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Chapter 6: Problem 9
What are the basic SI units for (a) the wavelength of light, (b) the frequency of light, (c) the speed of light?
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(a) What are "valence electrons"? (b) What are "core electrons"?(c) What does each box in an orbital diagram represent? (d) What quantity is represented by the direction (up or down) of the half-arrows in an orbital diagram?
For each of the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed during the transition: (a) from \(n=4\) to \(n=1\), (b) from \(n=5\) to \(n=2,(\mathrm{c})\) from \(n=3\) to \(n=6\). Does any of these transitions emit or absorb visible light?
(a) Account for formation of the following series of oxides in terms of the electron configurations of the elements and the discussion of ionic compounds in Section 2.7: \(\mathrm{K}_{2} \mathrm{O}, \mathrm{CaO}, \mathrm{Sc}_{2} \mathrm{O}_{3}, \mathrm{TiO}_{2}, \mathrm{~V}_{2} \mathrm{O}_{5}, \mathrm{CrO}_{3}\) (b) Name these oxides. (c) Consider the metal oxides whose enthalpies of formation (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) are listed here. $$\begin{array}{lllll} \text { Oxide } & \mathrm{K}_{2} \mathrm{O}(s) & \mathrm{CaO}(s) & \mathrm{TiO}_{2}(s) & \mathrm{V}_{2} \mathrm{O}_{5}(s) \\ \hline \Delta H_{f}^{\circ} & -363.2 & -635.1 & -938.7 & -1550.6 \\ \hline \end{array}$$ Calculate the enthalpy changes in the following general reaction for each case: $$\mathrm{M}_{n} \mathrm{O}_{m}(s)+\mathrm{H}_{2}(g) \longrightarrow n \mathrm{M}(s)+m \mathrm{H}_{2} \mathrm{O}(g)$$ (You will need to write the balanced equation for each case, then compute \(\Delta H^{\circ} .\) ) (d) Based on the data given, estimate a value of \(\Delta H_{f}^{\circ}\) for \(\mathrm{Sc}_{2} \mathrm{O}_{3}(s)\).
The series of emission lines of the hydrogen atom for which \(n_{f}=3\) is called the Paschen series. (a) Determine the region of the electromagnetic spectrum in which the lines of the Paschen series are observed. (b) Calculate the wavelengths of the first three lines in the Paschen series - those for which \(n_{i}=4,5\), and 6 .
The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58-71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and \(G\). von Hevesy, working in Bohr's laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (a) How would you use electron configuration arguments to justify Bohr's prediction? (b) Zirconium, hafnium's neighbor in group \(4 \mathrm{~B}\), can be produced as a metal by reduction of solid \(\mathrm{ZrCl}_{4}\) with molten sodium metal. Write a balanced chemical equation for the reaction. Is this an oxidation- reduction reaction? If yes, what is reduced and what is oxidized? (c) Solid zirconium dioxide, \(\mathrm{ZrO}_{2}\), is reacted with chlorine gas in the presence of carbon. The products of the reaction are \(\mathrm{ZrCl}_{4}\) and two gases, \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\) in the ratio \(1: 2 \mathrm{Write}\) a balanced chemical equation for the reaction. Starting with a 55.4-g sample of \(\mathrm{ZrO}_{2}\), calculate the mass of \(\mathrm{ZrCl}_{4}\) formed, assuming that \(\mathrm{ZrO}_{2}\) is the limiting reagent and assuming \(100 \%\) yield. (d) Using their electron configurations, account for the fact that \(\mathrm{Zr}\) and Hf form chlorides \(\mathrm{MCl}_{4}\) and oxides \(\mathrm{MO}_{2}\).
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