Final answer:
The molar mass of the gas is calculated using the ideal gas law equation, PV = nRT, to first determine the number of moles. Using the mass provided and the calculated moles, the molar mass is found to be 29.87 g/mol.
Step-by-step explanation:
The question asks for the molar mass of a gas given its mass, pressure, volume, and temperature. To find the molar mass, we will use the ideal gas law PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Reorganizing the equation to solve for n (n = PV/RT), and then using the mass of the gas and the moles calculated to find molar mass (molar mass = mass/n), we can find the answer.
First, we convert the given conditions to the appropriate units: temperature (K), volume (L), and pressure (atm). Temperature T is given in Kelvin (260 K), volume V is 7.00 L, and pressure P is 0.550 atm. Using R = 0.0821 (L·atm)/(K·mol), we can substitute the known values into the rearranged ideal gas law.
Moles (n) = (0.550 atm × 7.00 L) / (0.0821 L·atm/K·mol × 260 K) = 0.154 mol
Molar mass = mass / moles = 4.60 g / 0.154 mol = 29.87 g/mol