Deviation of real gases from ideal behaviour can be studied by plots of compressibility factor (Z) vs p. The copressibility factor is
`Z=(pV)/(nRT)`
The compressibility factor for 1 mole of a gas obeying van der Waals gas equation at `0^(@)C` and 100 atm pressure is found to be 0.5. The van der Waals gas equation is
`(p(an^(2))/(V^(2)))(V-nb)=nRT`
Calculate the value of 'a' assuming volume of molecules to be negligible.

Explanation

To solve the problem, we need to calculate the value of 'a' in the van der Waals equation for a gas given that the compressibility factor (Z) is 0.5 at a pressure of 100 atm and a temperature of 0°C. We will assume the volume of the gas molecules is negligible.

### Step-by-Step Solution:

1. **Understand the Compressibility Factor (Z)**:
The compressibility factor is defined as:
\[
Z = \frac{pV}{nRT}
...