Hello All:
Please let me know if I've made any mistakes in the analysis which follows.
Thank you...
Considering all the problems related to the Parkhomov Charge Amount and MFMP
Replication, I have decided to formulate an Engineered Version of the
Ideal Gas Law to calculate maximum theoretical pressures that may be obtained
in an experiment. This should be painstakingly simple but will
serve as a reference...
Recall the Ideal Gas Law:
PV = nRT, where P = Pressure, V = Volume, n = Number of Gas Species, R =
Gas Constant & T = Temperature.
Typically, T is given in Kelvin, n in moles (of gas) & V in Liters. Thus, if
one would like the Pressure in Pascals, R (the Gas Constant) would
be:
R = 8.314462 [L][kPa] / ([K][mole])
This would result in the pressure being in kilo-Pascals.
Please note that the Ideal Gas Law assumes an Ideal Gas as opposed to a Real
Gas, and is thus an approximation, valid in certain regimes...
Now let us take a look at the Relevant Parkhomov Experiment Values (or the
values used to make a pressure estimation):
900 mg Ni x (1 g Ni / (1000 mg Ni )) x (1 mole Ni
/ (58.69 g Ni )) = 0.01533 moles Ni
100 mg LiAlH4 x (1 g LiAlH4 / (1000 mg LiAlH4)) x (1 mole LiAlH4 /
(37.95 g LiAlH4)) = 0.002635 moles LiAlH4
V = 2 ml (please note that the calculated volume for the Parkhomov Cell is
actually 2.3562 ml; cylinder diameter 5 mm & length 120 mm)
T = 1300 C = 1573.15 K (maximum Parkhomov temperature obtained, but away
from the center and closer to the heater coils)
Starting Pressure: 1 Standard Atmosphere
If we assume the worst case scenario in which all of the Hydrogen evolves to H2
Gas, and that gas does not permeate the Ni or the Vessel Housing
(both unrealistic), then we will have twice as many moles of H2 Gas, as to
moles of LiAlH4:
n = 0.005270 moles H2 Gas
We also note that we will obtain 4 times the atomic Hydrogen, if all the
Hydrogen decomposes to H:
0.01054 moles H
If we compare this to the number of moles of Ni we see that we have less H
atoms than Ni atoms; recall that the maximum loading ratio for Ni:H is
1:1 . This is important to note, scientifically.
Now let us crunch through the ideal gas law equation, and determine the
Pressure. I will leave this as an exercise to you. Recall that:
1 Pascal = 0.000145037738 pounds per square inch
If I’ve done the calculation correctly, you will obtain close to 4999 psi of
pressure at T = 1300 C (1573.15 K). If one uses the method described
in the translation of Parkhomov's first set of slides (applying Boyle's Law,
then hand waving through Amonton's Law), one will obtain a value of
about 4548 psi.
In order to make this calculation easier for the experimenter, I have
reformulated the Ideal Gas Law into more manageable values:
Pressure [psi] = delta[psi] + (0.063553 x (w[mg LiAlH4] x (273.15 + T[C]))
/ V[ml]
where delta = starting pressure of 1 atmosphere = 14.6959488 pounds per
square inch
, w = measured weight of LiAlH4 charge in milligrams
, V = Headspace Volume in milliliters
, T = Temperature in degrees C
& P = Vessel Pressure in psi
Here I've added an additional term (delta), reflecting a starting pressure and
which introduces a small correction.
More succinctly,
P = delta + ((0.063553 x w x (273.15 + T)) / V)
delta = 14.6959488 psi
w = 100 mg
T = 1300 C
V = 2.3562 ml (Volume of a cylinder whose diameter is 5 mm (radius (r) = .25
cm) and length (L) is 120 mm (L = 12.0 cm), V = L*pi*r**2)
Using this formula, the calculated pressure for the above Parkhomov parameters
becomes 4258 psi. This is calculated using the actual volume of
2.3562 ml and assuming the solid charge takes up zero volume.
This form should be useful for quickly calculating maximum theoretical
pressures in Parkhomov-type Experiments.
Mark Jurich
