A large number of monoatomic ideal gas molecules are stored within a closed container at a temperature of 200 K. What is the average translational kinetic energy of the individual gas molecules? (Note: Use Boltzmann's constant k = 1.381 × 10⁻²³ J/K.)

Question

Quizplus · Accepted Answer

11ecba2d_1324_4013_a3bf_8d60a42bea57_MD0008_00 The kinetic molecular model describes macroscopic characteristics of gases that are related to the constant motion of freely moving gas molecules. The kinetic molecular model assumes that a rigid, closed container contains a large number N of monoatomic ideal gas molecules. The total kinetic energy (K_tr) of all gas molecules is related to the mass (m) of each molecule and the average value of velocity squared 11ecba2d_1324_4014_a3bf_7b264f15ad5b_MD0008_00 : 11ecba2d_1324_4015_a3bf_dd5a59e4d39f_MD0008_00 Applying the kinetic molecular model to a rigid cubic container allows the pressure (P) of the gas to be stated in terms of the total kinetic energy of all gas molecules and the container volume (V): 11ecba2d_1324_4016_a3bf_7bccec532dbb_MD0008_00 11ecba2d_1324_4017_a3bf_2df991023c43_MD0008_00 Furthermore, Boltzmann's constant (k = 1.381 × 10⁻²³ J/K) may be used to restate the ideal gas law in terms of the behavior of individual gas molecules as: 11ecba2d_1324_6728_a3bf_a9a4164ff4a7_MD0008_00 Combining the kinetic molecular model's expressions for ideal gas behavior and pressure produces an expression for the average kinetic energy 11ecba2d_1324_6729_a3bf_31d32f7e823a_MD0008_00 of an individual gas molecule at a given temperature in Kelvin (K): 11ecba2d_1324_672a_a3bf_69d0d30093ad_MD0008_00 11ecba2d_1324_672b_a3bf_b316041932d4_MD0008_00 11ecba2d_1324_672c_a3bf_8b7b43e2277b_MD0008_00 In this question, ideal gas molecules are stored within a fixed container at a temperature of 200 K. Therefore, the average translational kinetic energy of an individual monoatomic ideal gas molecule is: 11ecba2d_1324_672d_a3bf_c5c05d4c26dd_MD0008_00 11ecba2d_1324_8e3e_a3bf_2bfdd0d6b55f_MD0008_00 11ecba2d_1324_8e3f_a3bf_c3586ddaa3da_MD0008_00 11ecba2d_1324_8e40_a3bf_672c7dbc6dfe_MD0008_00 Therefore, the average kinetic energy of an ideal gas molecule stored within a closed container at 200 K is 4.2 × 10⁻²¹ J (Choice D). Educational objective: The kinetic molecular model uses the behavior of individual gas molecules to explain the macroscopic characteristics of gases. Boltzmann's constant can be used to determine the average translational kinetic energy of a single ideal gas molecule at a given temperature.

A Large Number of Monoatomic Ideal Gas Molecules Are Stored