The compression factor (compressibility factor) for `1 mol` of a van der Waals gas at `0^(@)C` and `100 atm` pressure is found to be `0.5`. Assuming that the volume of a gas molecule is neligible, calculate the van der Waals constant `a`.

Explanation

To calculate the van der Waals constant \( a \) for the given conditions, we will use the van der Waals equation and the provided information about the compressibility factor \( Z \).

### Step-by-Step Solution:

1. **Understand the Van der Waals Equation**:
The van der Waals equation is given by:
\[
\left( P + \frac{a}{V^2} \right)(V - b) = RT
...