What is the ratio of average kinetic energy between argon and chlorine at 27°C?

To determine the ratio of average kinetic energy between argon and chlorine at a given temperature, we can use the formula for the average kinetic energy of an ideal gas, which is directly proportional to the absolute temperature. The formula is given by:

[ KE = \frac{3}{2} kT ]

where KE is the average kinetic energy, k is the Boltzmann constant, and T is the temperature in Kelvin.

Since both gases are at the same temperature (27°C), we first convert this temperature to Kelvin:

[ T = 27 + 273.15 = 300.15 , K ]

The average kinetic energy will be identical for any monatomic gases at the same temperature. However, argon (Ar) is a monatomic gas while chlorine (Cl2) is diatomic. When comparing their kinetic energies, we need to consider the molecular mass as the kinetic energy also involves the mass of the molecules.

Kinetic energy can also be expressed as:

[ KE = \frac{1}{2} mv^2 ]

Here, m is the mass of a gas molecule. Because argon has a lower molar mass compared to chlorine, it will have a higher average speed at the same temperature.