important attributes.

1.     The precipitate must be of low solubility, high purity, and of known composition if its mass is to accurately reflect the analyte’s mass. Solubility-product (K_SP) must be less than 1×10^-8.

2.     The precipitate must be in a form that is easy to separate from the reaction mixture and be easy to recover by filtration and washing. From this point of view crystalline precipitates should preferred be used than amorphous.

3.     The precipitate must easy and completely transform to weighed form.

4.     The precipitate must be unreactive to air, water etc.

5.     The precipitate must be something where our analysed species is only a small portion of the precipitate.

 

Solubility Considerations

An accurate precipitation gravimetric method requires that the precipitate’s solubility be minimal. Many total analysis techniques can routinely be performed with an accuracy of better than ±0.1%. To obtain this level of accuracy, the isolated precipitate must account for at least 99.9% of the analyte. By extending this requirement to 99.99% we ensure that accuracy is not limited by the precipitate’s solubility.

Precipitation is the most important stage of gravimetry. Accuracy of gravimetric methods depends on:

–      precipitant choice,

–      precipitant amount,

–      precipitation conditions.

On precipitation process influence:

1)    precipitant amount. Precipitation is complete, when residue amount of analysed species is less than balance sensitivity (0,0002 g). Precipitant surplus causes common-ion effect or salting effect. As a rule, precipitant surplus caot be more than 50 % of stoichiometric amount;

2)    temperature. Temperature increasing, frequently, causes precipitate solubility increasing;

3)    pH value. Change the pH value represses dissociation of analysed weak electrolytes or dissolves its;

4)    complex formation process. Process of complex compounds formation competes with process of precipitate formation. Effect depends on solubility-product value and formation-constant value.

Solubility losses are minimized by carefully controlling the composition of the solution in which the precipitate forms. This, in turn, requires an understanding of the relevant equilibrium reactions affecting the precipitate’s solubility. For example, Ag⁺ can be determined gravimetrically by adding Cl^– as a precipitant, forming a precipitate of AgCl.

Ag⁺ + Cl^– ® AgCl¯                                                     (1)

 

Figure 1. Solubility of AgCl as a function of pCl. The dashed line shows the predicted S_AgCl, assuming that only reaction 1 and equation 2 affect the solubility of AgCl. The solid line is calculated using equation 7, and includes the effect of reactions 3–5. A ladder diagram for the AgCl complexation equilibria is superimposed on the pCl axis.

If this is the only reaction considered, we would falsely conclude that the precipitate’s solubility, SAgCl, is given by

S_AgCl = [Ag⁺] =                                            (2)

and that solubility losses may be minimized by adding a large excess of Cl^–. In fact, as shown in Figure 1, adding a large excess of Cl^– eventually increases the precipitate’s solubility.

To understand why AgCl shows a more complex solubility relationship than that suggested by equation 2, we must recognize that Ag⁺ also forms a series of soluble chloro-complexes

 

Ag⁺ + Cl^–  AgCl                                                         (3)

Ag⁺ +2Cl^–  AgCl₂^–                                             (4)

Ag⁺ + 3Cl^–  AgCl₃^2–                                           (5)

The solubility of AgCl, therefore, is the sum of the equilibrium concentrations for all soluble forms of Ag⁺.

S_AgCl = [Ag⁺] + [AgCl] + [AgCl₂^–] + [AgCl₃^2–]                        (6)

Substituting the equilibrium constant expressions for reactions 3–5 into equation 6 defines the solubility of AgCl in terms of the equilibrium concentration of Cl^–.

S_AgCl =  + K₁K_SP + b₂K_SP[Cl^–] + b₃K_SP[Cl^–]²                                       (7)

Equation 7 explains the solubility curve for AgCl shown in Figure 1. As Cl^– is added to a solution of Ag⁺, the solubility of AgCl initially decreases because of reaction 1. Note that under these conditions, the final three terms in equation 7 are small, and that equation 1 is sufficient to describe the solubility of AgCl. Increasing the concentration of chloride, however, leads to an increase in the solubility of AgCl due to the soluble chloro-complexes formed in reactions 3–5.

Also shown in Figure 1 is a ladder diagram for this system. Note that the increase in solubility begins when the higher-order soluble complexes, AgCl₂^– and AgCl₃^2–, become the dominant species.

