Final answer:
The molar mass of the gas at STP is calculated using the proportion between the mass of the gas, the volume it occupies, and the known molar volume of 22.4 L which results in a molar mass of 39.424 g/mol.
Step-by-step explanation:
To calculate the molar mass of the gas at standard temperature and pressure (STP), you can use the known fact that 1 mole of an ideal gas occupies 22.4 L at STP. Since you have 1.76 g of gas occupying 1.0 L, you can set up a proportion where the mass of the gas is directly proportional to the volume it occupies.
Using the molar volume of 22.4 L, you can find the amount of gas in moles and subsequently its molar mass. Here's the calculation:
Molar mass of the gas = (1.76 g / 1.0 L) × (22.4 L / 1 mol) = 39.424 g/mol.
Therefore, the molar mass of the gas is 39.424 g/mol.