4. Molecular Kinetic Energy and Potential Energy

Concept Explanation:
The total energy of a gas molecule is the sum of its kinetic and potential energies. In an ideal gas, the potential energy due to intermolecular forces is negligible, so the total energy is primarily kinetic.

Kinetic Energy:
The average kinetic energy of a molecule in an ideal gas is directly proportional to the temperature of the gas:
Kinetic Energy = (3/2) k_B T
where k_B is the Boltzmann constant, and T is the temperature in Kelvin.

Potential Energy:
In real gases, intermolecular forces become significant, and potential energy must be considered, especially at high pressures and low temperatures. The potential energy depends on the distance between molecules and the nature of the forces acting between them.

Example Problem:

Calculate the average kinetic energy of an oxygen molecule at room temperature (300 K). The Boltzmann constant k_B = 1.38 × 10⁻²³ J/K.

Solution:

The average kinetic energy is given by:
Kinetic Energy = (3/2) k_B T = (3/2) × 1.38 × 10⁻²³ × 300 ≈ 6.21 × 10⁻²¹ J

So, the average kinetic energy of an oxygen molecule at 300 K is approximately 6.21 × 10⁻²¹ J.