Clearly the equilibrium concentration of chloride is an important parameter if the concentration of silver is to be determined gravimetrically by precipitating AgCl. In particular, a large excess of chloride must be avoided.

Another important parameter that may affect a precipitate’s solubility is the pH of the solution in which the precipitate forms. For example, hydroxide precipitates, such as Fe(OH)₃, are more soluble at lower pH levels at which the concentration of OH^– is small. The effect of pH on solubility is not limited to hydroxide precipitates, but also affects precipitates containing basic or acidic ions. The solubility of Ca₃(PO₄)₂ is pH-dependent because phosphate is a weak base. The following four reactions, therefore, govern the solubility of Ca₃(PO₄)₂.

Ca₃(PO₄)₂  3Ca²⁺ + 2PO₄^3–                              (8)

PO₄^3– + H₂O  HPO₄^2– + OH^–                                      (9)

HPO₄^2– + H₂O  H₂PO₄^– + OH^–                                   (10)

H₂PO₄^– + H₂O  H₃PO₄ + OH^–                                    (11)

Depending on the solution’s pH, the predominate phosphate species is either PO₄^3–, HPO₄^2–, H₂PO₄^–, or H₃PO₄. The ladder diagram for phosphate, shown in Figure 2a, provides a convenient way to evaluate the pH-dependent solubility of phosphate precipitates. When the pH is greater than 12.4, the predominate phosphate species is PO₄^3–, and the solubility of Ca₃(PO₄)₂ will be at its minimum because only reaction 8 occurs to an appreciable extent (see Figure 2b). As the solution becomes more acidic, the solubility of Ca₃(PO₄)₂ increases due to the contributions of reactions 9–11.

 

 

Figure 2.    a) Ladder diagram for phosphate;

b) Solubility diagram for Ca₃(PO₄)₂ showing the predominate form of phosphate for each segment of the solubility curve.

Solubility can often be decreased by using a nonaqueous solvent. A precipitate’s solubility is generally greater in aqueous solutions because of the ability of water molecules to stabilize ions through solvation. The poorer solvating ability of nonaqueous solvents, even those that are polar, leads to a smaller solubility product. For example, PbSO₄ has a K_sp of 1.6 ´10^–8 in H₂O, whereas in a 50:50 mixture of H₂O/ethanol the K_SP at 2.6 ´10^–12 is four orders of magnitude smaller.

 

Avoiding Impurities

Precipitation gravimetry is based on a known stoichiometry between the analyte’s mass and the mass of a precipitate. It follows, therefore, that the precipitate must be free from impurities. Since precipitation typically occurs in a solution rich in dissolved solids, the initial precipitate is often impure. Any impurities present in the precipitate’s matrix must be removed before obtaining its weight.

The greatest source of impurities results from chemical and physical interactions occurring at the precipitate’s surface. A precipitate is generally crystalline, even if only on a microscopic scale, with a well-defined lattice structure of cations and anions. Those cations and anions at the surface of the precipitate carry, respectively, a positive or a negative charge as a result of their incomplete coordination spheres. In a precipitate of AgCl, for example, each Ag⁺ ion in the bulk of the precipitate is bound to six Cl^– ions. Silver ions at the surface, however, are bound to no more than five Cl^– ions, and carry a partial positive charge (Figure 3).

 

Figure 3. Schematic model of AgCl showing difference between bulk and surface atoms of silver. Silver and chloride ions are not shown to scale.

Precipitate particles grow in size because of the electrostatic attraction between charged ions on the surface of the precipitate and oppositely charged ions in solution. Ions common to the precipitate are chemically adsorbed, extending the crystal lattice. Other ions may be physically adsorbed and, unless displaced, are incorporated into the crystal lattice as a coprecipitated impurity. Physically adsorbed ions are less strongly attracted to the surface and can be displaced by chemically adsorbed ions.

Sources of coprecipitation

–      surface absorption. For example, on surface BaSO₄ precipitate adsorbs Pb⁺ ions;

–      occlusion. Coprecipitated impurities placed not on precipitant surface but into precipitate particles. For example, CaC₂O₄×Na₂C₂O₄;

–      mixed crystal formation. Different substances form the same crystal lattices. Ions of impurities built in the units cells of analysed species crystal lattices. For example, KAl(SO₄)₂×12H₂O, KCr(SO₄)₂×12H₂O;

–      mechanical entrapment.

