A gas is stored at high pressure where its compressibility factor Z is measured to be 1.18. What does this tell you about the dominant real-gas effect at these conditions?
AIntermolecular attractions dominate — the gas is easier to compress than the ideal law predicts
BThe gas is behaving ideally — Z is close enough to 1 to ignore corrections
CMolecular volume exclusion dominates — the gas is harder to compress than the ideal law predicts
DThe gas is near its saturation curve and about to condense
Z = Pv/RT > 1 means the actual specific volume v is larger than the ideal prediction RT/P — the gas occupies more space than ideal. This happens when molecular volume exclusion (finite size of molecules) dominates: molecules physically cannot be compressed into a smaller volume than their own size. Intermolecular attractions would pull Z below 1 (gas easier to compress, v smaller than ideal). Z > 1 typically occurs at very high pressures or for gases with weak attractions (like hydrogen or helium).
Question 2 Multiple Choice
An engineer is sizing a storage vessel for ammonia refrigerant at 150 bar and near-ambient temperature, which is close to ammonia's saturation curve. She uses the ideal gas law. What is the most likely consequence?
ANo significant error — ideal gas is always accurate for common engineering gases
BThe vessel will be oversized — real ammonia is harder to compress than the ideal law predicts
CThe vessel will be undersized — intermolecular attractions make real ammonia easier to compress than ideal, so Z < 1 and the actual specific volume is smaller than the ideal prediction
DThe result depends only on temperature, not pressure
Near saturation and at high pressure, ammonia (a polar molecule with strong intermolecular attractions) has Z significantly less than 1. This means the real specific volume is smaller than RT/P. If the engineer assumes ideal behavior, she calculates a specific volume larger than reality and therefore designs the vessel too small — it will not hold the required mass of refrigerant. This is a practical safety consequence: real-gas corrections are mandatory for ammonia, CO₂, and other refrigerants near their saturation curves.
Question 3 True / False
Real gases typically have a compressibility factor Z less than 1, because intermolecular attractions reduce pressure below the ideal gas prediction.
TTrue
FFalse
Answer: False
This is the most common misconception about real-gas behavior. Two competing effects determine Z: intermolecular attractions (pulling Z below 1) and molecular volume exclusion (pushing Z above 1). At moderate pressures, attractions often dominate first (Z < 1). At very high pressures, excluded volume wins (Z > 1). For gases with weak attractions like hydrogen or helium, Z > 1 even at moderate pressures. The compressibility chart shows both regions, and the actual Z depends on both reduced temperature and reduced pressure.
Question 4 True / False
For a gas at reduced temperature Tr > 2 and reduced pressure Pr < 0.5, using the ideal gas law introduces less than about 1% error.
TTrue
FFalse
Answer: True
This is the standard engineering rule of thumb for when ideal gas treatment is acceptable. At high reduced temperature (far above critical point) and low reduced pressure (far from condensation), molecules are dilute and fast-moving: intermolecular forces are negligible and molecular volume is tiny compared to total volume. The law of corresponding states tells us this condition generalizes across all gases — Tr > 2 and Pr < 0.5 reliably keeps Z within about 1% of 1.0 for most species.
Question 5 Short Answer
Why do intermolecular attractions and molecular volume exclusion affect the compressibility factor Z in opposite directions, and which effect typically becomes dominant first as you raise pressure from a low value?
Think about your answer, then reveal below.
Model answer: Intermolecular attractions pull molecules together, reducing the pressure the gas exerts on its container — effectively making the gas easier to compress than ideal (Z < 1). Molecular volume exclusion means molecules cannot occupy the same space, so the available volume is reduced — making the gas harder to compress than ideal (Z > 1). At low-to-moderate pressures, molecules are still far enough apart that attractions have more effect than the small correction for finite molecular size, so Z dips below 1 first. At very high pressures where molecules are tightly packed, volume exclusion dominates and Z rises above 1.
This directional competition is why compressibility charts show a minimum in Z versus pressure for most gases at moderate temperatures: Z drops below 1 at first (attractions win) then rises back above 1 (volume exclusion wins) as pressure increases. For the engineer, the practical takeaway is to always check the operating conditions against the Z chart rather than assuming corrections go in a fixed direction.