Compressibility factor, $Z$

The ratio of a gas's measured molar volume to the ideal-gas molar volume at the same temperature and pressure: $Z=PV_m/RT$.

What does $Z<1$ indicate?

The measured molar volume is smaller than the ideal-gas prediction at the same temperature and pressure.

Why does molecular volume matter more at high pressure?

Crowded molecules occupy a more significant fraction of the gas's total volume.

How can intermolecular attractions affect pressure at constant volume?

They can reduce pressure by pulling molecules toward one another and away from the container walls.

What do the van der Waals constants $a$ and $b$ represent?

$a$ measures attraction strength; $b$ represents effective molecular size.

General chemistryLesson 6 of 6 in the course Gases

Nonideal Gases: Compressibility and the van der Waals Model

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

The ideal gas law, $PV=nRT$ , works well in many situations, but real gases do not always follow it exactly. This lesson introduces the compressibility factor and explains how molecular size and intermolecular attractions cause deviations from ideal behavior.

$Z=\frac{V_{m,\text{measured}}}{V_{m,\text{ideal}}}=\frac{PV_m}{RT}$

For an ideal gas, $PV_m=RT$ , so $Z=1$ . A real gas with $Z$ different from 1 does not match ideal-gas predictions under those conditions. A value below 1 means the measured molar volume is smaller than the ideal prediction; a value above 1 means it is larger.

All flashcards

Compressibility factor, $Z$: The ratio of a gas's measured molar volume to the ideal-gas molar volume at the same temperature and pressure: $Z=PV_m/RT$ .
What does $Z<1$ indicate?: The measured molar volume is smaller than the ideal-gas prediction at the same temperature and pressure.
Why does molecular volume matter more at high pressure?: Crowded molecules occupy a more significant fraction of the gas's total volume.
How can intermolecular attractions affect pressure at constant volume?: They can reduce pressure by pulling molecules toward one another and away from the container walls.
What do the van der Waals constants $a$ and $b$ represent?: $a$ measures attraction strength; $b$ represents effective molecular size.

Quiz questions

Which equation is the van der Waals equation for $n$ moles of gas?Answer: $(P+a n^2/V^2)(V-nb)=nRT$
In the van der Waals equation, what does the constant $a$ represent?Answer: The strength of intermolecular attractions
In the van der Waals equation, what does the constant $b$ represent?Answer: The effective size of the gas molecules
When does the van der Waals equation approach the ideal gas law?Answer: When molecules are far apart, making both corrections small
Which expression gives pressure after rearranging the van der Waals equation?Answer: $P=\frac{nRT}{V-nb}-a\frac{n^2}{V^2}$

Based on Chemistry 2e by Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson, PhD (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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