Answer to Question #89300 in Molecular Physics | Thermodynamics for Shivam Nishad

Question

Write the Van der Waals equation of state for a real gas. What is the significance of the constants in this equation ?

Answer 1

Van der Waals equation of state for a real gas is

$$\left( P+\frac{a{{n}^{2}}}{{{V}^{2}}} \right)\left( V-nb \right)=nRT$$

where R is the universal gas constant, T is temperature, P is pressure, V  is volume and n is the number of moles of gas.

$a$ and $b$ are the Van der Waals' constants which have positive values and are characteristic of the individual gas. The constants $a$ and $b$ provide the corrections to pressure and volume in the ideal gas law

$$PV=nRT$$

taking into account the nonideality of gas.  

Constant $a$ take into account the force of attraction between gas molecules. Under the action of this force, the molecules attract each other, inside the gas, reducing the pressure on the wall. Intermolecular attraction is taken into account by adding to the observed pressure P in the equation of state of the term

$$\frac{a{{n}^{2}}}{{{V}^{2}}}$$

Constant $b$ is a correction for finite molecular size and its value is the volume of one mole of the atoms or molecules. As a result, if in the equation of state of an ideal gas the volume of space available for the movement of molecules was equal to V, now it becomes equal to

$$V-nb$$