# Gravimetric analysis

Gravimetric analysis describes a set of methods used in analytical chemistry for the quantitative determination of an analyte (the ion being analyzed) based on its mass. The principle of this type of analysis is that once an ion's mass has been determined as a unique compound, that known measurement can then be used to determine the same analyte's mass in a mixture, as long as the relative quantities of the other constituents are known.
The four main types of this method of analysis are precipitation, volatilization, electro-analytical and miscellaneous physical method. The methods involve changing the phase of the analyte to separate it in its pure form from the original mixture and are quantitative measurements.

## Precipitation method

The precipitation method is the one used for the determination of the amount of calcium in water. Using this method, an excess of oxalic acid, H$_2$C$_2$O$_4$, is added to a measured, known volume of water. By adding a reagent, here ammonium oxalate, the calcium will precipitate as calcium oxalate. The proper reagent, when added to aqueous solution, will produce highly insoluble precipitates from the positive and negative ions that would otherwise be soluble with their counterparts (equation 1).
The reaction is:
Formation of calcium oxalate:
Ca$^{2+}$(aq) + C$_2$O$_4$$^{2-}$ → CaC$_2$O$_4$
The precipitate is collected, dried and ignited to high (red) heat which converts it entirely to calcium oxide.
The reaction is pure calcium oxide formed
CaC$_2$O$_4$ → CaO(s) + CO(g)+ CO$_2$(g)
The pure precipitate is cooled, then measured by weighing, and the difference in weights before and after reveals the mass of analyte lost, in this case calcium oxide. That number can then be used to calculate the amount, or the percent concentration, of it in the original mix.

## Volatilization methods

Volatilization methods can be either direct or indirect. Water eliminated in a quantitative manner from many inorganic substances by ignition is an example of a direct determination. It is collected on a solid desiccant and its mass determined by the gain in mass of the desiccant.
Another direct volatilization method involves carbonates which generally decompose to release carbon dioxide when acids are used. Because carbon dioxide is easily evolved when heat is applied, its mass is directly established by the measured increase in the mass of the absorbent solid used.
Determination of the amount of water by measuring the loss in mass of the sample during heating is an example of an indirect method. It is well known that changes in mass occur due to decomposition of many substances when heat is applied, regardless of the presence or absence of water. Because one must make the assumption that water was the only component lost, this method is less satisfactory than direct methods.
This often faulty and misleading assumption has proven to be wrong on more than a few occasions. There are many substances other than water loss that can lead to loss of mass with the addition of heat, as well as a number of other factors that may contribute to it. The widened margin of error created by this all-too-often false assumption is not one to be lightly disregarded as the consequences could be far-reaching.
Nevertheless, the indirect method, although less reliable than direct, is still widely used in commerce. For example, it's used to measure the moisture content of cereals, where a number of imprecise and inaccurate instruments are available for this purpose.

### Types of volatilization methods

In volatilization methods, removal of the analyte involves separation by heating or chemically decomposing a volatile sample at a suitable temperature. In other words, thermal or chemical energy is used to precipitate a volatile species. For example, the water content of a compound can be determined by vaporizing the water using thermal energy (heat). Heat can also be used, if oxygen is present, for combustion to isolate the suspect species and obtain the desired results.
The two most common gravimetric methods using volatilization are those for water and carbon dioxide. An example of this method is the isolation of sodium hydrogen bicarbonate (the main ingredient in most antacid tablets) from a mixture of carbonate and bicarbonate. The total amount of this analyte, in whatever form, is obtained by addition of an excess of dilute sulfuric acid to the analyte in solution.
In this reaction, nitrogen gas is introduced through a tube into the flask which contains the solution. As it passes through, it gently bubbles. The gas then exits, first passing a drying agent (here CaSO$_4$, the common desiccant Drierite). It then passes a mixture of the drying agent and sodium hydroxide which lies on asbestos or Ascarite II, a non-fibrous silicate containing sodium hydroxide. The mass of the carbon dioxide is obtained by measuring the increase in mass of this absorbent. This is performed by measuring the difference in weight of the tube in which the ascarite contained before and after the procedure.
The calcium sulfate (CaSO$_4$) in the tube retains carbon dioxide selectively as it's heated, and thereby, removed from the solution. The drying agent absorbs any aerosolized water and/or water vapor (reaction 3.). The mix of the drying agent and NaOH absorbs the CO$_2$ and any water that may have been produced as a result of the absorption of the NaOH (reaction 4.).
The reactions are:
Reaction 3 - absorption of water
NaHCO$_3$(aq) + H$_2$SO$_4$(aq) → CO$_2$(g) + H$_2$O(l) + NaHSO$_4$(aq).
Reaction 4. Absorption of CO$_2$ and residual water
CO$_2$(g) + 2 NaOH(s) → Na$_2$CO$_3$(s) + H$_2$O(l).

