Final answer:
The molar mass of the unknown gas is found to be approximately 21.14 g/mol by applying the ideal gas law formula.
Step-by-step explanation:
To calculate the molar mass of the unknown gas using the information provided and the ideal gas law equation, we can rearrange the equation in terms of molar mass (MM):
MM = (mRT) / (PV)
where:
m = mass of the gas (3.87 g)
R = universal gas constant (0.0821 L·atm/K·mol)
T = temperature in Kelvin (325 K)
P = pressure (2.00 atm)
V = volume of the gas (2.45 L)
We need to plug in the numerical values into the equation:
MM = (3.87 g × 0.0821 L·atm/K·mol × 325 K) / (2.00 atm × 2.45 L)
MM = (103.59725 g·L·atm/K·mol) / (4.9 L·atm)
MM = 21.14 g/mol
The molar mass of the unknown gas is approximately 21.14 grams per mole.