Final answer:
To calculate the molecular weight of a gas, use the ideal gas law equation to find the number of moles and then use the formula mass/moles. In this case, the gas has a molecular weight of approximately 44.7 g/mol.
Step-by-step explanation:
To calculate the molecular weight of a gas, we can use the ideal gas law equation: 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. Rearranging the equation, we can solve for the number of moles (n) using the given density of the gas and the ideal gas law equation. Once we have the number of moles, we can use the formula: molecular weight = mass/moles, to calculate the molecular weight of the gas.
Given:
Density (d) = 2.41 g/L
Temperature (T) = 25°C = 298 K
Pressure (P) = 770 mm Hg = 770/760 atm = 1.01316 atm
Ideal gas constant (R) = 0.0821 L.atm/mol.K
Using the given density, we can calculate the number of moles:
n = d/V = 2.41 g/L / (1 L/22.4 L/mol) = 53.984 mol
Finally, we can calculate the molecular weight using the formula:
Molecular weight = mass/moles = 2.41 g / 53.984 mol = 0.0447 g/mol = 44.7 g/mol
Therefore, the molecular weight of the gas is approximately 44.7 g/mol.