Question

Explain the correction term for pressure and volume in Vanderwaal 's equation?

Answer 1

Answer:

van der Waals Equation of State. The ideal gas law treats the molecules of a gas as point particles with perfectly elastic collisions. ... Since the constant b is an indication of molecular volume, it could be used to estimate the radius of an atom or molecule, modeled as a sphere.

Answer 2

Answer:

Pressure correction term depends upon:

Number of molecules attracting the molecules which comes to strike the wall and as such it is proportional to density of gas i.e. proportional to n/Vn/V where nn is the number of moles of gas and VV is the volume of the container.

It also depends upon number of molecules which has a strike the unit area of the wall and is therefore proportional to the total number of molecules per unit volume, i.e. proportional to the density again (i.e. proportional to n/Vn/V).

So the pressure correction term is jointly proportional to n/Vn/V for factor 1 and again proportional to n/Vn/V for factor 2. Hence the pressure correction term is proportional to

(nV)(nV),(nV)(nV),

i.e. proportional to

n2V2.

Explanation:

The van der Waals equation for real gases is stated as follows:

(P+an2V2)(V−nb)=nRT(P+an2V2)(V−nb)=nRT

For the coefficient bb, we can reason out that more the number of molecules, the more volume will be occupied by the molecules (in turn reducing the free space available for the motion of the molecules). It must be linearly proportional to nn because bb represents the sum of the excluded volume of each molecule in a mole. Therefore, we must multiply it by nn to obtain the total excluded volume.

The coefficient aa is said to represent the strength of the intermolecular attractive forces. Intuitively, we can say that it must be proportional to the number of molecules per unit volume. The more the number of molecules around a molecule, the more attractive forces it shall feel.

Therefore, the correction term for pressure must be proportional to nVnV. But we know that in reality, it is proportional to the square of nVnV