Final answer:
To calculate the molecular weight of a gas, divide its mass by the number of moles. As 2.6 grams of the gas occupies 2.24 liters at STP, it permits the calculation of the moles of gas and subsequently the molecular weight, which is found to be 26 g/mol.
Step-by-step explanation:
To find the molecular weight of a gas, we start with the known volume the gas occupies at standard temperature and pressure (STP), which is 0°C and 1 atm. At STP, one mole of any ideal gas occupies 22.4 liters. By comparing the volume occupied by our unknown gas to the molar volume, we can determine the number of moles of gas we have. Then we can use the mass of the gas to find its molecular weight.
To solve this problem, we calculate the number of moles of gas present in 2.24 liters at STP using the formula for molar volume:
Moles of gas = Volume of gas / Molar volume at STP
Moles of gas = 2.24 L / 22.4 L/mol = 0.1 mol
The mass given is 2.6 g. The molecular weight (MW) is calculated by dividing the mass by the number of moles:
Molecular Weight = Mass of gas / Moles of gas
Molecular Weight = 2.6 g / 0.1 mol = 26 g/mol
Therefore, the molecular weight of the gas is 26 grams per mole (g/mol).