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Is pressure a state function in the van der Waals equation?

Last updated date: 13th Jul 2024
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Hint :Johannes Diderik van der Waals developed the Van der Waals equation in 1873. The equation is essentially a modified version of the Ideal Gas Law, which states that gases are made up of perfectly elastic collisions between point masses. This rule, however, fails to account for the behaviour of actual gases. As a result, the Van der Waals equation was developed, which aids in the definition of the physical state of a real gas.

Johannes Diderik van der Waals developed the Van der Waals equation in 1873. The equation is essentially a modified version of the Ideal Gas Law, which states that gases are made up of perfectly elastic collisions between point masses. This rule, however, fails to account for the behaviour of actual gases. As a result, the Van der Waals equation was developed, which aids in the definition of the physical state of a real gas.
Ideal Gas equation: PV = nRT
Van der waals equation: $(P + \dfrac{{a{n^2}}}{{{v^2}}})(v - nb) = nRT$
P, V, T, n are the gas's pressure, volume, temperature, and moles. Every gas has its own ‘a' and ‘b' constants.
For the correlation and prediction of lower critical solution activity in mixtures containing a solvent and a polymer, the van der Waals equation of state is used. Experimental volumetric data at low pressures are used to approximate the polymer's equation of state parameters.
For every quantity of a and b, there exists a unique value of Pressure
Hence, it is a State function
Van der Waals believed, in practise, the gaseous particles –
Are spheres with a rough surface.
Have a fixed volume and therefore can't be compressed past a certain stage.
When two particles collide at close range, they form an exclusive spherical volume around them.
Gaseous particles do interact with one another. The interactions between inside particles cancel each other out. However, particles on the container's surface and on the walls do not have particles above the surface or on the walls. As a result, there will be net interactions, or dragging, of bulk molecules away from the walls and surface. Molecules that are interacting with each other away from the walls can strike the walls with less force and strain. As a result, the particles in natural gases have a lower pressure than ideal gases.

Note :
There will be net interactions, or dragging, of bulk molecules away from the walls and surface. Molecules that are interacting with each other away from the walls can strike the walls with less force and strain. As a result, the particles in natural gases have a lower pressure than ideal gases.