One common type of impurity is an inclusion. Potential interfering ions whose size and charge are similar to a lattice ion may substitute into the lattice structure by chemical adsorption, provided that the interferent precipitates with the same crystal structure (Figure 4a). The probability of forming an inclusion is greatest when the interfering ion is present at substantially higher concentrations than the dissolved lattice ion. The presence of an inclusion does not decrease the amount of analyte that precipitates, provided that the precipitant is added in sufficient excess. Thus, the precipitate’s mass is always larger than expected.

Inclusions are difficult to remove since the included material is chemically part of the crystal lattice. The only way to remove included material is through reprecipitation. After isolating the precipitate from the supernatant solution, it is dissolved in a small portion of a suitable solvent at an elevated temperature. The solution is then cooled to re-form the precipitate. Since the concentration ratio of interferent to analyte is lower in the new solution than in the original supernatant solution, the mass percent of included material in the precipitate decreases. This process of reprecipitation is repeated as needed to completely remove the inclusion. Potential solubility losses of the analyte, however, cannot be ignored. Thus, reprecipitation requires a precipitate of low solubility, and a solvent for which there is a significant difference in the precipitate’s solubility as a function of temperature.

Figure 4. Example of coprecipitation: (a) schematic of a chemically adsorbed inclusion or a physically adsorbed occlusion in a crystal lattice, where C and A represent the cation–anion pair comprising the analyte and the precipitant, and [M] is the impurity; (b) schematic of an occlusion by entrapment of supernatant solution; (c) surface adsorption of excess C.

Occlusions, which are a second type of coprecipitated impurity, occur when physically adsorbed interfering ions become trapped within the growing precipitate. Occlusions form in two ways. The most common mechanism occurs when physically adsorbed ions are surrounded by additional precipitate before they can be desorbed or displaced (see Figure 4a). In this case the precipitate’s mass is always greater than expected. Occlusions also form when rapid precipitation traps a pocket of solution within the growing precipitate (Figure 4b). Since the trapped solution contains dissolved solids, the precipitate’s mass normally increases. The mass of the precipitate may be less than expected, however, if the occluded material consists primarily of the analyte in a lower-molecular-weight form from that of the precipitate.

Occlusions are minimized by maintaining the precipitate in equilibrium with its supernatant solution for an extended time. This process is called digestion and may be carried out at room temperature or at an elevated temperature. During digestion, the dynamic nature of the solubility–precipitation equilibrium, in which the precipitate dissolves and re-forms, ensures that occluded material is eventually exposed to the supernatant solution. Since the rate of dissolution and reprecipitation are slow, the chance of forming new occlusions is minimal.

After precipitation is complete the surface continues to attract ions from solution (Figure 4c). These surface adsorbates, which may be chemically or physically adsorbed, constitute a third type of coprecipitated impurity. Surface adsorption is minimized by decreasing the precipitate’s available surface area. One benefit of digestion is that it also increases the average size of precipitate particles. This is not surprising since the probability that a particle will dissolve is inversely proportional to its size. During digestion larger particles of precipitate increase in size at the expense of smaller particles. One consequence of forming fewer particles of larger size is an overall decrease in the precipitate’s surface area. Surface adsorbates also may be removed by washing the precipitate. Potential solubility losses, however, cannot be ignored.

Inclusions, occlusions, and surface adsorbates are called coprecipitates because they represent soluble species that are brought into solid form along with the desired precipitate. Another source of impurities occurs when other species in solution precipitate under the conditions of the analysis. Solution conditions necessary to minimize the solubility of a desired precipitate may lead to the formation of an additional precipitate that interferes in the analysis. For example, the precipitation of nickel dimethylgloxime requires a pH that is slightly basic. Under these conditions, however, any Fe³⁺ that might be present precipitates as Fe(OH)₃. Finally, since most precipitants are not selective toward a single analyte, there is always a risk that the precipitant will react, sequentially, with more than one species.

