valence
Practice
States of matterNational 2019

An adjustable-volume container holds 10.0 g pentane (M = 72.15, normal boiling point = 36.1 ºC). The pressure in the container is measured as a function of volume while maintaining the temperature at 30 ºC. Which graph shows the results of this experiment?

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Explanation

draft

Step 1 – Amount of pentane. n=10.0 g72.15 g/mol=0.1386 moln=\dfrac{10.0\text{ g}}{72.15\text{ g/mol}}=0.1386\text{ mol}.

Step 2 – What happens at 30 °C, below the normal boiling point (36.1 °C)? At this temperature pentane cannot be a gas at high pressure — some of it will condense to liquid whenever the container is small enough. As long as both liquid and vapor are present, the pressure in the container is fixed at the equilibrium vapor pressure of pentane at 30 °C (roughly 600–620 mmHg, close to but a bit below 1 atm since 30 °C is a little below the boiling point). This gives a flat (constant-pressure) region at small volumes, where liquid is still present.

Step 3 – When all the liquid has evaporated. Once the volume is large enough that all 0.1386 mol of pentane exists as vapor, the system behaves as an ideal gas and further increases in VV cause PP to drop according to PV=nRTPV=nRT.

Step 4 – Check the numbers. If all the pentane were vapor:
P=nRTV=(0.1386)(62.36)(303)VP=\frac{nRT}{V}=\frac{(0.1386)(62.36)(303)}{V}
- At V=8 L: P≈328 mmHgV=8\text{ L}:\ P\approx 328\text{ mmHg} — matches the low-pressure tail of the curve.
- At V=2 LV=2\text{ L}, the ideal-gas formula would predict P≈1311 mmHgP\approx1311\text{ mmHg}, but this exceeds the vapor pressure of pentane at 30 °C, so instead the pentane simply condenses and the pressure stays pinned at the vapor pressure (~600–620 mmHg) rather than rising that high.

So the correct curve must start flat (constant PP = vapor pressure) at small VV, then bend downward and follow the 1/V1/V ideal-gas curve once all the liquid has vaporized — this is exactly graph (C).

A

Assumes pentane behaves as an ideal gas at all volumes shown, ignoring that at small V and 30 °C (below the 36.1 °C boiling point) liquid must be present, which pins the pressure instead of letting it rise above the vapor pressure.

B

Reflects the correct trend of an ideal gas but with V and P mixed up in direction (pressure rising with volume), the opposite of Boyle's law behavior — an axis/trend misreading.

C

Correct: at small V, liquid and vapor coexist so P stays constant at the vapor pressure; once all liquid vaporizes, further volume increase makes P fall following PV=nRTPV=nRT.

D

Assumes the container always contains a two-phase liquid–vapor mixture over the entire volume range, so pressure never changes; ignores that the container is large enough at high V to vaporize all the liquid, after which pressure must decrease.

Concept · Vapor–liquid equilibrium and vapor pressure vs. ideal gas behavior

USNCO 2019 National Part I exam, question 16. © American Chemical Society; reproduced for non-commercial practice.