Problems with the Kamlet-Jacobs Equations

I had recently read about the Kamlet-Jacobs equations, and thought that they were very interesting, it was claimed that they could predict within about a 5% error the detonation pressure and VoD of energetic materials (at least those that have a density of above 1.0 g/cc and are composed solely of C-H-N-O atoms.)

I am writing a paper for a chemistry class (a high school class, not college) I'm in about predicting behavior of real and theoretical energetic materials using the equations.

In order to get familiar with the equations I decided to calculate VoD for TNT and EGDN to see how accurate the equations were. However, I always got values that were far above the real VoDs for the explosives.

I am using these equations:


D = A x (1 + B x p) x sqrt(phi)

PCJ = K x p^-2 x phi

phi = N (sqrt( M x Q ))

Where:

D = detonation velocity in mm/us (km/s)
PCJ = Detonation pressure in kilobar
N = moles gas/gram of explosive
M = Mean molar mass of gaseous products
Q = Explosive detonation enthalpy per gram
p = Density in grams per cubic centimeter

A, B and K are computed constants.

A = 1.01

B = 1.30

K = 15.58

(I apologize in advance if the formatting gets messed up)

German Wikipedia has a page on it:
https://de.wikipedia.org/wiki/Kamlet-Jacobs-Gleichungen


As for my sample calculations:


For EGDN:

N = 0.033
M = 30.41
Q = 7400
p = 1.49

C₂H₄N₂O₆ -> 2CO₂ + 2H₂O + N₂

That's 5 moles gas per mole EGDN. And the molar mass is 152.1g/mol

5/152.1 = 0.03287

The mean molar mass of the products would be ((18.02)2 + (44.01)2 + 28.01)/5 = 30.41g/mol

As for Q:

(-285.8kJ/mol)2 + (-393.5kJ/mol) + (0kJ/mol) = -1358.6kJ/mol

-1358kJ/mol - (-233kJ/mol) = -1125.6kJ/mol enthalpy of detonation

-285.8 being the enthalpy of formation of water, -393.5 that of carbon dioxide, and -233 being that of EGDN

-1125.6 / 152.1 = 7.4004 kJ/g or 7400.4 J/g

(the enthalpy of formation of EGDN was taken from NIST https://webbook.nist.gov/cgi/cbook.cgi?ID=C628966&Mask=2)

So the equation would seem to be:

phi = 0.033 ( sqrt(30.41 x 7400.4) ) = 15.65

D = 1.01 (1 + 1.3 x 1.49) x sqrt(15.65)
D = 11.74 km/s

Which is obviously way too high, that would be higher than for any known explosive.

For TNT:

N = 0.0253
M = 28.52
Q = 5883
p = 1.65

I'll spare all the other calculations, but note that since TNT is very oxygen-deficient, I calculated moles of gas and detonation enthalpy using the assumption that H₂O and CO₂ were produced, not CO gas, as the production of CO₂ seems more favorable (at least at standard conditions, of course an explosion is not that, but still).

The equation is then


phi = 0.0253 ( sqrt(28.52 x 5883) ) = 10.36

D = 1.01 x (1 + 1.3 x 1.65) x sqrt(10.36)
D = 10.23 km/s

Which is also obviously too high, closer to that of octanitrocubane than TNT.

Interestingly enough, if the equation is amended to:

D = A x (B x p) x sqrt(phi)

D = 1.01 x (1.3 x 1.65) x sqrt(10.36)
D = 6.97 km/s

and

D = 1.01 (1.3 x 1.49) x sqrt(15.65) = 7.74 km/s

For TNT, that is pretty close to the literature value of 6900m/s, and for EGDN the literature says 7500m/s, also pretty close.

However, this doesn't make any sense. I must be calculating something wrong, but I've calculated several times and I get the same results.

So, any ideas? I could really use the help. Thanks!

Quote: Originally posted by MineMan

There is a paper by an Iranian prof. It’s a much better and simpler equation.

Quote: Originally posted by Microtek

The Iranian scientist referred to is probably Mohammad Keshavarz, who has written a host of papers on different mathematical models of energetics. Just be aware that it is inherently problematic to extrapolate fitted empircal models to unknown substances. You can use the models to locate candidate energetics for further experimental studies though.