It was found that argon effused through a membrane in 24 hours, and an unknown gas diffused through the same membrane in 22.1 hours. What was the molecular weight of the gas?
To determine the molecular weight of the unknown gas, we can use Graham's law of effusion. Graham's law states that the rate at which a gas effuses or diffuses is inversely proportional to the square root of its molar mass.
Let's denote the rate of effusion for argon as Rargon, and the rate of effusion for the unknown gas as Runknown. According to the problem, it is given that:
Rargon = 1 (since it effuses in 24 hours)
Runknown = 1 / 22.1 (since it diffuses in 22.1 hours)
Now, let's use Graham's law to find the ratio of the rates of effusion:
Rargon / Runknown = √(Munknown / Margon)
Substituting the known values, we have:
1 / (1 / 22.1) = √(Munknown / 40)
Simplifying further:
22.1 = √(Munknown / 40)
Squaring both sides:
22.1^2 = Munknown / 40
Munknown = 22.1^2 * 40
Calculating this expression, we find:
Munknown ≈ 194.216
Therefore, the approximate molecular weight of the unknown gas is 194.216 units.