compressibility factor (Z)

ratio of the experimentally measured molar volume for a gas to its molar volume as computed from the ideal gas equation

van der Waals equation

modified version of the ideal gas equation containing additional terms to account for non-ideal gas behavior

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Chemistry 2e · 9.6 Non-Ideal Gas Behavior

Non-Ideal Gas Behavior: practice problems

4 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 99
Graphs showing the behavior of several different gases follow. Which of these gases exhibit behavior significantly different from that expected for ideal gases?
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Exercises 101
Under which of the following sets of conditions does a real gas behave most like an ideal gas, and for which conditions is a real gas expected to deviate from ideal behavior? Explain.
(a) high pressure, small volume
(b) high temperature, low pressure
(c) low temperature, high pressure
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Exercises 103
For which of the following gases should the correction for the molecular volume be largest:
CO, CO₂, H₂, He, NH₃, SF₆?
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Exercises 105
Answer the following questions:
(a) If XX behaved as an ideal gas, what would its graph of Z vs. P look like?
(b) For most of this chapter, we performed calculations treating gases as ideal. Was this justified?
(c) What is the effect of the volume of gas molecules on Z? Under what conditions is this effect small? When is it large? Explain using an appropriate diagram.
(d) What is the effect of intermolecular attractions on the value of Z? Under what conditions is this effect small? When is it large? Explain using an appropriate diagram.
(e) In general, under what temperature conditions would you expect Z to have the largest deviations from the Z for an ideal gas?
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Key terms · 2

compressibility factor (Z): ratio of the experimentally measured molar volume for a gas to its molar volume as computed from the ideal gas equation
van der Waals equation: modified version of the ideal gas equation containing additional terms to account for non-ideal gas behavior

Learn 9.6 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 9.6 in the textbook · This section on openstax.org

Non-Ideal Gas Behavior: practice problems

4 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 99

Graphs showing the behavior of several different gases follow. Which of these gases exhibit behavior significantly different from that expected for ideal gases?

This figure includes 6 graphs. The first, which is labeled, “Gas A,” has a horizontal axis labeled, “Temperature,” and a vertical axis labeled, “Volume.” A straight blue line segment extends from the lower left to the upper right of this graph. The open area in the lower right portion of the graph contains the label, “n, P constant.” The second, which is labeled, “Gas B,” has a horizontal axis labeled, “P,” and a vertical axis labeled, “P V.” A straight blue line segment extends horizontally across the center of this graph. The open area in the lower right portion of the graph contains the label, “n, T constant.” The third, which is labeled, “Gas C,” has a horizontal axis labeled,“P V divided by R T,” and a vertical axis labeled, “Moles.” A blue curve begins about halfway up the vertical axis, dips slightly, then increases steadily to the upper right region of the graph. The fourth, which is labeled, “Gas D,” has a horizontal axis labeled, “P V divided by R T,” and a vertical axis labeled, “Moles.” A straight blue line segment extends horizontally across the center of this graph. The open area in the lower right portion of the graph contains the label “n, P constant.” The fifth, which is labeled, “Gas E,” has a horizontal axis labeled, “Temperature,” and a vertical axis labeled, “Volume.” A blue curve extends from the lower left to the upper right of this graph. The open area in the lower right portion of the graph contains the label “n, P constant.” The sixth graph, which is labeled, “Gas F,” has a horizontal axis labeled, “Temperature,” and a vertical axis labeled, “Pressure.” A blue curve begins toward the lower left region of the graph, increases at a rapid rate, then continues to increase at a relatively slow rate moving left to right across the graph. The open area in the lower right portion of the graph contains the label, “n, V constant.”

Exercises 101

Under which of the following sets of conditions does a real gas behave most like an ideal gas, and for which conditions is a real gas expected to deviate from ideal behavior? Explain.

(a) high pressure, small volume

(b) high temperature, low pressure

Exercises 103

For which of the following gases should the correction for the molecular volume be largest:

CO, CO₂, H₂, He, NH₃, SF₆?

Exercises 105

Answer the following questions:

(a) If XX behaved as an ideal gas, what would its graph of Z vs. P look like?

(b) For most of this chapter, we performed calculations treating gases as ideal. Was this justified?

(c) What is the effect of the volume of gas molecules on Z? Under what conditions is this effect small? When is it large? Explain using an appropriate diagram.

(d) What is the effect of intermolecular attractions on the value of Z? Under what conditions is this effect small? When is it large? Explain using an appropriate diagram.

(e) In general, under what temperature conditions would you expect Z to have the largest deviations from the Z for an ideal gas?

Key terms · 2

compressibility factor (Z): ratio of the experimentally measured molar volume for a gas to its molar volume as computed from the ideal gas equation
van der Waals equation: modified version of the ideal gas equation containing additional terms to account for non-ideal gas behavior

Learn 9.6 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 9.6 in the textbook · This section on openstax.org