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

step 1 Let's calculate the fraction of space occupied by the neon atoms. We're told that the atomic rad

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

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

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

Key Concepts

Ideal Gas Law

The ideal gas law connects pressure, volume, temperature, and the number of particles in a gas, providing a basis to understand how gas molecules or atoms are distributed in space. This concept is fundamental in thermodynamics and kinetic molecular theory, and it allows one to estimate quantities like the spacing between particles under assumed ideal conditions.

Atomic Radius and Volume Calculation

The atomic radius is used to estimate the volume of a single atom by treating it as a sphere. Calculating the spherical volume from the radius is key to determining how much space each atom occupies. This concept is critical when comparing microscopic atomic volumes to the macroscopic volume of a gas sample.

Packing Fraction in Gases

The packing fraction is the ratio of the total volume occupied by the actual atoms (or molecules) to the overall volume of the container holding the gas. In gaseous systems, this fraction is extremely small, demonstrating that the atoms occupy only a minor portion of the available space, with most of the volume being empty.

Interatomic Spacing

Interatomic spacing refers to the average distance between neighboring atoms or molecules in a gas. Given the low packing fraction, atoms in a gaseous phase are widely separated relative to their own sizes. This large separation accounts for the low density and compressibility of gases, as well as the minimal interactions between atoms at typical conditions.

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