Problem 21
The earliest determinations of elemental atomic weights were accomplished gravimetrically. To determine the atomic weight of manganese, a carefully purified sample of \(\mathrm{MnBr}_{2}\) weighing \(7.16539 \mathrm{~g}\) is dissolved and the \(\mathrm{Br}^{-}\) precipitated as \(\mathrm{AgBr}\), yielding \(12.53112 \mathrm{~g}\). What is the atomic weight for \(\mathrm{Mn}\) if the atomic weights for \(\mathrm{Ag}\) and \(\mathrm{Br}\) are taken to be 107.868 and 79.904 , respectively?
Problem 23
Asolidsamplehasapproximately equalamounts of two or more of the following soluble salts: \(\mathrm{AgNO}_{3}, \mathrm{ZnCl}_{2}, \mathrm{~K}_{2} \mathrm{CO}_{3}, \mathrm{MgSO}_{4}, \mathrm{Ba}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{2}\), and \(\mathrm{NH}_{4} \mathrm{NO}_{3} .\) A sample of the solid, sufficient to give at least 0.04 moles of any single salt, is added to \(100 \mathrm{~mL}\) of water, yielding a white precipitate and a clear solution. The precipitate is collected and rinsed with water. When a portion of the precipitate is placed in dilute \(\mathrm{HNO}_{3}\) it completely dissolves, leaving a colorless solution. A second portion of the precipitate is placed in dilute \(\mathrm{HCl}\), yielding a solid and a clear solution; when its filtrate is treated with excess \(\mathrm{NH}_{3}\), a white precipitate forms. Identify the salts that must be present in the sample, the salts that must be absent, and the salts for which there is insufficient information to make this determination. \({ }^{13}\)
Problem 24
Two methods have been proposed for the analysis of pyrite, \(\mathrm{FeS}_{2},\) in impure samples of the ore. In the first method, the sulfur in \(\mathrm{FeS}_{2}\) is determined by oxidizing it to \(\mathrm{SO}_{4}^{2-}\) and precipitating it as \(\mathrm{BaSO}_{4} .\) In the second method, the iron in \(\mathrm{FeS}_{2}\) is determined by precipitating the iron as \(\mathrm{Fe}(\mathrm{OH})_{3}\) and isolating it as \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) Which of these methods provides the more sensitive determination for pyrite? What other factors should you consider in choosing between these methods?
Problem 27
If a precipitate of known stoichiometry does not form, a gravimetric analysis is still feasible if we can establish experimentally the mole ratio between the analyte and the precipitate. Consider, for example, the precipitation gravimetric analysis of \(\mathrm{Pb}\) as \(\mathrm{PbCrO}_{4}{ }^{14}\) (a) For each gram of \(\mathrm{Pb}\), how many grams of \(\mathrm{PbCrO}_{4}\) will form, assuming the reaction is stoichiometric? (b) In a study of this procedure, Grote found that \(1.568 \mathrm{~g}\) of \(\mathrm{PbCrO}_{4}\) formed for each gram of \(\mathrm{Pb}\). What is the apparent stoichiometry between \(\mathrm{Pb}\) and \(\mathrm{PbCrO}_{4} ?\) (c) Does failing to account for the actual stoichiometry lead to a positive determinate error or a negative determinate error?
Problem 29
A \(38.63-\mathrm{mg}\) sample of potassium ozonide, \(\mathrm{KO}_{3}\), is heated to \(70^{\circ} \mathrm{C}\) for \(1 \mathrm{~h}\), undergoing a weight loss of \(7.10 \mathrm{mg}\). A 29.6 -mg sample of impure \(\mathrm{KO}_{3}\) experiences a \(4.86-\mathrm{mg}\) weight loss when treated under similar condition. What is the \(\% \mathrm{w} / \mathrm{w} \mathrm{KO}_{3}\) in the sample?
Problem 30
The water content of an \(875.4-\mathrm{mg}\) sample of cheese is determined with a moisture analyzer. What is the \(\% \mathrm{w} / \mathrm{w} \mathrm{H}_{2} \mathrm{O}\) in the cheese if the final mass was found to be \(545.8 \mathrm{mg} ?\)
Problem 32
The iron in an organometallic compound is determined by treating a \(0.4873-\mathrm{g}\) sample with \(\mathrm{HNO}_{3}\) and heating to volatilize the organic material. After ignition, the residue of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) weighs \(0.2091 \mathrm{~g}\). (a) What is the \(\% \mathrm{w} / \mathrm{w}\) Fe in this compound? (b) The carbon and hydrogen in a second sample of the compound are determined by a combustion analysis. When a \(0.5123-\mathrm{g}\) sample is carried through the analysis, \(1.2119 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.2482 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) re collected. What are the \(\% \mathrm{w} / \mathrm{w} \mathrm{C}\) and \(\% \mathrm{w} / \mathrm{w} \mathrm{H}\) in this compound and what is the compound's empirical formula?
Problem 34
In the presence of water vapor the surface of zirconia, \(\mathrm{ZrO}_{2}\), chemically adsorbs \(\mathrm{H}_{2} \mathrm{O},\) forming surface hydroxyls, \(\mathrm{ZrOH}\) (additional water is physically adsorbed as \(\mathrm{H}_{2} \mathrm{O}\) ). When heated above \(200^{\circ} \mathrm{C}\), the surface hydroxyls convert to \(\mathrm{H}_{2} \mathrm{O}(g),\) releasing one molecule of water for every two surface hydroxyls. Below \(200^{\circ} \mathrm{C}\) only physically absorbed water is lost. Nawrocki, et al. used thermogravimetry to determine the density of surface hydroxyls on a sample of zirconia that was heated to \(700^{\circ} \mathrm{C}\) and cooled in a desiccator containing humid \(\mathrm{N}_{2}{ }^{15}\) Heating the sample from \(200^{\circ} \mathrm{C}\) to \(900^{\circ} \mathrm{C}\) released \(0.006 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) for every gram of dehy- droxylated \(\mathrm{ZrO}_{2}\). Given that the zirconia had a surface area of \(33 \mathrm{~m}^{2} / \mathrm{g}\) and that one molecule of \(\mathrm{H}_{2} \mathrm{O}\) forms two surface hydroxyls, calculate the density of surface hydroxyls in \(\mu \mathrm{mol} / \mathrm{m}^{2}\).
Problem 35
The concentration of airborne particulates in an industrial workplace is determined by pulling the air for 20 min through a single-stage air sampler equipped with a glass-fiber filter at a rate of \(75 \mathrm{~m}^{3} / \mathrm{h}\). At the end of the sampling period, the filter's mass is found to have increased by \(345.2 \mathrm{mg}\). What is the concentration of particulates in the air sample in \(\mathrm{mg} / \mathrm{m}^{3}\) and \(\mathrm{mg} / \mathrm{L}\) ?
