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Ch.1 - Matter, Measurement & Problem Solving
Chapter 1, Problem 126

A sample of gaseous neon atoms at atmospheric pressure and 0 °C contains 2.69×1022 atoms per liter. The atomic radius of neon is 69 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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1
Calculate the volume of a single neon atom using the formula for the volume of a sphere: $V = \frac{4}{3} \pi r^3$, where $r$ is the atomic radius.
Convert the atomic radius from picometers to centimeters to match the units of volume in liters.
Calculate the total volume occupied by all neon atoms in one liter by multiplying the volume of a single atom by the number of atoms per liter.
Determine the fraction of space occupied by the neon atoms by dividing the total volume occupied by the atoms by the volume of the container (1 liter).
Interpret the result to understand the separation between atoms in the gaseous phase, noting that a small fraction indicates large separation between atoms.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Radius

The atomic radius is a measure of the size of an atom, typically defined as the distance from the nucleus to the outermost electron shell. For neon, the atomic radius is 69 picometers (pm), which indicates how closely packed the atoms can be in a given volume. Understanding atomic radius is crucial for calculating the volume occupied by individual atoms in a gas.
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Molar Volume of a Gas

The molar volume of a gas at standard temperature and pressure (STP) is approximately 22.4 liters per mole. This concept helps in determining how much space one mole of gas occupies, which is essential for calculating the total volume of gas in relation to the number of atoms present. It allows us to compare the volume occupied by the atoms themselves to the total volume of the gas.
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Fraction of Space Occupied by Atoms

The fraction of space occupied by atoms in a gas can be calculated by comparing the volume occupied by the atoms to the total volume of the gas. This fraction reveals how much of the gas's volume is filled with matter versus how much is empty space, highlighting the significant separation between atoms in the gaseous phase. In gases, this fraction is typically very small, indicating that atoms are mostly spaced apart.
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