Question

One assumption of the ideal gas law is that the atoms or molecules themselves occupy a negligible volume. Verify that this assumption is reasonable by considering gaseous xenon (Xe). Xenon has an atomic radius of 2.0 x 10-10 m. For STP conditions, calculate the percentage of the total volume occupied by the atoms. Express your answer as a percentage with no units.

Answer 1

The correct answer is 0.09 percent.

Step-by-step explanation:

Based on the given information, the atomic radius is 2 × 10⁻¹⁰ m. Now the atomic volume can be determined by using the formula, 4/3πr³. by putting the values we get,

v = 4/3πr³ = 4/3π(2×10⁻¹⁰ m)³

v = 3.35 × 10⁻²⁹ m³

The no. of atoms present in one mole of xenon is 6.02 × 10²³ atoms. Therefore, the total atomic volume will be,

Va = 6.02 × 10²³ × 3.35 × 10⁻²⁹

Va = 2.02 × 10⁻⁵ m³

The %age of total volume occupied can be determined by dividing the total atomic volume with the volume under STP. Under STP, the volume is 22.4 m³ or 2.24 × 10⁻² m³.

Va/V = 2.02 × 10⁻⁵ m³ / 2.24 × 10⁻² m³

= 9.02 × 10⁻⁴ or 0.09 %