Answer :
Final answer:
Using Graham's law of effusion and the given effusion rates, the molecular mass of the unknown gas is calculated to be approximately 66.0 g/mol. The correct answer is option: b. 66.0 g/mol
Explanation:
The question involves calculating the molecular mass of an unknown gas using Graham's law of effusion. According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
The relationship can be represented as (Rate of Gas1 / Rate of Gas2) = sqrt(Molar Mass of Gas2 / Molar Mass of Gas1). To find the molecular weight of the first gas, we apply this formula using the given rates of effusion:
R1 = 83.3 cm²/s for the unknown gas
R2 = 0.102 dm²/s for the known gas (which is CO2 with a molar mass of 44.0 g/mol)
Note: 1 dm² = 10000 cm², so R2 needs to be converted to cm²/s:
R2 = 0.102 dm²/s * 10000 cm²/dm² = 1020 cm²/s
Now we can solve for the molar mass of the unknown gas (M1):
(83.3 cm²/s) / (1020 cm²/s) = sqrt(44.0 g/mol / M1)
=> (83.3 / 1020)^2
= 44.0 g/mol / M1
M1 = 44.0 g/mol / (83.3 / 1020)^2
M1 = 66.0 g/mol
Therefore, the molecular mass of the unknown gas is approximately 66.0 g/mol, which corresponds to option b.
