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Chapter 28: Q3TY (page 775)
By what factor must the mass increase to reduce the sampling standard deviation by a factor of 2?
The mass needs to be increased four times to reduce the sampling standard deviation by a factor of 2.
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Barium titanate, a ceramic used in electronics, was analyzed by the following procedure: Into a Pt crucible was placed \(1.2\;{\rm{g}}\)of \({\rm{N}}{{\rm{a}}_2}{\rm{C}}{{\rm{O}}_3}\) and \(0.8\;{\rm{g}}\)of \({\rm{N}}{{\rm{a}}_2}\;{{\rm{B}}_4}{{\rm{O}}_7}\)plus \(0.3146\;{\rm{g}}\)of unknown. After fusion at \({1000^\circ }{\rm{C}}\)in a furnace for\(30\;{\rm{min}}\), the cooled solid was extracted with \(50\;{\rm{mL}}\)of\(6{\rm{MHCl}}\), transferred to a \(100 - {\rm{mL}}\) volumetric flask, and diluted to the mark. A \(25.00 - {\rm{mL}}\)aliquot was treated with \(5\;{\rm{mL}}\)of \(15\% \)tartaric acid (which complexes \({\rm{T}}{{\rm{i}}^{4 + }}\)and keeps it in aqueous solution) and \(25\;{\rm{mL}}\)of ammonia buffer,\({\rm{pH}}9.5\). The solution was treated with organic reagents that complex\({\rm{B}}{{\rm{a}}^{2 + }}\), and the \({\rm{Ba}}\)complex was extracted into \({\rm{CC}}{{\rm{l}}_4}.\)After acidification (to release the \({\rm{B}}{{\rm{a}}^{2 + }}\) from its organic complex), the \({\rm{B}}{{\rm{a}}^{2 + }}\)was backextracted into\(0.1{\rm{MHCl}}\). The final aqueous sample was treated with ammonia buffer and methylthymol blue (a metal ion indicator) and titrated with \(32.49\;{\rm{mL}}\) of \(0.01144{\rm{M}}\)EDTA. Find the weight per cent of Ba in the ceramic.
To pre-concentrate cocaine and benzoylecgonine from river water described at the opening of this chapter, solid-phase extraction was carried out at \({\rm{pH}}\,\,2\) using the mixed-mode cation-exchange resin in Figure 28-19. After passing \(500\;{\rm{mL}}\)of river water through \(60{\rm{mg}}\)of resin, the retained analytes were eluted first with \(2\;{\rm{mL}}\)of \({\rm{C}}{{\rm{H}}_3}{\rm{OH}}\)and then with \(2\;\,\,{\rm{mL }}of\,\,\,2\% \) ammonia solution in\({\rm{C}}{{\rm{H}}_3}{\rm{OH}}\). Explain the purpose of using \({\rm{pH}}2\) for retention and dilute ammonia for elution.
Question: Consider a random mixture containing \(4.00\;{\rm{g}}\)of \({\rm{N}}{{\rm{a}}_2}{\rm{C}}{{\rm{O}}_3}\) (density\(2.532g/mL\)) and \(96.00\;{\rm{g}}\)of \({{\rm{K}}_2}{\rm{C}}{{\rm{O}}_3}\) (density\(2.428\;{\rm{g}}/{\rm{mL}}\)) with a uniform spherical particle radius of\(0.075\;{\rm{mm}}\).
(a) Calculate the mass of a single particle of \({\rm{N}}{{\rm{a}}_2}{\rm{C}}{{\rm{O}}_3}\) and the number of particles of \({\rm{N}}{{\rm{a}}_2}{\rm{C}}{{\rm{O}}_3}\) in the mixture. Do the same for\({{\rm{K}}_2}{\rm{C}}{{\rm{O}}_3}\).
(b) What is the expected number of particles in \(0.100\;{\rm{g}}\)of the mixture?
(c) Calculate the relative sampling standard deviation in the number of particles of each type in a \(0.100\;{\rm{g}}\)sample of the mixture.
How many 2.8-g samples must be analyzed to give 95% confidence that the mean is known to within ±4%?
In an experiment analogous to that in Figure 28-3, the sampling constant is found to be \({K_{\rm{s}}} = 20\;{\rm{g}}.\)
(a) What mass of sample is required for a \( \pm 2\% \)sampling standard deviation?
(b) How many samples of the size in part (a) are required to produce \(90\% \)confidence that the mean is known to within\(1.5\% \)?
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