Final answer:
The volume occupied by one mole of a gas at standard temperature and pressure (STP) is not dependent on the molar mass of the gas; this volume is referred to as the molar volume, which is 22.4 L for any gas, assuming ideal behavior. However, the density of a gas is dependent on its molar mass.
Step-by-step explanation:
The statement that the volume occupied by one mole of a gas is dependent on the molar mass of the gas is false. According to Avogadro's Hypothesis, at standard temperature and pressure (STP), the volume of one mole of any gas, assuming ideal gas behavior, is 22.4 liters. This volume is known as the molar volume of a gas. Hence, the volume occupied by a mole of gas is irrespective of the gas's molar mass.
However, when it comes to the density of a gas, it is indeed dependent on the gas's molar mass because density is calculated as the mass per unit volume. Since all gases occupy the same molar volume at STP, the density of a gas can be calculated simply by its molar mass and the standard molar volume (22.4 L).