At low temperatures and pressures, how does the volume of a real gas compare with the volume of an ideal gas under the same conditions?

Question

BlackTom AI · Accepted Answer

When comparing real gases to ideal gases at the same temperature and pressure, the real gas behavior deviates due to molecular size (finite volume) and intermolecular forces. Here we consider low temperatures and pressures.
Option 1: 'It is greater.' Real gases take up a finite volume because molecules occupy space themselves (the excluded volume). In the van der Waals picture, the available volume for movement is V - nb, which means the space effectively accessible to the gas is smaller than the container volume. To achieve the same pressure and temperature, the actual container volume required for the real gas is larger than the ideal-gas prediction, leading to a greater volume than the ideal gas under the same conditions. Moreover, at low P, intermolecular attractions are less dominant than repulsions due to finite size, so the dominant correction is the finite molecular volume, pushing the real-gas volume upward relative to the ideal case.
Option 2: 'It is less.' This would imply real gases can fit into a smaller volume than predicted by the ideal model at the same P and T, which contradicts the idea of finite molecular size reducing the accessible space. In the van der Waals framework, the volume correction (nb) reduces available space, not increases the packing efficiency, so this option is incorrect.
Option 3: 'There is no difference.' The ideal-gas model neglects molecular size and interactions, which become noticeable even at relatively low P and T; therefore, a difference in volume is expected, making this option incorrect.
Option 4: 'It depends on the type of gas.' While strong deviations can vary with conditions and gas, at the stated regime of low temperature and low pressure, the primary correction arises from finite molecular size and not from a qualitative dependence on gas type; thus this statement is not appropriately accurate for the given scenario and is considered incorrect.

Chemistry (H) - Varnold - Preparatory Academy - 2nd Semester - 2024/2025 Gases Practice Test for the Final

At low temperatures and pressures, how does the volume of a real gas compare with the volume of an ideal gas under the same conditions?

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