Final answer:
The molecular weight of the gas is 38.07 g/mol, calculated by multiplying its given density by its volume. The density of the gas at STP is 1.70 g/L, found by dividing the molar mass by the molar volume of the gas at STP conditions.
Step-by-step explanation:
To find the molecular weight of a gas when given its volume, density, and the fact that it's 1 mole, we use the formula density = mass/volume. In this case, the gas has a density of 1.41 g/L and occupies 27.0 L. By multiplying the density by the volume, we get the mass (1.41 g/L × 27.0 L = 38.07 g), which is the molar mass since it's for 1 mole of the gas.
Next, to determine the density of the gas at STP (standard temperature and pressure), we use the fact that one mole of an ideal gas occupies 22.4 L at STP. Since the molar mass is 38.07 g/mol (from our first calculation), the density at STP can be calculated by dividing molar mass by molar volume at STP: Density at STP = 38.07 g/mol ÷ 22.4 L/mol = 1.70 g/L.