Explanation Consider the volume occupied by the molecule to be spherical. The intermolecular distance will be the twice of the radius of the molecules. The typical diameter of a gas molecule is 0.3 nm . Compare the diameter and the intermolecular distance between the molecules. At standard condition of temperature and pressure, the temperature of the gas is 0 °C or 273 K and the pressure of the gas is 1.013 × 10 5 Pa . Write the expression for the volume occupied by one gas molecule. V N = 4 3 π r 3 (I) Here, V is the volume gas, N is the number of molecules and r is the radius of the gas molecule. Write the expression for the ideal gas equation. P V = N k T Substitute 4 3 π r 3 for V N and rearrange the above expression for the volume per molecule. r = ( 3 k T 4 π P ) 1 / 3 (II) Here, P is the pressure of the gas, N is the number of molecules, k is the Boltzmann constant and T is the temperature of the gas. The intermolecular distance is twice the radius of the molecule. Write the expression for the comparison of the intermolecular distance and average molecular diameter. n = 2 ⋅ r d molecule (III) Here, d molecule is the diameter of the molecule and n is the factor of comparison between the diameter of molecule and the intermolecular distance. Conclusion: Substitute 1.38 × 10 − 23 J / K for k , 273 K for T and 1.013 × 10 5 Pa for P in equation (II). r = ( 3 ( 1

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780136139225

Author: Douglas C. Giancoli

Publisher: Prentice Hall

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Boltzmann statistics of Ideal gas

In statistical mechanics and thermodynamics, Maxwell - Boltzmann statistics explains the statistical distribution of the energies of the classic gas molecules over different states in thermal equilibrium. Maxwell Boltzmann statistics helps us to derive t…

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Chapter 18, Problem 61GP

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The intermolecular distance considering a ping pong ball to be a molecule of size 4 cm.

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Chapter 18, Problem 60GP

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Physics for Scientists and Engineers with Modern Physics

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The intermolecular distance considering a ping pong ball to be a molecule of size 4 cm .

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Chapter 18 Solutions