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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