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Chapter 11: Problem 95

Describe the behavior of carbon dioxide gas when compressed at the following temperatures: a. \(20^{\circ} \mathrm{C}\) b. \(-70^{\circ} \mathrm{C}\) c. \(40^{\circ} \mathrm{C}\) The triple point of carbon dioxide is \(-57^{\circ} \mathrm{C}\) and \(5.1 \mathrm{~atm}\), and the critical point is \(31^{\circ} \mathrm{C}\) and 73 atm.

Short Answer

Expert verified
20掳C: liquid possible; -70掳C: solid (dry ice); 40掳C: supercritical fluid.

Step by step solution

01

Understanding the Problem

We need to determine the behavior of carbon dioxide gas when compressed at different temperatures. This involves knowing where these temperatures lie with respect to key points such as the triple point and the critical point of CO2.
02

Identify Key Points

The triple point of CO2 is at -57掳C and 5.1 atm, where solid, liquid, and gas phases coexist. The critical point is at 31掳C and 73 atm, where the gas can't be liquefied by pressure alone.
03

Analyze Behavior at 20掳C

At 20掳C, CO2 is above the triple point but below the critical point. This means it will remain a gas and can be condensed into a liquid if the pressure is increased sufficiently (up to the critical pressure of 73 atm).
04

Analyze Behavior at -70掳C

At -70掳C, CO2 is below the triple point. Here, upon compression, CO2 is more likely to transition to a solid state, known as dry ice, due to sublimation rather than becoming liquid.
05

Analyze Behavior at 40掳C

At 40掳C, CO2 is above the critical point. In this state, compressing it won't result in condensation into a liquid; it will remain a supercritical fluid, exhibiting properties of both gases and liquids.
06

Summarize the Findings

At 20掳C, CO2 can turn into a liquid with sufficient pressure; at -70掳C it transitions to solid form; at 40掳C, it stays a supercritical fluid, regardless of pressure increase.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Critical Point
The critical point is an important concept when considering the phase behavior of substances like carbon dioxide. At the critical point, a substance cannot exist as a distinct liquid or gas. For carbon dioxide, this occurs at 31掳C and 73 atm. At this juncture, the liquid and gas phases become indistinguishable, forming what is known as a supercritical fluid.
  • Beyond the critical temperature, no amount of pressure can liquefy the gas.
  • The density of the fluid is somewhere between that of a gas and a liquid.
Understanding the critical point is key to manipulating substances for industrial and scientific purposes, such as in supercritical fluid extraction techniques.
Triple Point
The triple point is the temperature and pressure at which a substance can coexist in solid, liquid, and gas phases. For carbon dioxide, this point is at -57掳C and 5.1 atm. At the triple point:
  • Solid, liquid, and vapor phases are in equilibrium.
  • Slight changes in temperature or pressure can cause phase transitions.
Understanding the triple point is vital for contexts where phase transitions are carefully controlled, like in cryogenics and material sciences.
Supercritical Fluid
A supercritical fluid arises when a substance is above its critical temperature and pressure. For CO2, this state occurs above 31掳C at pressures higher than 73 atm. In this state, CO2 behaves neither just as a gas nor as a liquid, but with mixed characteristics:
  • Flows like a gas, which allows it to easily penetrate materials.
  • Dissolves substances like a liquid, useful in applications such as decaffeinating coffee.
Using supercritical CO2 is beneficial in industries due to its low toxicity and environmental impact compared to conventional solvents.
Sublimation
Sublimation is the process by which a solid turns directly into a gas without passing through a liquid phase. For carbon dioxide, this can occur below its triple point at -57掳C. This is commonly observed with dry ice when:
  • CO2 transitions directly from solid to gas as it absorbs heat.
  • Applicable in cooling and creating fog effects in special events.
Sublimation is advantageous for preserving temperature-sensitive goods in transport and storage due to its quick phase transition under atmospheric pressure.
Phase Transition
Phase transitions involve a substance changing from one state of matter to another, typically between solid, liquid, and gas forms. For carbon dioxide:
  • At 20掳C, it transitions between gas and liquid under sufficient pressure.
  • Below its triple point, it transitions from solid to gas by sublimation.
  • At 40掳C, it remains in a supercritical state.
Phase transitions are pivotal in fields like climatology and engineering, where understanding how substances change states under different conditions is critical for process optimizations and innovations.

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Most popular questions from this chapter

Calculate the percent of volume that is actually occupied by spheres in a body-centered cubic lattice of identical spheres. You can do this by first relating the radius of a sphere, \(r\), to the length of an edge of a unit cell, \(l\). (Note that the spheres do not touch along an edge, but do touch along a diagonal passing through the body-centered sphere.) Then calculate the volume of a unit cell in terms of \(r .\) The volume occupied by spheres equals the number of spheres per unit cell times the volume of a sphere \(\left(4 \pi r^{3} / 3\right)\).

The heats of vaporization of liquid \(\mathrm{O}_{2}\), liquid Ne, and liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), are \(6.8 \mathrm{~kJ} / \mathrm{mol}, 1.8 \mathrm{~kJ} / \mathrm{mol}\), and \(34.5 \mathrm{~kJ} / \mathrm{mol}\), respectively. Are the relative values as you would expect? Explain.

Describe the face-centered cubic unit cell.

Steam at \(100^{\circ} \mathrm{C}\) was passed into a flask containing \(275 \mathrm{~g}\) of water at \(21^{\circ} \mathrm{C}\), where the steam condensed. How many grams of steam must have condensed if the temperature of the water in the flask was raised to \(83{ }^{\circ} \mathrm{C} ?\) The heat of vaporization of water at \(100^{\circ} \mathrm{C}\) is \(40.7 \mathrm{~kJ} / \mathrm{mol}\) and the specific heat is \(4.18 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\)

Pentylamine, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\), is a liquid that boils at \(104^{\circ} \mathrm{C}\) and has a viscosity of \(10 \times 10^{-4} \mathrm{~kg} /(\mathrm{m} \cdot \mathrm{s})\) Triethylamine, \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{3} \mathrm{~N}\), is a liquid that boils at \(89^{\circ} \mathrm{C}\) and has a viscosity of about \(4 \times 10^{-4} \mathrm{~kg} /(\mathrm{m} \cdot \mathrm{s})\). Explain the differences in properties of these two compounds.
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