How is Average Kinetic Energy (AvgKE) calculated for a gas?

The calculation of Average Kinetic Energy (AvgKE) for a gas is based on the kinetic theory of gases, which establishes that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas. The correct formula, AvgKE = 3/2 n R T, reflects this relationship.

In this equation, n represents the number of moles of the gas, R is the universal gas constant, and T is the absolute temperature measured in Kelvin. The factor of 3/2 arises from the fact that gas molecules in a three-dimensional space have kinetic energy contributions from motion in all three spatial dimensions (x, y, and z). The factor accounts for the translation of molecular movement, which involves averaging over all directions.

This formula implies that as the temperature of the gas increases, the average kinetic energy of the molecules also increases, confirming that higher temperatures lead to faster-moving molecules. Understanding this relationship is essential when analyzing gas behavior and is fundamental in various applications such as thermodynamics and physical chemistry.

In contrast, the other choices present formulas that do not correctly represent the kinetic energy for a gas under the assumptions of the kinetic molecular theory. Such disparities highlight the importance of recognizing the correct factors involved when calculating AvgKE.