## Example

A chunk of ore is to be analyzed for sulfur content. It is treated with concentrated nitric acid and potassium chlorate to convert all of the sulfur to sulfate (SO$^{2−}$ $_4$). The nitrate and chlorate are removed by treating the solution with concentrated HCl. The sulfate is precipitated with barium (Ba$^{2+}$) and weighed as BaSO$_4$.

## Advantages

Gravimetric analysis, if methods are followed carefully, provides for exceedingly precise analysis. In fact, gravimetric analysis was used to determine the atomic masses of many elements in the periodic table to six figure accuracy. Gravimetry provides very little room for instrumental error and does not require a series of standards for calculation of an unknown. Also, methods often do not require expensive equipment. Gravimetric analysis, due to its high degree of accuracy, when performed correctly, can also be used to calibrate other instruments in lieu of reference standards. Gravimetric analysis is currently used to allow undergraduate chemistry/Biochemistry students to experience a grad level laboratory and it is a highly effective teaching tool to those who want to attend medical school or any research graduate school.

## Disadvantages

Gravimetric analysis usually only provides for the analysis of a single element, or a limited group of elements, at a time. Comparing modern dynamic flash combustion coupled with gas chromatography with traditional combustion analysis will show that the former is both faster and allows for simultaneous determination of multiple elements while traditional determination allowed only for the determination of carbon and hydrogen. Methods are often convoluted and a slight mis-step in a procedure can often mean disaster for the analysis (colloid formation in precipitation gravimetry, for example). Compare this with hardy methods such as spectrophotometry and one will find that analysis by these methods is much more efficient.

## Solubility in the presence of diverse ions

Diverse ions have a screening effect on dissociated ions which leads to extra dissociation. Solubility will show a clear increase in presence of diverse ions as the solubility product will increase. Look at the following example:
Find the solubility of AgCl (K$_{sp}$ = 1.0 x 10$^{−10}$) in 0.1 M NaNO$_3$. The activity coefficients for silver and chloride are 0.75 and 0.76, respectively.
    AgCl(s) = Ag$^+$ + Cl$^−$
We can no longer use the thermodynamic equilibrium constant (i.e. in absence of diverse ions) and we have to consider the concentration equilibrium constant or use activities instead of concentration if we use Kth:
    K$_{sp}$ = aAg$^+$ aCl$^−$
    K$_{sp}$ = [Ag$^+$] fAg$^+$ [Cl$^−$] fCl$^−$
    1.0 x 10$^{−10}$ = s x 0.75 x s x 0.76
    s = 1.3 x 10$^{−5}$ M
We have calculated the solubility of AgCl in pure water to be 1.0 x 10$^{−5}$ M, if we compare this value to that obtained in presence of diverse ions we see % increase in solubility = {(1.3 x 10$^{−5}$ – 1.0 x 10$^{−5}$) / 1.0 x 10$^{−5}$} x 100 = 30% Therefore, once again we have an evidence for an increase in dissociation or a shift of equilibrium to right in presence of diverse ions.