Examples of Gravimetric Calculations

We now illustrate how to relate the mass of a gravimetric precipitate to the quantity of original analyte. The general approach is to relate the moles of product to the moles of reactant. 

The piperazine content of an impure commercial material can be determined by precipitating and weighing piperazine diacetate  

In one experiment, 0.312 6 g of sample was dissolved in 25 mL of acetone, and 1 mL of acetic acid was added. After 5 min, the precipitate was filtered, washed with acetone, dried at 110°C, and found to be 0.712 1 g. Find wt% piperazine in the commercial material. 

We know the mass of sample (0.312 6 g), so we need to find the mass of piperazine. The experiment gives us the mass of the product piperazine diacetate (0.712 1 g) made from piperazine. How much piperazine is contained in 0.712 1 g of piperazine diacetate Each mole of piperazine diacetate contains one mole of piperazine in Reaction 7-1. If we compute the moles of piperazine diacetate product, we can find the moles of piperazine in the sample. From the moles of piperazine, we can calculate the grams of piperazine and its weight percent. 

If you were performing this analysis, it would be Important to determine that Impurities in the piperazine are not also precipitated. 

Solution For each mole of piperazine in the impure material. 1 mol of product is formed. 

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More examples of gravimetric calculations are given in Chapter 7. 

Quantitative Calculations In precipitation gravimetry the relationship between the analyte and the precipitate is determined by the stoichiometry of the relevant reactions. As discussed in Section 2C, gravimetric calculations can be simplified by applying the principle of conservation of mass. The following example demonstrates the application of this approach to the direct analysis of a single analyte. 

The weight of the precipitate after filtering and drying can then be measured free of any influence from the NaCl and converted back to the weight of the analyte with the use of a gravimetric factor (see the next section) and its percent in the sample calculated. Examples are given in Section 3.6.4. 

A gravimetric factor is a number used to convert, by multiplication, the weight of one chemical to the weight of another. Such a conversion can be very useful in an analytical laboratory. For example, if a recipe for a solution of iron calls for 55 g of FeCl3 but a technician finds only iron wire on the chemical shelf, he or she would want to know how much iron metal is equivalent to 55 g of FeCl3 so that he or she could prepare the solution with the iron wire instead and have the same weight of iron in either case. In one formula unit of FeCl3, there is one atom of Fe, so the fraction of iron(III) chloride that is iron metal is calculated as follows ... 

The ultimate goal of any titrimetric analysis is to determine the amount of the analyte in a sample. This involves the stoichiometry calculation mentioned in the Work the Data section of the analytical strategy flow chart in Figure 4.1. This amount of analyte is often expressed as a percentage, as it was for the gravimetric analysis examples in Chapter 3. This percentage is calculated via the basic equation for percent used previously for the gravimetric analysis examples ... 

This procedure is based on the measurement of the contraction of volume that results from the different densities of the monomer and polymer. The conversion of the volume contraction to the yield of polymer can be made by means of a gravimetrically determined calibration curve or by calculation from the specific volumes (see Example 3-6). 

Worked example 5.1 — soil water and air contents, and bulk density A soil core of 5 cm diameter and 8 cm height contains 257 g of fresh soil. After drying the soil at 110°C, the soil weighed 196 g. Calculate (i) the gravimetric soil water content, (ii) the volumetric soil water content, (iii) the soil bulk density, (iv) the % pore space, (v) the % water-filled pore space, and (vi) the % air-filled pore space. 

For example, the experimentally measured density of copper is 8.92 g/cm, the unit cell dimension of its cubic unit cell is a = 3.615 A, and the molecular mass of a formula unit is 63.55 a.m.u., which is the molar mass of copper, one atom per formula unit. Thus, Eq. 6.4 results in Z = 3.99 4 atoms per unit cell. The same equation may be used to calculate the density of a material when its crystal structure has been established. It is worth noting that the computed value of the material s gravimetric density is known as the x-ray density, and it is usually slightly higher than the measured density because real materials always have some defects and porosity that are not accounted in Eq. 6.4. 

As a final exercise, retrieve the spreadsheet that we created in Chapter 3 for the gravimetric determination of chloride, which we called grav chloride.xls. Enter formulas into cells B12—B14 to compute the mean, standard deviation, and the RSD in parts per thousand of the percent chloride in the samples. In this example, multiply the relative standard deviation by 1000 in cell B14. Adjust the decimal point in the results to display the proper number of significant figures. The worksheet below shows the results. Save your worksheet so that you can use it as a model for making laboratory calculations. 

Among the molecule or ion adsorption methods, gas adsorption is the most important one. It uses a reversible van der Waals adsorption or physisorption. A gas molecule adsorbed on the sample surface occupies a specific space. For example, the nitrogen molecule N2 requires a surface area of 16.2x 10 m. If one assumes that the entire surface of a powder sample, including those pores that are accessible to the molecules, is covered with a monomolecular layer of the adsorbate, the surface can be calculated from the number of adsorbed molecules and their space requirement. Measurements of the adsorbed amount of gas can be accomplished either volumetrically or gravimetrically and by means of carrier gas or radioactive methods. 

The various methods of determining an analyte can be classified as either absolute or relative. Absolute methods rely upon accurately known fundamental constants for calculating the amount of analyte, for example, atomic weights. In gravimetric analysis, for example, an insoluble derivative of the analyte of known chemical composition is prepared and weighed, as in the formation of AgCl for... 

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