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Chapter 9: Problem 70

A liquid has a vapor pressure of \(159 \mathrm{~mm} \mathrm{Hg}\) at \(20^{\circ} \mathrm{C}\) and \(165 \mathrm{~mm} \mathrm{Hg}\) at \(30^{\circ} \mathrm{C}\). Different amounts of the liquid are added to three identical evacuated steel tanks kept at \(20^{\circ} \mathrm{C}\). The tanks are all fitted with pressure gauges. For each part, write \(\mathbf{L} / \mathbf{G}\) if both liquid and gas are present. G if only gas is present. I if the situation is impossible. (a) The pressure gauge in Flask I registers a pressure of \(256 \mathrm{~mm} \mathrm{Hg}\). (b) The pressure gauge in Flask II registers a pressure of \(135 \mathrm{~mm} \mathrm{Hg}\). (c) The pressure gauge in Flask III registers a pressure of \(165 \mathrm{~mm} \mathrm{Hg}\) at \(30^{\circ} \mathrm{C}\). The temperature is lowered to \(20^{\circ} \mathrm{C}\), and the gauge registers a pressure of \(159 \mathrm{~mm} \mathrm{Hg}\).

Short Answer

Expert verified
Answer: In Flask I, both liquid and gas (L/G) are present. In Flask II, only gas (G) is present. In Flask III, both liquid and gas (L/G) are present.

Step by step solution

01

Recall the concept of vapor pressure

Vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid (or solid) phase at a given temperature. The higher the temperature, the higher the vapor pressure (usually). In this exercise, the vapor pressure of the liquid is given at two temperatures, 20°C and 30°C.
02

Analyze Flask I

In Flask I, the pressure gauge registers a pressure of 256 mm Hg at 20°C. Recall that the vapor pressure at 20°C is 159 mm Hg. Since the measured pressure (256 mm Hg) is greater than the vapor pressure (159 mm Hg), there must be both liquid and gas present in the flask. Therefore, the answer for Flask I is L/G.
03

Analyze Flask II

In Flask II, the pressure gauge registers a pressure of 135 mm Hg at 20°C. Recall that the vapor pressure at 20°C is 159 mm Hg. Since the measured pressure (135 mm Hg) is lower than the vapor pressure (159 mm Hg), only gas is present in the flask. Hence, the answer for Flask II is G.
04

Analyze Flask III

In Flask III, the pressure gauge registers a pressure of 165 mm Hg at 30°C. Recall that the vapor pressure at 30°C is 165 mm Hg. The pressure gauge measures the same pressure as the vapor pressure as the temperature is lowered to 20°C, the gauge registers a pressure of 159 mm Hg, which is the vapor pressure at 20°C. Since the measured pressure is equal to the vapor pressure at both temperatures, there must be both liquid and gas present in equilibrium with each other in the flask. Consequently, the answer for Flask III is L/G.

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Most popular questions from this chapter

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 \(60^{\circ} \mathrm{C}\).

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Of the four general types of solids, which one(s) (a) are generally insoluble in water? (b) have very high melting points? (c) conduct electricity as solids?

19\. 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 \(48 \mathrm{~atm}\). 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 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.

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