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Chapter 11: Problem 59

Referring to Figure 11.28 , describe all the phase changes that would occur in each of the following cases: (a) Water vapor originally at \(500 \mathrm{~Pa}\) and \(-0.5^{\circ} \mathrm{C}\) is slowly compressed at constant temperature until the final pressure is $2000 \mathrm{kPa}\(. (b) Water originally at \)100.0^{\circ} \mathrm{C}\( and \)50 \mathrm{kPa}$ is cooled at constant pressure until the temperature is \(-10^{\circ} \mathrm{C}\).

Short Answer

Expert verified
In case (a), water vapor initially at \(500 \: \mathrm{Pa}\) and \(-0.5^{\circ} \mathrm{C}\) undergoes a phase change from vapor to liquid as it is compressed at constant temperature until the final pressure is \(2000 \: \mathrm{kPa}\). In case (b), water initially at \(100.0^{\circ} \mathrm{C}\) and \(50 \: \mathrm{kPa}\) undergoes three phase changes as it is cooled at constant pressure to \(-10^{\circ} \mathrm{C}\): first, the liquid water turns into water vapor as it cools below the boiling point; then, the water vapor turns back into liquid water as it cools below the condensation point; finally, the liquid water solidifies into ice as the temperature goes below the freezing point.

Step by step solution

01

Identify the initial state of water vapor

In this case, water vapor starts at a pressure of \(500\) Pa and a temperature of \(-0.5^{\circ} \mathrm{C}\).
02

Determine the final state of the water vapor

The water vapor is compressed at a constant temperature, so the temperature remains the same, \(-0.5^{\circ} \mathrm{C}\), and the pressure increases to \(2000 \mathrm{kPa}\) or \(2 \times 10^6 \mathrm{Pa}\).
03

Describe the phase changes that occur in this case

As the water vapor is compressed, it undergoes a phase change from vapor to liquid. As the pressure increases to the final value of \(2 \times 10^6 \mathrm{Pa}\) at a constant temperature of \(-0.5^{\circ}\mathrm{C}\), the water vapor becomes liquid water. #Phase Changes in Case (b)#
04

Identify the initial state of water

In this case, water starts at a temperature of \(100^{\circ} \mathrm{C}\) and a pressure of \(50 \mathrm{kPa}\) or \(5 \times 10^4 \mathrm{Pa}\).
05

Determine the final state of the water

The water is cooled at a constant pressure, so the pressure remains the same, \(5 \times 10^4 \mathrm{Pa}\), and the temperature decreases to \(-10^{\circ}\mathrm{C}\).
06

Describe the phase changes that occur in this case

As the water cools at a constant pressure, the following phase changes occur: 1. The liquid water starts to boil and turn into water vapor as it cools below the boiling point at this pressure (\(100^{\circ} \mathrm{C}\)). 2. After all the liquid water becomes vapor, the temperature keeps decreasing, and the water vapor turns back into liquid water as it cools below the condensation point at this pressure. 3. Finally, the temperature reaches \(-10^{\circ}\mathrm{C}\), which is below the freezing point of water at this pressure, and the liquid water solidifies into ice.

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Most popular questions from this chapter

Which type of intermolecular force accounts for each of these differences? (a) Acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO},\) boils at $56^{\circ} \mathrm{C} ;\( dimethyl sulfoxide or DMSO, (CH \)\left._{3}\right)_{2}$ SO, boils at \(189^{\circ}\) C. (b) \(\mathrm{CCl}_{4}\) is a liquid at atmospheric pressure and room temperature, whereas \(\mathrm{CH}_{4}\) is a gas under the same conditions. \((\mathbf{c})\) \(\mathrm{H}_{2} \mathrm{O}\) boils at \(100^{\circ} \mathrm{C}\) but \(\mathrm{H}_{2} \mathrm{~S}\) boils at \(-60^{\circ} \mathrm{C}\). (d) 1 -propanol boils at \(97^{\circ} \mathrm{C}\), whereas 2 -propanol boils at \(82.6^{\circ} \mathrm{C}\).

(a) What phase change is represented by the "heat of vaporization" of a substance? (b) Is the process of vaporization endothermic or exothermic? (c) If you compare a substance's heat of vaporization to the amount of heat released during condensation, which one is generally larger (consider the numerical value only)?

Benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH},\) melts at \(122^{\circ} \mathrm{C}\). The density in the liquid state at $130^{\circ} \mathrm{C}\( is \)1.08 \mathrm{~g} / \mathrm{cm}^{3} .$ The density of solid benzoic acid at \(15^{\circ} \mathrm{C}\) is $1.266 \mathrm{~g} / \mathrm{cm}^{3}$. (a) In which of these two states is the average distance between molecules greater? (b) If you converted a cubic centimeter of liquid benzoic acid into a solid, would the solid take up more, or less, volume than the original cubic centimeter of liquid?

Butane and 2-methylpropane, whose space-filling models are shown here, are both nonpolar and have the same molecular formula, $\mathrm{C}_{4} \mathrm{H}_{10}\(, yet butane has the higher boiling point \)\left(-0.5^{\circ} \mathrm{C}\right.\( compared to \)\left.-11.7^{\circ} \mathrm{C}\right) .$ Explain.

Describe how a cholesteric liquid crystalline phase differs from a smectic A liquid crystalline phase.
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