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A Z versus P (compressibility factor vs pressure) graph at 25 degree C shows curves for several gases. In the graph, H2 lies above Z = 1, O2 lies below Z = 1 at low pressures (then rises above), and a third gas (marked '?') lies between H2 and O2 (above Z=1 for all P). Identify the missing gas.

1. He
2. Ar
3. H2O
4. NH3

Correct answer: He

Solution

At 25 C, the van der Waals forces are the dominant factor for Z. For H2: very small 'a' (weak attraction), Z > 1 for almost all pressures. For He: 'a' is even smaller than H2 but the molecule is smaller; He has Z > 1 for all P and is positioned between Z=1 and the H2 curve. For O2: moderate 'a', Z < 1 at moderate pressures. For Ar: 'a' is larger than H2/He, so Z < 1 at low/moderate pressures. For H2O and NH3: strong intermolecular forces, Z << 1 at low pressures. The gas marked '?' lies above Z=1 (like H2) but below the H2 curve -- this is He. He has the lowest critical temperature and weakest intermolecular forces, giving Z > 1 at all practical pressures at 25 C, positioned just below H2.

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