A sample of gaseous neon atoms at atmospheric pressure and 0^∘ C contains 2.69 ×10^22 atoms per

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A sample of gaseous neon atoms at atmospheric pressure and...

A sample of gaseous neon atoms at atmospheric pressure and $0^{\circ} \mathrm{C}$ contains $2.69 \times 10^{22}$ atoms per liter. The atomic radius of neon is 69 $\mathrm{pm}$ . What fraction of the space do the atoms themselves occupy? What does this reveal about the separation between atoms in the gaseous phase?

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Key Concepts

Ideal Gas Behavior

This concept explains that under conditions of low density and moderate temperature, gases obey the ideal gas law, where the properties of the gas (pressure, volume, and temperature) and the number of particles are interrelated. The number density provided in the problem is typical for ideal gases, reinforcing that the atoms are sparsely distributed over a large volume.

Atomic Volume and Spherical Approximation

Atoms can be approximated as spheres characterized by a specific atomic radius. By computing the volume of a sphere using the formula (4/3 ? r^3) and multiplying it by the number of atoms, one can determine the total volume physically occupied by atoms. This step is essential for understanding how the actual physical space taken up by atoms compares to the overall volume of the gas.

Volume Fraction and Interatomic Separation

The volume fraction (or packing fraction) measures the ratio of the volume occupied by the atoms to the total volume available. In gases, this fraction is typically very small, which reveals that there is significant empty space between atoms. This large separation between atoms is a key characteristic of gases and underpins much of the kinetic theory of gases and their often-collisional nature.

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