The equation for Cp of a diatomic gas is represented by which formula?

The formula for the heat capacity at constant pressure, Cp, of a diatomic gas can be derived from kinetic theory and statistical mechanics. For ideal gases, the heat capacity can be calculated based on the degrees of freedom associated with molecular motion.

A diatomic gas has several types of energy contributions:

1. Translational motion (which is related to movement in three dimensions) contributes 3/2 R per mole.

2. Rotational motion (which generally includes rotation around two perpendicular axes) adds another R per mole, since each rotational degree of freedom contributes 1/2 R at constant temperature.

3. Vibrational modes may also contribute at higher temperatures, but for the basic calculation of Cp for diatomic gases at lower temperatures, they are often not considered initially.

Putting all these contributions together:

• Translational: 3/2 R

• Rotational: 1 R

• Total for a diatomic gas: Cp = (3/2)R + R = (5/2)R

However, at higher temperatures where vibrational modes become significant, the vibrational contribution would need to be included. This can lead the overall calculation to suggest that for certain vibrational modes activated, the total can account for additional energy,