If 4.83 mL of an unknown gas effuses through a hole in a plate in the same time it takes 9.23 mL of argon, Ar, to effuse through the same hole under the same conditions, what is the molecular weight of the unknown gas?
(rate 1/rate 2) = sqrt(M2/M1)
rate = 4.83/sec and 9.23/sec.
To determine the molecular weight of the unknown gas, we can use Graham's Law of Effusion.
Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In mathematical terms, we can write it as:
Rate A / Rate B = √(Molar mass B / Molar mass A)
In this case, we are comparing the rate of effusion of the unknown gas (A) to that of argon (B).
Let's assign the following variables:
Rate A = 4.83 mL
Rate B = 9.23 mL
Molar mass A = unknown gas
Molar mass B = molar mass of argon (39.95 g/mol)
Using the given information, we can rewrite Graham's Law equation as:
4.83 mL / 9.23 mL = √(39.95 g/mol / Molar mass A)
Now, let's solve for the unknown molar mass A:
(4.83 mL / 9.23 mL)^2 = 39.95 g/mol / Molar mass A
Simplifying further:
(4.83 / 9.23)^2 = 39.95 / Molar mass A
Taking the square root of both sides:
4.83 / 9.23 = √(39.95 / Molar mass A)
Now, let's solve for the unknown molar mass A:
Molar mass A = (39.95 / (√(4.83 / 9.23)))^2
Calculating this expression will give you the molecular weight of the unknown gas.