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Chapter 10: Problem 76

Indicate which of the following statements regarding the kinetic-molecular theory of gases are correct. (a) The average kinetic energy of a collection of gas molecules at a given temperature is proportional to \(m^{1 / 2}\). (b) The gas molecules are assumed to exert no forces on each other. (c) All the molecules of a gas at a given temperature have the same kinetic energy. (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained. (e) All gas molecules move with the same speed if they are at the same temperature.

Short Answer

Expert verified
Statements (b) and (d) are correct. In the kinetic-molecular theory of gases, gas molecules are assumed to exert no forces on each other (statement b), and the volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained (statement d). Statements (a), (c), and (e) are incorrect.

Step by step solution

01

Statement a: Average kinetic energy

Statement a says that the average kinetic energy of a collection of gas molecules at a given temperature is proportional to \(m^{1/2}\). This is incorrect. According to the kinetic-molecular theory of gases, the average kinetic energy of a collection of gas molecules at a given temperature is proportional to the temperature, not the square root of their mass.
02

Statement b: No forces between gas molecules

Statement b states that gas molecules are assumed to exert no forces on each other. This is correct. One of the main assumptions of the kinetic-molecular theory of gases is that gas particles do not experience any long-range forces, which allows gases to easily expand to fill any container they are placed in.
03

Statement c: Same kinetic energy at a given temperature

Statement c says that all the molecules of a gas at a given temperature have the same kinetic energy. This is incorrect. Although the average kinetic energy of all the molecules within a gas at a given temperature is the same, individual gas particles can have a wide range of kinetic energies due to their varying velocity.
04

Statement d: Negligible volume of gas molecules

Statement d states that the volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained. This is correct. According to the kinetic-molecular theory of gases, the individual gas particles are assumed to have no volume in relation to the space they occupy. This allows us to approximate the behavior of gases in many situations.
05

Statement e: Same speed at the same temperature

Statement e states that all gas molecules move with the same speed if they are at the same temperature. This is incorrect. While the average speed of gas particles is related to the temperature, individual gas particles can have a wide range of speeds due to their varying masses and initial speeds. The distribution of their speeds is given by the Maxwell-Boltzmann distribution.

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Most popular questions from this chapter

A rigid vessel containing a \(3: 1 \mathrm{~mol}\) ratio of carbon dioxide and water vapor is held at \(200^{\circ} \mathrm{C}\) where it has a total pressure of \(202.7 \mathrm{kPa}\). If the vessel is cooled to \(10^{\circ} \mathrm{C}\) so that all of the water vapor condenses, what is the pressure of carbon dioxide? Neglect the volume of the liquid water that forms on cooling.

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Which statement concerning the van der Waals constants \(a\) and \(b\) is true? (a) The magnitude of \(a\) relates to molecular volume, whereas \(b\) relates to attractions between molecules. (b) The magnitude of \(a\) relates to attractions between molecules, whereas \(b\) relates to molecular volume. (c) The magnitudes of \(a\) and \(b\) depend on pressure. (d) The magnitudes of \(a\) and \(b\) depend on temperature.

(a) What conditions are represented by the abbreviation STP? (b) What is the molar volume of an ideal gas at STP? (c) Room temperature is often assumed to be \(25^{\circ} \mathrm{C}\). Calculate the molar volume of an ideal gas at \(25^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa}\) pressure. \((\mathbf{d})\) If you measure pressure in bars instead of atmospheres, calculate the corresponding value of \(R\) in \(\mathrm{L}\) -bar \(/ \mathrm{mol}-\mathrm{K}\).
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