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Chapter 9: Problem 21

Given the following data about xenon, $$ \begin{aligned} &\text { normal boiling point }=-108^{\circ} \mathrm{C} \\ &\text { normal melting point }=-112^{\circ} \mathrm{C} \\ &\text { triple point }=-121^{\circ} \mathrm{C} \text { at } 281 \mathrm{~mm} \mathrm{Hg} \\ &\text { critical point }=16.6^{\circ} \mathrm{C} \text { at } 58 \mathrm{~atm} \end{aligned} $$ (a) Construct an approximate phase diagram for xenon. (b) Estimate the vapor pressure of xenon at \(-115^{\circ} \mathrm{C}\). (c) Is the density of solid Xe larger than that for liquid Xe?

Short Answer

Expert verified
Question: Based on the constructed phase diagram for Xenon, estimate the vapor pressure of Xenon at -115°C, and determine if the density of solid Xenon is greater than the density of liquid Xenon. Answer: At -115°C, the vapor pressure of Xenon can be estimated by finding the corresponding pressure on the liquid-gas boundary line in the phase diagram. Additionally, since the slope of the solid-liquid boundary line is negative, the density of solid Xenon is greater than the density of liquid Xenon.

Step by step solution

01

1. Plot the phase diagram for Xenon

To construct the phase diagram, we need to plot the given temperature and pressure points for each phase transition. We know the normal boiling point, normal melting point, triple point, and critical point of xenon. Plot these points on a pressure-temperature (P-T) graph with temperature on the x-axis and pressure on the y-axis.
02

2. Identify phase boundaries

Based on the location of the plotted points on the P-T graph, draw phase boundaries to separate the different phases: solid, liquid, and gas. 1. Solid-liquid boundary: Connect the normal melting point and the solid-liquid side of the triple point with a straight line. 2. Liquid-gas boundary: Connect the normal boiling point and the liquid-gas side of the triple point with a straight line. 3. Solid-gas boundary: Connect the critical point and the solid-gas side of the triple point with a curve that follows the general shape of a phase diagram. Now the phase diagram for xenon is complete.
03

3. Estimate the vapor pressure at given temperature

From the phase diagram, look at the liquid-gas boundary line to estimate the vapor pressure of xenon at \(-115^{\circ}\mathrm{C}\). At this temperature, the liquid-xenon and gas-xenon phases coexist, which means the pressure along this line represents the vapor pressure at that temperature.
04

4. Compare solid and liquid Xe densities

To determine if the density of solid Xe is larger than that of liquid Xe, look at the solid-liquid boundary in the phase diagram. If the solid-liquid boundary slope is positive, the density of solid Xe is smaller than that of liquid Xe. If the slope is negative, the density of solid Xe is larger than that of liquid Xe. Since the slope is negative, the density of solid Xe is larger than that of liquid Xe.

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Most popular questions from this chapter

In the blanks provided, answer the questions below, using LT (for is less than), GT (for is greater than), \(\mathrm{EQ}\) (for is equal to), or MI (for more information required). (a) The boiling point of \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(\mathrm{MM}=60.0 \mathrm{~g} / \mathrm{mol})\) the boiling point of \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{C}=\mathrm{O}(\mathrm{MM}=58.0 \mathrm{~g} / \mathrm{mol})\). (b) The vapor pressure of \(\mathrm{X}\) is \(250 \mathrm{~mm} \mathrm{Hg}\) at \(57^{\circ} \mathrm{C}\). Given a sealed flask at \(57^{\circ} \mathrm{C}\) that contains only gas, the pressure in the flask \(245 \mathrm{~mm} \mathrm{Hg}\) (c) The melting-point curve for Y tilts to the right of a straight line. The density of \(\mathrm{Y}(l) \quad\) the density of \(\mathrm{Y}(s)\). (d) The normal boiling point of \(\mathrm{A}\) is \(85^{\circ} \mathrm{C}\), while the normal boiling point of \(\mathrm{B}\) is \(45^{\circ} \mathrm{C}\). The vapor pressure of \(\mathrm{A}\) at \(85^{\circ} \mathrm{C}\) pressure of \(\mathrm{B}\) at \(45^{\circ} \mathrm{C}\). (e) The triple point of \(A\) is \(25 \mathrm{~mm} \mathrm{Hg}\) and \(5^{\circ} \mathrm{C}\). The melting point of \(\mathrm{A}\) \(5^{\circ} \mathrm{C}\)

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Which of the following would you expect to show dispersion forces? Dipole forces? (a) \(\mathrm{PH}_{3}\) (b) \(\mathrm{N}_{2}\) (c) \(\mathrm{CH}_{4}\) (d) \(\mathrm{H}_{2} \mathrm{O}\)

Benzene, a known carcinogen, was once widely used as a solvent. \(\mathrm{A}\) sample of benzene vapor in a flask of constant volume exerts a pressure of \(325 \mathrm{~mm} \mathrm{Hg}\) at \(80^{\circ} \mathrm{C}\). The flask is slowly cooled. (a) Assuming no condensation, use the ideal gas law to calculate the pressure of the vapor at \(50^{\circ} \mathrm{C} ;\) at \(60^{\circ} \mathrm{C}\). (b) Compare your answers in (a) to the equilibrium vapor pressures of benzene: \(269 \mathrm{~mm} \mathrm{Hg}\) at \(50^{\circ} \mathrm{C}, 389 \mathrm{~mm} \mathrm{Hg}\) at \(60^{\circ} \mathrm{C}\). (c) On the basis of your answers to (a) and (b), predict the pressure exerted by the benzene at \(50^{\circ} \mathrm{C} ;\) at \(60^{\circ} \mathrm{C}\).

Which of the following statements are true? (a) The critical temperature must be reached to change liquid to gas. (b) To melt a solid at constant pressure, the temperature must be above the triple point. (c) \(\mathrm{CHF}_{3}\) can be expected to have a higher boiling point than \(\mathrm{CHCl}_{3}\) because CHF \(_{3}\) has hydrogen bonding. (d) One metal crystallizes in a body-centered cubic cell and another in a face-centered cubic cell of the same volume. The two atomic radii are related by the factor \(\sqrt{1.5}\)
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