The formation of these additional precipitates can usually be minimized by carefully controlling solution conditions. Interferents forming precipitates that are less soluble than the analyte may be precipitated and removed by filtration, leaving the analyte behind in solution. Alternatively, either the analyte or the interferent can be masked using a suitable complexing agent, preventing its precipitation.

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 Ca²⁺ may be adversely affected by the presence of Mg²⁺. 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 quantitative analysis for Ca²⁺ 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 Ca²⁺ and Mg²⁺ can be analyzed for both cations by first isolating a mixed precipitate of CaCO₃ and MgCO₃. After weighing, the mixed precipitate is heated, converting it to a mixture of CaO and MgO. Thus

Grams of mixed precipitate 1 = grams CaCO₃ + grams MgCO₃

Grams of mixed precipitate 2 = grams CaO + grams MgO

Although these equations contain four unknowns (grams CaCO₃, grams MgCO₃, grams CaO, and grams MgO), the stoichiometric relationships between CaCO₃ and CaO

Moles CaCO₃ = moles CaO

and between MgCO₃ and MgO

Moles MgCO₃ = moles MgO

 

provide enough additional information to determine the amounts of both Ca²⁺ and Mg²⁺ in the sample.

Controlling Particle Size

Following precipitation and digestion, the precipitate must be separated from the supernatant solution and freed of any remaining impurities, 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: nucleation, 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.

A solute’s relative supersaturation, RSS, can be expressed as

RSS =                                                                  (12)

where Q is the solute’s actual concentration, S is the solute’s expected concentration at equilibrium, and Q – S is a measure of the solute’s supersaturation when precipitation begins. A large, positive value of RSS indicates that a solution is highly supersaturated. Such solutions are unstable and show high rates of nucleation, 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 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 stirring 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 addition, 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 BaSO₄ under conditions in which the initial RSS is 5.

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 particles. As additional precipitant is created, nucleation is eventually superseded by particle growth. This process is called homogeneous precipitation.

Two general methods are used for homogeneous precipitation. If the precipitate’s solubility is pH-dependent, then the analyte and precipitant can be mixed under conditions in which precipitation does not occur. The pH is then raised or lowered as needed by chemically generating OH^– or H₃O⁺. For example, the hydrolysis of urea can be used as a source of OH^–.

CO(NH₂)₂ + H₂O « CO₂ + 2NH₃

NH₃ + H₂O « NH₄⁺ + OH^–

The hydrolysis of urea is strongly temperature-dependent, with the rate being negligible at room temperature. The rate of hydrolysis, and thus the rate of precipitate formation, can be controlled by adjusting the solution’s temperature. Precipitates of BaCrO₄, 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, Ba²⁺ can be homogeneously precipitated as BaSO₄ by hydrolyzing sulphamic acid to produce SO₄^2–.

NH₂SO₃H + 2H₂O « NH₄⁺ + H₃O⁺ + SO₄^2–

Homogeneous precipitation affords the dual advantages of producing large particles of precipitate that are relatively free from impurities. These advantages, however, may be offset by increasing the time needed to produce the precipitate, and a tendency for the precipitate to deposit as a thin film on the container’s walls. The latter problem is particularly severe for hydroxide precipitates generated using urea.

 

Figure 5. Schematic model of the solid–solution interface at a particle of AgCl in a solution containing excess AgNO3.

An additional method for increasing particle size deserves mention. When a precipitate’s particles are electrically neutral, they tend to coagulate into larger particles. Surface adsorption of excess lattice ions, however, provides the precipitate’s particles with a net positive or negative surface charge. Electrostatic repulsion between the particles prevents them from coagulating into larger particles.

Consider, for instance, the precipitation of AgCl from a solution of AgNO₃, using NaCl as a precipitant. Early in the precipitation, when NaCl is the limiting reagent, excess Ag⁺ ions chemically adsorb to the AgCl particles, forming a positively charged primary adsorption layer (Figure 5). Anions in solution, in this case NO₃^– and OH^–, are attracted toward the surface, forming a negatively charged secondary adsorption layer that balances the surface’s positive charge. The solution outside the secondary adsorption layer remains electrically neutral. Coagulation cannot occur if the secondary adsorption layer is too thick because the individual particles of AgCl are unable to approach one another closely enough.

