Questions: Gas phase sulfur (S) and gas phase oxygen (O2) have the same molar mass. At the same temperature, they also have the same A C(v) B average KE per mole C average rotation KE per mole D average translational KE per mole

Solution Steps

We are given that gas phase sulfur (S) and gas phase oxygen (\(\mathrm{O}_2\)) have the same molar mass and are at the same temperature. We need to determine which of the given options they have in common under these conditions.

Let's analyze each option to see which property is the same for both gases:

• Option A: \(C(v)\)
  \(C(v)\) is the molar heat capacity at constant volume. This property depends on the molecular structure and degrees of freedom of the gas, not just the molar mass or temperature. Therefore, it is not necessarily the same for sulfur and oxygen.

• Option B: Average KE per mole
  The average kinetic energy per mole of a gas is given by \(\frac{3}{2}RT\), where \(R\) is the gas constant and \(T\) is the temperature. Since both gases are at the same temperature, they have the same average kinetic energy per mole.

• Option C: Average rotation KE per mole
  The average rotational kinetic energy depends on the molecular structure and degrees of freedom. Since sulfur and oxygen have different molecular structures, this energy is not necessarily the same.

• Option D: Average translational KE per mole
  The average translational kinetic energy per mole is also given by \(\frac{3}{2}RT\). Since both gases are at the same temperature, they have the same average translational kinetic energy per mole.

From the analysis, both options B and D are correct because they both relate to the average kinetic energy per mole, which depends only on temperature for ideal gases.

Final Answer