We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law in the final state ? (Hydrogen molecules can be consider as spheres of radius `1Å`).

Explanation

To determine whether we can assume the ideal gas law in the final state after compressing hydrogen gas to a pressure of 100 atm, we will follow these steps:

### Step 1: Calculate the Volume of a Hydrogen Molecule
Given that the radius of a hydrogen molecule is \(1 \, \text{Å} = 1 \times 10^{-10} \, \text{m}\), we can calculate the volume of a single hydrogen molecule using the formula for the volume of a sphere:

\[ V = \frac{4}{3} \pi R^3 \]
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