Final answer:
The number of moles of gas is 2.14 moles and the molar mass (Mr) is approximately 122.43 g/mol. Based on the molar mass, the gas could be diatomic sulfur (S₂) or another substance with a similar molar mass.
Step-by-step explanation:
To determine the number of moles of a gas from a given mass and volume, we use the ideal gas law and the concept of molar mass. When we are given that 48 dm³ of a gas has a mass of 262 grams, we can first convert the volume to liters since standard molar volume is commonly used in these units.
Since 1 dm³ equals 1 L, the volume of the gas is 48 L. At standard temperature and pressure (STP), 1 mole of an ideal gas occupies 22.4 L. Therefore, to find the number of moles, we divide the volume of gas by the molar volume at STP:
Number of moles (n) = Volume of the gas at STP / Molar volume at STP
= 48 L / 22.4 L/mol
= 2.14 moles.
To find the molar mass (Mr), we use the mass of the gas divided by the moles of the gas:
Mr = Mass / Moles
= 262 g / 2.14 mol
= 122.43 g/mol.
Based on the molar mass, the element could be Sulfur (S), which has an approximate molar mass of 32.07 g/mol when formed as a diatomic molecule (S₂), or another substance with a molar mass around 122.43 g/mol.