Final answer:
To determine the molar mass of the unknown gas, Graham's law of effusion is used, comparing the known molar mass of argon and the measured pressures to calculate the unknown molar mass.
Step-by-step explanation:
To calculate the molar mass of the unknown gas in the effusion experiment, we can apply Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Since the conditions and the time allowed for effusion were kept the same for both argon and the unknown gas, we can compare their effusion rates through the pressures observed.
The formula for Graham's law is:
Rate of Effusion1 / Rate of Effusion2 = √(Molar mass2 / Molar mass1)
We know the molar mass of argon (Ar) is 39.948 g/mol, and it effused into the flask to create a pressure of 15.0 mm Hg. The unknown gas created a pressure of 47.4 mm Hg. Let's assume the effusion rate is directly proportional to the pressure the gases exerted in the flask since they effused for the same duration. We can set up the following equation using Graham's law with pressures to represent the rates of effusion:
15.0 mm Hg / 47.4 mm Hg = √(39.948 g/mol / Molar mass of unknown gas)
Solving this for the molar mass of the unknown gas gives:
Molar mass of unknown gas = 39.948 g/mol × (√(47.4 mm Hg/15.0 mm Hg))2
From this equation, you can calculate the molar mass of the unknown gas.