Van der Waals Equation

Van der Waals Equation (or Van der Waals equation of state) helps us in understanding the behaviour of real gas. It is used extensively in chemistry and thermodynamics. In 1873 Johannes Van der Waals formulated this equation. This is basically an upgraded version of the ideal gas law. If you have heard about this equation for the first time then don’t miss out reading this article. Today, we will tell what is the Van der Waals equation, units of A and B in the Van der Waals equation, volume correction and pressure correction in Van der Waals equation in great detail. So, as you can see this is going to be an amazing learning journey.

What is Van der Waals Equation?

The Van der Waals Equation shows the relationship between the pressure, volume, temperature, and amount of real gases.

This new equation is an extension to the ideal gas law which included the effects of interaction between molecules of a gas as well discussed the finite size of the molecules. The key difference between both of them is that ideal gas law is only applicable to the ideal gases whereas the Van der Waals equation is applicable to both the ideal gases and real gases.

The Van der Waals equation is as follows:

(P+an2V2) (V-nb) = n RT

Where,

P=  pressure

V=  volume

a= constant that measures attractive force between the molecules

b=  volume correction factor

nb= volume occupied by the gas molecules

T= Temperature

Volume Correction in Van der Waals Equation:

Ideal gas law equation:

PV=nRT

Where,

P= Pressure of gas

V= Volume of gas

n= Number of moles of gas

R= Universal gas constant

T= Absolute temperature of the gas

This above equation can be written for one mole of gas as follows: 

PV=RT

When the ideal gas equation PV=RT was derived the following assumptions were made:

• The volume which is occupied by the gas molecules is negligible when compared with the total volume of the gas.

• No force is exerted by the molecules on one another.

Although both of the above assumptions don’t hold true at high pressure. This is because when the gas is at high pressure there is volume at a small capacity. Thus, we must consider the volume which is occupied by a single molecule of gas.

The second thing here is that molecules tend to come closer to each other at high pressure. This shows that considerable cohesive forces are acting on them. Therefore, at high pressure and low temperature, the gases don’t follow the above relation.

Let us assume that a container is filled with gas. The gas molecules are in the form of hard elastic spheres. So, the distance between the two molecules will be under 2r.

Therefore, one molecule will take up space of another molecule by;

43(2r)3

So, there is not enough space available for the free motion of the gas when compared to the actual volume of the gas. At the end the corrected volume is (V-b).

The correction term b is called the co-volume. It is 4 times the actual volume occupied by the molecules.

Pressure Correction in Van der Waals Equation:

Imagine a rectangular container where there are many molecules of gas present. Among them there are two molecules named A and B. Molecule A is placed inside the room far from the boundary. Other molecules which are equally distributed in all directions are surrounding the molecule A. Due to the cohesive forces the net intermolecular force becomes zero.

Now, another molecule B is present near the wall of the container. Molecule B is experiencing cohesive forces due to adjacent molecules. The adhesive force is occurring because of the attraction between atoms of the wall with which molecules collide that ultimately creates an inward pull of B.

So, in total there are two pressures: 

Inward pressure p

Observed pressure p

Therefore, the right pressure is (p+p).

The inward pressure is dependent on the following factors:

• How many molecules are there which are striking per unit area of the wall per unit time (p ∝ n)

• How many molecules have the ability to attract the colliding molecule per unit volume  (p ∝ n)

The above two factors are proportional to the density of the gas

Therefore, 

p ∝ n2

Let N: Number of molecules

      V: Volume of the gas

  Then,

n=N/V

p a N2/V2

p a 1/V2

Here, a is constant

Therefore, the corrected pressure is (P+p) becomes

Units of Van der Waals Constant a and b:

Van der Waals equations utilises the calculation of units and dimensions of constant a and b

Pa= an2/V2

Where,  

Pa is the unit of internal pressure

Thus, the unit of Van der Waals constant is;

a= atm lit2 mol-2

nb is the unit of volume

b=lit mol-1

In the SI unit;

The unit of a=(newton metrer-2) meter6 mol-2= N meter4 mol-2 and b=meter3 mol-1

The dimensions of Van der Waals constant a and b=[ML5T-2 mol-2] and [L3 mol-1]

Conclusion:

We hope that you were able to understand this equation in great detail. At its core Van der Waals Equation helps in understanding both the ideal gases and real gases. This equation holds a great importance in chemistry and thermodynamics.