The molar weight of water vapor is about 18g per mole, while the molar weight of dry air is about 29g per mole since almost all of it is N2 (28g/mole) and O2 (32g/mole). If a moist air mass and a dry air mass of equivalent volumes were at the same temperature and pressure, which air mass would be denser?

Density is defined as mass per unit volume. Hence the density of a substance (solid, liquid or gas) is directly proportional to its mass and inversely proportional to the volume occupied.

The mass of a gas is the product of its number of moles and its molar mass (mass = number of moles × molar mass), which indicates that the mass is directly proportional to molar mass, so the higher the molar mass, the higher the mass of different gases at equal volumes, temperature and pressure.

From the information given, the molar weight of dry air = 29g/mole.

The molar weight of moist air = molar weight of dry air + molar weight of water vapour = 29 + 18 = 47g/mole.

Therefore since higher molar mass transits to higher mass, it can be said that moist air of molar mass 47g/mole is denser than dry air of molar mass 29g/mole at equal volume, temperature and pressure.

Simple picture the two gasses in two transparent jars, the heavier gas (moist air) settles more at the bottom of the jar, and has less random motion hence is more compressed and denser, than dry air that has more freedom to move randomly because of its lesser weight.