# Van der Waals Equation

Van der Waals equation also known as Van der Waals equation of state is for real gases as they do not follow ideal gas law. PV=nRT is the ideal gas equation where P is pressure, V is volume, n is no.of moles of gas, R is universal gas constant and T is the temperature in Kelvin.

## What is Van der Waals Equation?

$\large (p+\frac{n^{2}a}{v^{2}})(V-nb)=nRT$

Where,

p: pressure in Pascal

N: $n=\frac{N}{N_{A}}$ no.of moles

a: average attraction between particles

b: volume excluded by mole particles

R: universal gas constant (8.3144621)

V: volume

T: temperature in K

### Van der Waals Force

The electrostatic force that is weak and short ranged which is experienced between uncharged molecules is known as Van der Waals force. The main properties of Van der Waals forces are:

• Normal covalent and ionic bonds are stronger than these forces
• Unlike dipole-dipole interactions, these forces are independent of temperature.

Van der Waals force leads to intermolecular attractions. As the name itself suggests, these are the attractions that happen in between the neighbouring molecules (for example covalent bond). These are seen in dipole-dipole interactions because of dispersion force, which is the weakest force in intermolecular attractions.

• Directional characteristic is absent.

#### Van der Waals Force Example

Example of Van der Waals force is a real gas. These gases are non-hypothetical as space is occupied the molecules.

## Application of Van der Waals Equations

$(p+A)(V-B)=CT$

Where,

p: pressure

A,B,C: parameters

V: specific volume

T: temperature

The above equation is a modified version of Van der Waals equation for compressible fluids (fluid whose flow changes along the density like polymers which is the branch of fluid mechanics).

### Limitations of Van der Waals Equation

• As the temperature reaches extremes, real gas starts to deviate from Van der Waals equation.
• Values of a (average attraction between particles) and b(volume excluded by mole particles) in the equation are valid only for specific temperature as they vary for different ranges of temperature and pressure.

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## Frequently Asked Questions on Van der Waals Equation

#### What is a real gas?

A real gas is a non-hypothetical gas that doesn’t behave as an ideal gas due to the interaction between gas molecules

#### What is Van Der Waals equation?

Van der Waals equation also known as Van der Waals equation of state is for real gases as they do not follow ideal gas law.

#### What are the limitations of Van Der Waal equation ?

Values of an (average attraction between particles) and b(volume excluded by mole particles) in the equation are valid only for specific temperature as they vary for different ranges of temperature and pressure. As the temperature reaches extremes, real gas starts to deviate from Van der Waals equation.

#### Practise This Question

We understand 'temperature' as a measure of the 'hotness' or 'coldness' of a body. Which of these properties do you think explicitly depend on the temperature?