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For one mole of a van der Waals gas at low pressure, Z = 1 - a/(RTV). This relation indicates that under these conditions the gas is:

Answer: more compressible than ideal, Z below one.

A exactly ideal, with Z equal to one
B more compressible than ideal, Z below one
C not compressible under any condition
D less compressible than ideal, Z above one

Correct answer: B. more compressible than ideal, Z below one

Explanation: The attractive-force term a/(RTV) makes Z less than 1, so the real gas is more compressible than an ideal gas at low pressure.

Graph of pressure versus volume for a fixed amount of gas at constant temperature: the curve falls steeply then flattens, a hyperbola showing pressure inversely proportional to volume.

Boyle's law: at constant temperature the pressure of a fixed mass of gas is inversely proportional to its volume (P ∝ 1/V), so the P–V plot is a hyperbola — halving the volume doubles the pressure. Image: Reginaprice2013, CC BY-SA 3.0, via Wikimedia Commons.

Concept context

Discover why gases expand to fill any container while liquids flow and solids hold their shape. Master the gas laws, the ideal gas equation, and the reasons real gases deviate from ideal behavior.

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For one mole of a van der Waals gas at low pressure, Z = 1 - a/(RTV). This relation indicates that under these conditions the gas is:

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