Why are pressure and volume corrections different in the van der Waals equation?

[requal]

Homework Statement

Why in the van der waals equation, is the pressure correction term added on to the measured pressure but the volume correction term subtracted from the measured volume?

Homework Equations

(p+n^2a/V^2)(V-nb)=nRT

The Attempt at a Solution

I thought that the pressure term is added on because some of the pressure is reduced by the role of the intermolecular forces near condensation point. But I thought that the ideal gas law tends to overestimate volumes too because as pressure gets higher, the particles will have less free volume(ie. ideal volume) to move around because their molecular volume is taking up significant room?

 

[nate808]

I can provide some insight into why the pressure correction term is added to the measured pressure while the volume correction term is subtracted from the measured volume in the van der Waals equation.

Firstly, it is important to understand that the van der Waals equation is a modification of the ideal gas law to account for the deviations from ideal gas behavior at high pressures and low temperatures. The ideal gas law assumes that gas particles have zero volume and do not interact with each other. However, at high pressures and low temperatures, gas particles are no longer far apart and start to interact with each other through intermolecular forces.

The pressure correction term, represented by n^2a/V^2, takes into account the attractive forces between molecules. This term is added to the measured pressure because it reduces the overall pressure of the gas. At high pressures, the attractive forces between molecules become significant and cause the gas particles to be closer together, resulting in a lower pressure than what would be predicted by the ideal gas law.

On the other hand, the volume correction term, represented by nb, takes into account the volume occupied by the gas particles themselves. This term is subtracted from the measured volume because the actual volume available for gas particles to move around in is less than the ideal volume due to the finite size of the gas particles. As pressure increases, the gas particles are pushed closer together, resulting in a smaller volume available for them to move around in.

In summary, the pressure correction term is added to account for the attractive forces between gas molecules, while the volume correction term is subtracted to account for the finite size of gas particles. Both of these corrections help to improve the accuracy of the van der Waals equation at high pressures and low temperatures.