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The van der Waals Equation

The van der Waals equation corrects for the volume of, and attractive forces between, gas molecules:

(P + )(V - nb) = nRT    

There are two corrective factors in van der Waals equation. The first, , alters the pressure in the ideal gas equation. It accounts for the intermolecular attractive forces between gas molecules. The magnitude of a is indicative of the strength of the intermolecular attractive force. a has units of .

The factor - nb accounts for the volume occupied by the gas molecules. b has units of L/mol. Since b corresponds to the total volume per mole occupied by gas molecules, it closely corresponds to the volume per mole of the liquid state, whose molecules are closely layered. b is generally much smaller in magnitude than a . The values of a and b generally increase with the size and complexity of the molecule.

Unfortunately, the values of a and b must be experimentally determined. By now you should be at ease manipulating the ideal gas law. Van der Waals equation isn't much different. The only trick is remembering the corrective factors.

Even if you forget the equations of the corrective factors, don't panic. You can deduce them from the values of a and b , which the question will most likely give you since they are experimental. More importantly, the question must give you the units of a and b . If you know the units of a and b , you should be able to work backwards to pressure or volume. Note that the units of a do not include volume, and that the units of b do not include pressure. So you shouldn't get them confused. Try working backwards from the units of a and b to their full corrective factors.

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