Les,
My kid finked out on me. He has his chem books spread between my place and my ex-wife's and I couldn't convince him to drop by her house to get his CRC Chem-Physics reference---even though he lives ten minutes away.
So, I am left to my own resources. Luckily his intro chem text is here at my place. So here are some numbers and techiques that apply to the gas constant.
The point here is to figure out the capacity and efficiency of a gas centrifuge of a given physical size, while processing UF6 gas.
UF6 has two versions, florine plus uranium to give two values for mass:
(19 x 6) + 235 = 349
(19 x 6) + 238 = 353
According to wikipedia the molar mass of UF6 is 352.02 g/mol.
GAS CONSTANT. (From Principles of Chemistry, Oxtoby, Nachtrieb)
The gas constant R is figured: R = PV/nT.
P = pressure
V = volume
T = temperature
n = 1 mole (Avagadro's number of `particles', could be atoms or molecules) atm = 1 atmosphere pressure
For 1 mole of water at ice point T which approaches the value 22.414 L atm at low temperature:
R = (1.01325 x 10^5 newton m^-2 atm^-1)(10^-3 m^3 L^-1)(22.414 L atm)/
(1.0000 mole)(273.15 K)
= 8.314 newton m mol^-1 K^-1.
Since one newton-meter is the work done by a force of one newton per one meter distance, defined as one joule, then the gas constant is:
R = 8.314 J mol^-1 K^-1. (GAS CONSTANT)
PROBLEM. How many grams of helium are needed to fill a balloon?
(Assume, one atm pressure, 22.414 liter-atomspheres V, PV = C. Boyle's Law)
PV = nRT
n = PV/RT
If P is expressed in atmospheres and V in litres, then
R = 0.08206 L atm mol^-1 K^-1.
n = (1.00 atm)(1.00 x 10^4 L)/
(0.08206 L atm mol^-1 K^-1)(303.15 K)
= 402 moles
The molar weight of Helium is 4.00 g mol_1, the mass of Helium required is:
(402 mol)(4.00 g mol^-1) = 1610 g = 1.61 kg
BOLTZMANN'S CONSTANT. (Also possibly useful)
The number of moles n is the number of molecules N divided by Avagadro's number N_0 (6.0221 x 10^23 mol^-1). Rewriting the gas law:
PV = (N/N_0) x RT
= Nk_B T
where k_B = R/N_0.
k_b = R/N_0 = (8.314 J mol^-1 K^-1)/(6.022 x 10^23 mol^-1)
= 1.3807 x 10^23 J K^-1. (BOLTZMANNS CONSTANT)
I'll work on the diffusion constant tomorrow night.
CG