Answer :
Final answer:
To calculate the molar mass of an unknown gas using Graham's Law of Effusion, we set the rate of effusion of Ar equal to that of the unknown gas and solve for the molar mass, revealing that the unknown gas could be methane (CH4).
Explanation:
The student's question involves calculating the molar mass of an unknown gas using Graham's Law of Effusion. This law posits that the rate of effusion for a gas is inversely proportional to the square root of its molar mass (M). If the conditions are the same and 1% of gas effuses in 97.6 seconds, we can use the known effusion time for argon (Ar) and the given time to solve for the molar mass of the unknown gas.
Using Graham's Law, we have:
(Rate of effusion of Ar) / (Rate of effusion of unknown gas) = sqrt(Molar mass of unknown gas) / sqrt(Molar mass of Ar)
Assuming we know the molar mass of Ar to be approximately 39.95 g/mol and given that the unknown gas effuses in the same time as Ar, then we can state:
(1 / 97.6) / (1 / 97.6) = sqrt(Molar mass of unknown gas) / sqrt(39.95)
Which simplifies to:
1 = sqrt(Molar mass of unknown gas) / sqrt(39.95)
Thus,
Molar mass of unknown gas = 39.95 g/mol, suggesting that the gas could be methane (CH4), the only gas with this molar mass.