What is the formula for calculating the average kinetic energy of a gas?

The formula for calculating the average kinetic energy of a gas is correctly represented by the equation ( KE_{\text{avg}} = \frac{3}{2}RT ). This equation arises from the kinetic molecular theory of gases, which states that the average kinetic energy of gas particles is directly proportional to the absolute temperature (measured in Kelvin) of the gas.

In this formula, ( R ) is the universal gas constant (8.314 J/(mol·K)), and ( T ) is the absolute temperature in Kelvin. The factor of ( \frac{3}{2} ) comes from the idea that the average kinetic energy is derived from considering the energy contributions from the three degrees of freedom (motion in the x, y, and z directions) that each molecule has. Thus, this relationship illustrates how temperature affects the kinetic energy of a gas.

The other choices, while they do involve concepts related to gas behavior, do not accurately represent the average kinetic energy in the context of kinetic molecular theory as directly as the correct formula does. For instance, the equation ( KE_{\text{avg}} = nRT ) pertains to the total energy for one mole of gas but doesn’t account for the average on a per