Coagulation can be induced in two ways: by increasing the concentration of the ions responsible for the secondary adsorption layer or by heating the solution. One way to induce coagulation is to add an inert electrolyte, which increases the concentration of ions in the secondary adsorption layer. With more ions available, the thickness of the secondary absorption layer decreases. Particles of precipitate may now approach one another more closely, allowing the precipitate to coagulate. The amount of electrolyte needed to cause spontaneous coagulation is called the critical coagulation concentration.

Heating the solution and precipitate provides a second way to induce coagulation. As the temperature increases, the number of ions in the primary adsorption layer decreases, lowering the precipitate’s surface charge. In addition, increasing the particle’s kinetic energy may be sufficient to overcome the electrostatic repulsion preventing coagulation at lower temperatures.

Filtering the Precipitate

After precipitation and digestion are complete, the precipitate is separated from solution by filtration using either filter paper or a filtering crucible. The most common filtering medium is cellulose-based filter paper, which is classified according to its filtering speed, its size, and its ash content on ignition. Filtering speed is a function of the paper’s pore size, which determines the particle sizes retained by the filter. Filter paper is rated as fast (retains particles > 20–25 mm), medium fast (retains particles > 16 mm), medium (retains particles > 8 mm), and slow (retains particles > 2–3 mm). The proper choice of filtering speed is important. If the filtering speed is too fast, the precipitate may pass through the filter paper resulting in a loss of precipitate. On the other hand, the filter paper can become clogged when using a filter paper that is too slow.

Filter paper is hygroscopic and is not easily dried to a constant weight. As a result, in a quantitative procedure the filter paper must be removed before weighing the precipitate. This is accomplished by carefully igniting the filter paper. Following ignition, a residue of noncombustible inorganic ash remains that contributes a positive determinate error to the precipitate’s final mass. For quantitative analytical procedures a low-ash filter paper must be used. This grade of filter paper is pretreated by washing with a mixture of HCl and HF to remove inorganic materials. Filter paper classed as quantitative has an ash content of less than 0.010% w/w. Qualitative filter paper typically has a maximum ash content of 0.06% w/w.

An alternative method for filtering the precipitate is a filtering crucible. The most common is a fritted glass crucible containing a porous glass disk filter. Fritted glass crucibles are classified by their porosity: coarse (retaining particles > 40–60 mm), medium (retaining particles > 10–15 mm), and fine (retaining particles > 4–5.5 mm). Another type of filtering crucible is the Gooch crucible, a porcelain crucible with a perforated bottom. A glass fiber mat is placed in the crucible to retain the precipitate, which is transferred to the crucible in the same manner described for filter paper. The supernatant is drawn through the crucible with the assistance of suction from a vacuum aspirator or pump.

Rinsing the Precipitate

Filtering removes most of the supernatant solution. Residual traces of the supernatant, however, must be removed to avoid a source of determinate error. Rinsing the precipitate to remove this residual material must be done carefully to avoid significant losses of the precipitate. Of greatest concern is the potential for solubility losses. Usually the rinsing medium is selected to ensure that solubility losses are negligible. In many cases this simply involves the use of cold solvents or rinse solutions containing organic solvents such as ethanol. Precipitates containing acidic or basic ions may experience solubility losses if the rinse solution’s pH is not appropriately adjusted. When coagulation plays an important role in determining particle size, a volatile inert electrolyte is often added to the rinse water to prevent the precipitate from reverting into smaller particles that may not be retained by the filtering device. This process of reverting to smaller particles is called peptization. The volatile electrolyte is removed when drying the precipitate.

When rinsing a precipitate there is a trade-off between introducing positive determinate errors due to ionic impurities from the precipitating solution and introducing negative determinate errors from solubility losses. In general, solubility losses are minimized by using several small portions of the rinse solution instead of a single large volume. Testing the used rinse solution for the presence of impurities is another way to ensure that the precipitate is not overrinsed. This can be done by testing for the presence of a targeted solution ion and rinsing until the ion is no longer detected in a freshly collected sample of the rinse solution. For example, when Cl^– is known to be a residual impurity, its presence can be tested for by adding a small amount of AgNO₃ to the collected rinse solution. A white precipitate of AgCl indicates that Cl^– is present and additional rinsing is necessary. Additional rinsing is not needed, however, if adding AgNO₃ does not produce a precipitate.

