The ideal gas law provides one way to estimate the pressure exerted by a gas in a container. The law is

�=

���

�

More accurate estimates can be made with the van der Waals equation

���

� = −

�− ��

��
^{
2
}

� 2

where the term �� is a correction for the volume of the molecules and the term

�� 2

� 2 is a correction

for molecular attractions. The values of � and � depend on the type of gas. The gas constant is � , the

absolute temperature is � , the gas volume is � , and the number of gas molecules is indicated by � . If �= 1 [mol] of an ideal gas were confined to a volume of = 22.41 [L] at 0°C (273.2 K), it would

J

exert a pressure of 1 atm. In these units, �= 0.08206 [

] .

K⋅mol

3 3

For
chlorine (
Cl
),
�= 0.6343 [
Pa⋅m
]
and
�= 5.62 ×
10
^{
−5
}
[
m
]
(Reid et
al, 1987). Compare the

2 mol 2

mol

pressure
estimates given by the ideal gas law and the van der Waals equation
for 1 mol of
Cl
_{
2
}
in
22.41

L at 273.2
K. What is the main cause of the difference in the two pressure
estimates, the molecular volume or the molecular attractions?
Use
*
disp
*
function to
produce both values, including units, and show the percentage
difference.

References: Reid, R. C, Prausnitz, J. M., and Poling, B. E., The Properties of Gases and Liquids, Fourth Edition, McGraw-Hill, New York, 1987

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