Question

Argon gas has its triple point at \(-189.3^{\circ} \mathrm{C}\) and \(516 \mathrm{~mm} \mathrm{Hg} .\) It has a critical point at \(-122{ }^{\circ} \mathrm{C}\) and 48 atm. The density of the solid is \(1.65 \mathrm{~g} / \mathrm{cm}^{3}\), whereas that of the liquid is \(1.40 \mathrm{~g} / \mathrm{cm}^{3}\). Sketch the phase diagram for argon and use it to fill in the blanks below with the words "boils," "melts," "sublimes," or "condenses." (a) Solid argon at \(500 \mathrm{~mm} \mathrm{Hg}\) __________ when the temperature is increased. (b) Solid argon at 2 atm _________ when the temperature is increased. (c) Argon gas at \(-150^{\circ} \mathrm{C}\) _____________when the pressure is increased. (d) Argon gas at \(-165^{\circ} \mathrm{C}\) _____________ when the pressure is increased.

Short answer

(a) Solid argon at 500 mm Hg when the temperature is increased: __sublimes__ (b) Solid argon at 2 atm when the temperature is increased: __melts__ (c) Argon gas at -150°C when the pressure is increased: __condenses__ (d) Argon gas at -165°C when the pressure is increased: __sublimes__

Step-by-step solution

Draw the phase diagram

First, let's sketch the phase diagram for argon based on the given information: 1. Triple point: \(-189.3^{\circ}\mathrm{C}\) and \(0.516~\mathrm{atm}\) 2. Critical point: \(-122^{\circ}\mathrm{C}\) and \(48~\mathrm{atm}\) 3. Densities: - Solid phase: \(1.65~\mathrm{g/cm}^3\) - Liquid phase: \(1.40~\mathrm{g/cm}^3\) The phase diagram should display temperature (\(x\)-axis) against pressure (\(y\)-axis): - The solid-liquid boundary should show a positive slope due to the solid having a higher density than the liquid. - The triple point and critical point should be as given by their coordinates.

Analyze each case

Now, we will use the phase diagram to analyze each case (a to d) and fill in the blanks. (a) Solid argon at \(500~\mathrm{mm} \mathrm{Hg}\) (or \(0.657~\mathrm{atm}\)) when the temperature is increased: Looking at the phase diagram, when we increase the temperature at a constant pressure above the triple point pressure, we see that solid argon transitions directly to the gas phase. Therefore, solid argon sublimes. (b) Solid argon at \(2~\mathrm{atm}\) when the temperature is increased: At this pressure, again looking at the phase diagram, when we increase the temperature, we see that solid argon transitions to the liquid phase. Therefore, solid argon melts. (c) Argon gas at \(-150^{\circ} \mathrm{C}\) when the pressure is increased: In the argon phase diagram, when the pressure is increased at a constant temperature below the critical temperature, argon gas changes to a liquid phase. Therefore, argon gas condenses. (d) Argon gas at \(-165^{\circ} \mathrm{C}\) when the pressure is increased: Here, looking at the phase diagram, when the pressure is increased at this temperature, the argon gas changes directly to the solid phase. Therefore, argon gas sublimes.

Final answer

Using the phase diagram and the analysis of each case, we can fill in the blanks: (a) Solid argon at \(500~\mathrm{mm} \mathrm{Hg}\) sublimes when the temperature is increased. (b) Solid argon at 2 atm melts when the temperature is increased. (c) Argon gas at \(-150^{\circ} \mathrm{C}\) condenses when the pressure is increased. (d) Argon gas at \(-165^{\circ} \mathrm{C}\) sublimes when the pressure is increased.