8.1: Overview of Gravimetric Methods

Before we consider specific gravimetric methods, let’s take a moment to develop a broad survey of gravimetry. Later, as you read through the descriptions of specific gravimetric methods, this survey will help you focus on their similarities instead of their differences. You will find that it is easier to understand a new analytical method when you can see its relationship to other similar methods.

8.1.1 Using Mass as an Analytical Signal

Suppose you are to determine the total suspended solids in the water released by 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. After collecting a sample, you pass it through a preweighed filter that retains the suspended solids, and dry the filter and solids to remove any residual moisture. The mass of suspended solids is the difference between the filter’s final mass and its original mass. We call this a direct analysis because the analyte—the suspended solids in this example—is the species that is weighed.

Note

Method 2540D in Standard Methods for the Examination of Waters and Wastewaters, 20th Edition (American Public Health Association, 1998) provides an approved method for determining total suspended solids. The method uses a glass-fiber filter to retain the suspended solids. After filtering the sample, the filter is dried to a constant weight at 103–105^oC.

What if our analyte is an aqueous ion, such as Pb²⁺? Because the analyte is not a solid, we cannot isolate it by filtration. We can still measure the analyte’s mass directly if we first convert it into a solid form. If we suspend a pair of Pt electrodes in the sample and apply a sufficiently positive potential between them for a long enough time, we can force the following reaction to completion.

\[\mathrm{Pb}^{2+}(aq)+4\mathrm{H_2O}(l)\rightleftharpoons\mathrm{PbO_2}(s)+\mathrm{H_2}(g)+2\mathrm{H_3O^+}(aq)\]

Oxidizing Pb²⁺ deposits PbO₂ on the Pt anode. If we weigh the anode before and after applying the potential, the change in its mass gives the mass of PbO₂ and, from the reaction’s stoichiometry, the amount of Pb²⁺ in the sample. This is a direct analysis because PbO₂ contains the analyte.

Sometimes it is easier to remove the analyte and let a change in mass serve as the analytical signal. Suppose you need to determine a food’s moisture content. One approach is to heat a sample of the food to a temperature that vaporizes the water, capturing it in a preweighed absorbent trap. The change in the absorbent’s mass provides a direct determination of the amount of water in the sample. An easier approach 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. We call this an indirect analysis because we determine the analyte using a signal that is proportional its disappearance.

Note

Method 925.10 in Official Methods of Analysis, 18th Edition (AOAC International, 2007) provides an approved method for determining the moisture content of flour. A preweighed sample is heated for one hour in a 130^oC oven and transferred to a desiccator while it cools to room temperature. The loss in mass gives the amount of water in the sample.

The indirect determination of a sample’s moisture content is done by difference. The sample’s initial mass includes the water, but its final mass does not. We can also determine an analyte indirectly without its ever being weighed. For example, phosphite, PO₃^3–, reduces Hg²⁺ to Hg₂²⁺, which in the presence of Cl^– precipitates as Hg₂Cl₂.

\[\mathrm{2HgCl_2}(aq)+\mathrm{PO_3^{3-}}(aq)+\mathrm{3H_2O}(l)\rightleftharpoons \mathrm{Hg_2Cl_2}(s)+\mathrm{2H_3O^+}(aq)+\mathrm{2Cl^-}(aq)+\mathrm{2PO_4^{3-}}(aq)\]

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

8.1.2 Types of Gravimetric Methods

The four examples in the previous section illustrate different ways in which the measurement of mass may serve as an analytical signal. When the signal is the mass of a precipitate, we call the method precipitation gravimetry. The indirect determination of PO₃^3– by precipitating Hg₂Cl₂ is an example, as is the direct determination of Cl^– by precipitating AgCl.

In electrogravimetry, we deposit the analyte as a solid film an electrode in an electrochemical cell. The deposition as PbO₂ at a Pt anode is one example of electrogravimetry. The reduction of Cu²⁺ to Cu at a Pt cathode is another example of electrogravimetry.

Note

We will not consider electrogravimetry in this chapter. See Chapter 11 on electrochemical methods of analysis for a further discussion of electrogravimetry.

When we use thermal or chemical energy to remove a volatile species, we call the method volatilization gravimetry. In determining the moisture content of bread, for example, we use thermal energy to vaporize the water in the sample. To determine the amount of carbon in an organic compound, we use the chemical energy of combustion to convert it to CO₂.

Finally, in particulate gravimetry we determine the analyte by separating it from the sample’s matrix using a filtration or an extraction. The determination of total suspended solids is one example of particulate gravimetry.

8.1.3 Conservation of Mass

An accurate gravimetric analysis requires that the analytical signal—whether it is a mass or a change in mass—be proportional to the amount of analyte in our sample. For all gravimetric methods this proportionality involves a conservation of mass. If the method relies on one or more chemical reactions, then the stoichiometry of the reactions must be known. Thus, for the analysis of PO₃^3– described earlier, we know that each mole of Hg₂Cl₂ corresponds to a mole of PO₃^3– in our sample. If we remove the analyte from its matrix, then the separation must be selective for the analyte. When determining the moisture content in bread, for example, we know that the mass of H₂O in the bread is the difference between the sample’s final mass and its initial mass.

Note

We will return to this concept of applying a conservation of mass later in the chapter when we consider specific examples of gravimetric methods.

8.1.4 Why Gravimetry is Important

Except for particulate gravimetry, which is the most trivial form of gravimetry, you probably will not use gravimetry after you complete this course. Why, then, is familiarity with gravimetry still important? The answer is that gravimetry is one of only a small number of definitive techniques whose measurements require only base SI units, such as mass or the mole, and defined constants, such as Avogadro’s number and the mass of ¹²C. Ultimately, we must be able to trace the result of an analysis to a definitive technique, such as gravimetry, that we can relate to fundamental physical properties.² Although most analysts never use gravimetry to validate their results, they often verifying an analytical method by analyzing a standard reference material whose composition is traceable to a definitive technique.³

Note

Other examples of definitive techniques are coulometry and isotope-dilution mass spectrometry. Coulometry is discussed in Chapter 11. Isotope-dilution mass spectrometry is beyond the scope of an introductory textbook; however, you will find some suggested readings in this chapter’s Additional Resources.

Contributors

David Harvey (DePauw University)