Drying the Precipitate

Finally, after separating the precipitate from its supernatant solution the precipitate is dried to remove any residual traces of rinse solution and any volatile impurities. The temperature and method of drying depend on the method of filtration, and the precipitate’s desired chemical form. A temperature of 110 °C is usually sufficient when removing water and other easily volatilized impurities. A conventional laboratory oven is sufficient for this purpose. Higher temperatures require the use of a muffle furnace, or a Bunsen or Meker burner, and are necessary when the precipitate must be thermally decomposed before weighing or when using filter paper. To ensure that drying is complete the precipitate is repeatedly dried and weighed until a constant weight is obtained.

Filter paper’s ability to absorb moisture makes its removal necessary before weighing the precipitate. This is accomplished by folding the filter paper over the precipitate and transferring both the filter paper and the precipitate to a porcelain or platinum crucible. Gentle heating is used to first dry and then to char the filter paper. Once the paper begins to char, the temperature is slowly increased. Although the paper will often show traces of smoke, it is not allowed to catch fire as any precipitate retained by soot particles will be lost. After the paper is completely charred the temperature is slowly raised to a higher temperature. At this stage any carbon left after charring is oxidized to CO₂.

Fritted glass crucibles cannot withstand high temperatures and, therefore, should only be dried in an oven at temperatures below 200 °C. The glass fiber mats used in Gooch crucibles can be heated to a maximum temperature of approximately 500 °C.

 

Composition of Final Precipitate

The quantitative application of precipitation gravimetry, which is based on a conservation of mass, requires that the final precipitate have a well-defined composition. Precipitates containing volatile ions or substantial amounts of hydrated water are usually dried at a temperature that is sufficient to completely remove the volatile species. For example, one standard gravimetric method for the determination of magnesium involves the precipitation of MgNH₄PO₄ ´ 6H₂O. Unfortunately, this precipitate is difficult to dry at lower temperatures without losing an inconsistent amount of hydrated water and ammonia. Instead, the precipitate is dried at temperatures above 1000 °C, where it decomposes to magnesium pyrophosphate, Mg₂P₂O₇.

An additional problem is encountered when the isolated solid is nonstoichiometric. For example, precipitating Mn²⁺ as Mn(OH)₂, followed by heating to produce the oxide, frequently produces a solid with a stoichiometry of MnO_x, where x varies between 1 and 2. In this case the nonstoichiometric product results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure.

 

Evaluating Precipitation Gravimetry

Scale of Operation. The scale of operation for precipitation gravimetry is governed by the sensitivity of the balance and the availability of sample. To achieve an accuracy of ±0.1% using an analytical balance with a sensitivity of ±0.1 mg, the precipitate must weigh at least 100 mg. As a consequence, precipitation gravimetry is usually limited to major or minor analytes, and macro or meso samples. The analysis of trace level analytes or micro samples usually requires a microanalytical balance.

Accuracy. For macro–major samples, relative errors of 0.1–0.2% are routinely achieved. The principal limitations are solubility losses, impurities in the precipitate, and the loss of precipitate during handling. When it is difficult to obtain a precipitate free from impurities, an empirical relationship between the precipitate’s mass and the mass of the analyte can be determined by an appropriate standardization.

Precision. The relative precision of precipitation gravimetry depends on the amount of sample and precipitate involved. For smaller amounts of sample or precipitate, relative precisions of 1–2 ppt are routinely obtained. When working with larger amounts of sample or precipitate, the relative precision can be extended to several parts per million. Few quantitative techniques can achieve this level of precision.

Sensitivity. For any precipitation gravimetric method, we can write the following general equation relating the signal (grams of precipitate) to the absolute amount of analyte in the sample

Grams precipitate = k ´ grams of analyte                                    (13)

where k, the method’s sensitivity, is determined by the stoichiometry between the precipitate and the analyte. Note that equation 13 assumes that a blank has been used to correct the signal for the reagent’s contribution to the precipitate’s mass.

