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In the article "A Simple Laboratory Experiment
for the Determination of Absolute Zero" (J. Chem.
Educ. 2001, 78, 238-240), Kim et al. introduce a
quantity called partial volume. Used in the context of
a Charles's law analysis, I found the term
confusing, as it seems to imply that different components of
a gaseous mixture can occupy different volumes
within the same container. Unless I have overlooked
a simple point, the authors appear to assume a law
of partial volumes for a gas mixture analogous to
the law of partial pressures.
I would suggest a more straightforward derivation
of their final result, which shows a Charles's law proportionality between volume and absolute
temperature for air trapped in an inverted
graduated cylinder submerged in water. Treating the air as
an ideal gas, the following relation holds:
PairV = nairRT
where the symbols have their usual meanings. In particular,
Pair is the partial pressure of the
trapped air and V is the total volume. Inserting
Pair = P - PH2O
from Dalton's law of partial pressures (where
P is the total--approximately, barometric--pressure and
PH2O is the water vapor pressure) and dividing both
sides by P yields
The left side of the equation can be interpreted as
an effective volume, which is proportional to the
absolute temperature T. (The moles of air and
total pressure are considered fixed.) The ratio of
pressures is a dimensionless correction factor
that accounts for the variation in water vapor
pressure with temperature. While the result here is
apparently identical to that reached in the article, I believe
the present approach, which avoids the artifice of
partial volume, is pedagogically more sound.
See Author's Reply.
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