Problems
1) What is the rms speed in m/s of uranium hexafluoride, UF6 at 25 degrees C?
2) If it takes 4.83 ml of an unknown gas the same amount of time it take 9.23 ml of argon, Ar to effuse through the same hole, what is the molecular weight of the unknown gas?
3) Using the van der waals equation calculate the pressure of ethanol C2H5OH vapor at 82.0 degrees C, if 1.00 mol occupies 30.0 L. (a = 12.56 L2 atm/mol2, b = 0.08710 L/mol)
Answers
1) Molecular weight of uranium hexafluoride is 352.02 g/mol.
Rms is determined by the equation u = (3RT/Mm)^1/2
U = (3*(8.31J/K*mol)*298K/(0.352kg))^1/2 = 145 m/s
2) Recall that the rate of effusion of a gas is inversely proportional to the square root of an elements molecular weight. We can set up an expression like this:
Rate of diffusion of unknown/rate of diffusion AR = (MAr/Munknown)1/2
(4.83mL/9.23mL)2 = (40 g/mol/x)
0.27x = 40g/mol
x = 148 g/mol
3) Manipulating the vander waals equation in terms of pressure:
P = [(nRT/V-nB)] – [(n2a/V2)]
I like to determine the correction factors separately
V – nB = 30.0L – 1.00mol*0.08710 L/mol = 29.91L
n2a/V2 = (1.00mol)212.56 L2 atm/mol2/(30.0L)2 = 0.01396 atm
P = (1.00 mol*0.08206 L*atm/(K*mol)*355K)/29.91L – 0.01396atm = 0.960 atm