For example, the determination of Fe as Fe₂O₃. Using a conservation of mass for Fe we write

2 ´ moles Fe₂O₃ = moles Fe

Converting moles to grams and rearranging yields an equation in the form of 13

 

g Fe₂O₃ = ´ g Fe

where k is equal to

k =                                                   (14)

As can be seen from equation 14, a method’s sensitivity may be improved in two ways. The most obvious way is to increase the ratio of the precipitate’s molar mass to that of the analyte. In other words, it is desirable to form a precipitate with as large a formula weight as possible. A less obvious way to improve the calibration sensitivity is indicated by the term of 1/2 in equation 14, which accounts for the stoichiometry between the analyte and precipitate. Sensitivity also may be improved by forming precipitates containing fewer units of the analyte.

Selectivity. Due to the chemical nature of the precipitation process, precipitants are usually not selective for a single analyte. For example, silver is not a selective precipitant for chloride because it also forms precipitates with bromide and iodide. Consequently, interferents are often a serious problem that must be considered if accurate results are to be obtained.

 

Volatilization Gravimetry

A second approach to gravimetry is to thermally or chemically decompose a solid sample. The volatile products of the decomposition reaction may be trapped and weighed to provide quantitative information. Alternatively, the residue remaining when decomposition is complete may be weighed. In thermogravimetry, which is one form of volatilization gravimetry, the sample’s mass is continuously monitored while the applied temperature is slowly increased.

Whether the analysis is direct or indirect, volatilization gravimetry requires that the products of the decomposition reaction be known. This requirement is rarely a problem for organic compounds for which volatilization is usually accomplished by combustion and the products are gases such as CO₂, H₂O, and N₂. For inorganic compounds, however, the identity of the volatilization products may depend on the temperature at which the decomposition is conducted.

Thermogravimetry. The products of a thermal decomposition can be deduced by monitoring the sample’s mass as a function of applied temperature. (Figure 9). The loss of a volatile gas on thermal decomposition is indicated by a step in the thermogram. The change in mass at each step in a thermogram can be used to identify both the volatilized species and the solid residue.

 

Figure 9. Thermogram for CaC₂O₄ ´H₂O.

 

Once the products of thermal decomposition have been determined, an analytical procedure can be developed. For example, the thermogram in Figure 9 shows that a precipitate of CaC₂O₄´H₂O must be heated at temperatures above 250 °C, but below 400 °C if it is to be isolated as CaC₂O₄. Alternatively, by heating the sample to 1000 °C, the precipitate can be isolated as CaO. Knowing the identity of the volatilization products also makes it possible to design an analytical method in which one or more of the gases are trapped. Thus, a sample of CaC₂O₄´H₂O could be analyzed by heating to 1000 °C and passing the volatilized gases through a trap that selectively retains H₂O, CO, or CO₂.

Equipment. Depending on the method, the equipment for volatilization gravimetry may be simple or complex. In the simplest experimental design, the weight of a solid residue is determined following either thermal decomposition at a fixed temperature or combustion. Thermal decomposition or combustion is accomplished using a Bunsen or Meker burner, a laboratory oven or a muffle furnace, with the volatile products vented to the atmosphere. The weight of the sample and the solid residue are determined using an analytical balance.

Constant-temperature decomposition or combustion followed by trapping and weighing the volatilized gases, requires more specialized equipment. Decomposition of the sample is conducted in a closed container, and the volatilized gases are carried by a purge-gas stream through one or more selective absorbent traps.

In a thermogravimetric analysis, the sample is placed in a small weighing boat attached to one arm of a specially designed electromagnetic balance and placed inside an electric furnace. The temperature of the electric furnace is slowly increased at a fixed rate of a few degrees per minute, and the sample’s weight is monitored.

 

Qualitative Applications of Gravimetry

Although not in common use, precipitation gravimetry still provides a reliable means for assessing the accuracy of other methods of analysis or for verifying the composition of standard reference materials.

Inorganic Analysis. The most important precipitants for inorganic cations are chromate, the halides, hydroxide, oxalate, sulphate, sulphide, and phosphate. A summary of selected methods, grouped by precipitant, is shown in Table 1. Many inorganic anions can be determined using the same reactions by reversing the analyte and precipitant. For example, chromate can be determined by adding BaCl₂ and precipitating BaCrO₄. Methods for other selected inorganic anions are summarized in Table 2. Methods for the homogeneous generation of precipitants are shown in

Table 3.

