At a particular pressure and temperature, it takes just 2.040 min for a 3.632 L sample of F2 to effuse through a porous membrane. How long would it take for the same volume of UF4 to effuse under the same conditions
rate F2 = 3.632L/2.040 min = ?
(?/rate UF4) = sqrt(molar mass UF4/2*19)
Solve for rate UF4 gas, then
rate = 3.632 L/min.
You have rate and L, solve for min.
To find the time it would take for the same volume of UF4 to effuse under the same conditions, 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.
First, we need to determine the molar mass of F2 and UF4. The molar mass of F2 (fluorine gas) is approximately 38.00 g/mol (2 × 19.00 g/mol). The molar mass of UF4 (uranium tetrafluoride) is approximately 352.04 g/mol (238.03 g/mol + 4 × 18.99 g/mol).
Now, we can set up the ratio of the rates of effusion:
(Rate of effusion of F2) / (Rate of effusion of UF4) = sqrt(molar mass of UF4) / sqrt(molar mass of F2)
Let's call the unknown time it takes for UF4 to effuse as "t". According to Graham's law, the ratio of the rates remains the same:
2.040 min / t = sqrt(molar mass of UF4) / sqrt(molar mass of F2)
Solving this equation for "t":
t = (2.040 min) * (sqrt(molar mass of F2) / sqrt(molar mass of UF4))
Substituting the molar masses we found:
t = (2.040 min) * (sqrt(38.00 g/mol) / sqrt(352.04 g/mol))
Evaluating this expression:
t ≈ 0.458 min (rounded to three decimal places)
Therefore, it would take approximately 0.458 minutes for the same volume of UF4 to effuse under the same conditions.