In gas laws and physical chemistry, the molecular mass of a gas is ________.

Introduction / Context:
In physical chemistry, several different properties describe gases, including molecular mass, vapour pressure, density and temperature. It is important not to confuse these properties or assume simple proportional relationships where none exist. Molecular mass is an intrinsic property of the gas molecules, while vapour pressure is a property of a liquid in equilibrium with its vapour at a given temperature. This question checks whether you understand that molecular mass and vapour pressure are not directly proportional in the simple ways suggested.

Given Data / Assumptions:

• Molecular mass (also called molecular weight) is the mass of one mole of gas molecules, measured in kg per mole or gram per mole.
• Vapour pressure is the pressure exerted by a vapour in equilibrium with its liquid at a given temperature.
• The options suggest simple proportional relationships between molecular mass and vapour pressure such as twice, equal to or half.
• We assume ideal or near ideal behaviour but focus on conceptual relationships rather than exact equations.

Concept / Approach:
Molecular mass depends on the types and numbers of atoms in a molecule and is fixed for a given substance. Vapour pressure depends mainly on the temperature and the nature of intermolecular forces in the liquid form of the substance. For example, a liquid with weak intermolecular forces tends to have a higher vapour pressure at a given temperature. There is no universal rule that vapour pressure is equal to, half of or twice the molecular mass. While lighter molecules may sometimes correspond to higher vapour pressures, many exceptions occur because intermolecular forces and molecular structure are more important. Therefore, molecular mass and vapour pressure are not directly related by any simple multiplicative factor.

Step-by-Step Solution:
Step 1: Define molecular mass as the mass of a single molecule times Avogadro number, specific to each gas.Step 2: Define vapour pressure as the pressure of gas in equilibrium with its liquid at a given temperature.Step 3: Note that molecular mass is measured in g/mol or kg/mol, while vapour pressure is measured in pascal or related units.Step 4: Recognise that having different dimensions means they cannot be numerically equal in a meaningful unit consistent way.Step 5: Realise that there is no general law stating vapour pressure is half or twice molecular mass; such relationships would be arbitrary.Step 6: Conclude that, in general, the molecular mass of a gas is not directly related to its vapour pressure by a simple fixed factor.

Verification / Alternative check:
Consider water and ethanol. Water has a molecular mass of about 18 g/mol, while ethanol has about 46 g/mol. At room temperature, ethanol has a significantly higher vapour pressure than water despite having a larger molecular mass. This simple comparison shows that vapour pressure does not increase or decrease uniformly with molecular mass. Instead, hydrogen bonding and other intermolecular interactions control vapour pressure. Many pairs of substances show different trends, confirming that no simple proportionality connects molecular mass and vapour pressure.

Why Other Options Are Wrong:
The statements that molecular mass is twice its vapour pressure, equal to its vapour pressure or half its vapour pressure are not based on any accepted physical law. They mix quantities with different units and dimensional forms. Even if one tried to assign numerical values, these relationships would fail across different substances and temperatures. Therefore, these options are incorrect general statements about gases.

Common Pitfalls:
Students sometimes assume that every property of a substance must have a direct simple relationship with every other property. In reality, some properties are independent. Another mistake is to confuse vapour density, which does have a relation with molecular mass under some conditions, with vapour pressure. Vapour density is proportional to molecular mass for gases at the same temperature and pressure, but vapour pressure is a different concept. To avoid confusion, keep clear definitions of each property and avoid assuming proportionality without a known law.

Final Answer:
The molecular mass of a gas is not directly related to its vapour pressure by any simple fixed factor.