The majority of inorganic precipitants show poor selectivity. Most organic precipitants, however, are selective for one or two inorganic ions. Several common organic precipitants are listed in Table 4.

 

Table 1. Selected Gravimetric Method for Inorganic Cations Based on Precipitation

 

 

Table 2. Selected Gravimetric Methods for Inorganic Anions Based on Precipitation

 

Table 3. Reactions for the Homogeneous Preparation of Selected Inorganic Precipitants

Table 4. Selected Gravimetric Methods for Inorganic Cations

Based on Precipitation with Organic Precipitants

 

 

Organic Analysis. Several organic functional groups or heteroatoms can be determined using gravimetric precipitation methods; examples are outlined in Table 5. Note that the procedures for the alkoxy and alkimide functional groups are examples of indirect analyses.

 

Quantitative Applications of Gravimetry

Unlike precipitation gravimetry, which is rarely used as a standard method of analysis, gravimetric methods based on volatilization reactions continue to play an important role in chemical analysis.

Inorganic Analysis. Determining the inorganic ash content of organic materials, such as polymers and paper, is an example of a direct volatilization gravimetric analysis. The sample is weighed, placed in an appropriate crucible, and the organic material is carefully removed by combustion. The crucible containing the residue is then heated to a constant weight using either a burner or an oven.

Another example of volatilization gravimetry is the determination of dissolved solids in water and wastewater. In this method a sample of the water is transferred to a weighed dish and dried to a constant weight at either 103–105 °C, or at 180 °C. Samples dried at the lower temperature retain some occluded water and lose some carbonate as CO₂. The loss of organic material, however, is minimal. At the higher temperature, the residue is free from occluded water, but losses of carbonate are greater. In addition, some chloride, nitrate, and organic material are lost through thermal decomposition. The residue remaining after drying at either temperature can be ignited to constant weight at 500 °C. The loss in weight on ignition provides an indirect measure of the amount of volatile solids in the sample, and the weight of the remaining residue gives the amount of fixed solids.

 

Table 5. Selected Gravimetric Methods for the Analysis of Organic Functional Groups and Heteroatoms Based on Precipitation

 

 

Indirect analyses based on the weight of the residue remaining after volatilization are commonly used in determining moisture in a variety of products and in determining silica in water, wastewater, and rocks. Moisture is determined by drying a preweighed sample with an infrared lamp or in a low-temperature oven. The difference between the original weight and the weight after drying equals the mass of water lost.

The determination of silicon is commonly encountered in metallurgical and mining laboratories responsible for the analysis of ores, slags, and alloys. The volatilization gravimetric method, which is appropriate for samples containing high concentrations of silicon. The determination of carbon in steels and other metal alloys can be determined by heating the sample. The carbon is converted to CO₂, which is collected in an appropriate absorbent trap, providing a direct measure of the amount of C in the original sample.

Organic Analysis. The most important application of volatilization gravimetry to the analysis of organic materials is an elemental analysis. When burned in a stream of pure O₂, many elements, such as carbon and hydrogen, are released as gaseous combustion products, such as CO₂ and H₂O. The combustion products are passed through preweighed tubes containing appropriate absorbents. The increase in the mass of these tubes provides a direct indication of the mass percent of carbon and hydrogen in the organic material.

Alkaline metals and earths in organic materials can be determined by adding H₂SO₄ to the sample before combustion. Following combustion, the metal remains behind as a solid residue of metal sulfate. Silver, gold, and platinum can be determined by burning the organic sample, leaving a metallic residue of Ag, Au, or Pt. Other metals are determined by adding HNO₃ before combustion, leaving a residue of the metal oxide.

Volatilization gravimetry is also used to determine biomass in water and wastewater. Biomass is a water quality index, providing an indication of the total mass of organisms contained within a sample of water. A known volume of the sample is passed through a preweighed 0.45-mm membrane filter or a glass-fiber filter and dried at 105 °C for 24 h. The residue’s mass provides a direct measure of biomass. If samples are known to contain a substantial amount of dissolved inorganic solids, the residue can be ignited at 500 °C for 1 h, thereby removing all organic materials. The resulting residue is wetted with distilled water to rehydrate any clay minerals and dried to a constant weight at 105 °C. The difference in weight before and after ignition provides an indirect measure of biomass.