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Chapter 12: Problem 62
Diamond is often used as a cutting medium in glass cutters. What property of diamond makes this possible? Could graphite function as well?
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One of the following substances is a liquid at room temperature and the others are gaseous: \(\mathrm{CH}_{3} \mathrm{OH}\) \(\mathrm{C}_{3} \mathrm{H}_{8} ; \mathrm{N}_{2} ; \mathrm{N}_{2} \mathrm{O} .\) Which do you think is the liquid? Explain.
One handbook lists the sublimation pressure of solid benzene as a function of Kelvin temperature, \(T\), as \(\log \mathrm{P}(\mathrm{mmHg})=9.846-2309 / \mathrm{T} .\) Another hand- book lists the vapor pressure of liquid benzene as a function of Celsius temperature, \(t,\) as \(\log P(\mathrm{mmHg})=\) \(6.90565-1211.033 /(220.790+t) .\) Use these equations to estimate the normal melting point of benzene, and compare your result with the listed value of \(5.5^{\circ} \mathrm{C}\)
In an ionic crystal lattice each cation will be attracted by anions next to it and repulsed by cations near it. Consequently the coulomb potential leading to the lattice energy depends on the type of crystal. To get the total lattice energy you must sum all of the electrostatic interactions on a given ion. The general form of the electrostatic potential is $$V=\frac{Q_{1} Q_{2} e^{2}}{d_{12}}$$ where \(Q_{1}\) and \(Q_{2}\) are the charges on ions 1 and \(2, d_{12}\) is the distance between them in the crystal lattice. and \(e\) is the charge on the electron. (a) Consider the linear "crystal" shown below. The distance between the centers of adjacent spheres is \(R .\) Assume that the blue sphere and the green spheres are cations and that the red spheres are anions. Show that the total electrostatic energy is $$V=-\frac{Q^{2} e^{2}}{d} \times \ln 2$$ (b) In general, the electrostatic potential in a crystal can be written as $$V=-k_{M} \frac{Q^{2} e^{2}}{R}$$ where \(k_{M}\) is a geometric constant, called the Madelung constant, for a particular crystal system under consideration. Now consider the NaCl crystal structure and let \(R\) be the distance between the centers of sodium and chloride ions. Show that by considering three layers of nearest neighbors to a central chloride ion, \(k_{M}\) is given by $$k_{M}=\left(6-\frac{12}{\sqrt{2}}+\frac{8}{\sqrt{3}}-\frac{6}{\sqrt{4}} \cdots\right)$$ (c) Carry out the same calculation for the CsCl structure. Are the Madelung constants the same?
Explain the important distinctions between each pair of terms: (a) adhesive and cohesive forces; (b) vaporization and condensation; (c) triple point and critical point; (d) face-centered and body-centered cubic unit cell; (e) tetrahedral and octahedral hole.
A 7.53 I. sample of \(\mathrm{N}_{2}(\mathrm{g})\) at \(742 \mathrm{mmHg}\) and \(45.0^{\circ} \mathrm{C}\) is bubbled through \(\mathrm{CCl}_{4}(1)\) at \(45.0^{\circ} \mathrm{C} .\) Assuming the gas becomes saturated with \(\mathrm{CCl}_{4}(\mathrm{g}),\) what is the volume of the resulting gaseous mixture, if the total pressure remains at \(742 \mathrm{mm} \mathrm{Hg}\) and the temperature remains at \(45^{\circ} \mathrm{C} ?\) The vapor pressure of \(\mathrm{CCl}_{4}\) at \(45^{\circ} \mathrm{C}\) is \(261 \mathrm{mmHg}\)
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