I think you are trying to make a complex problem even more so. I made, what I think are very generous assumptions to the anti-ID crowd, and considered this as a simple probability problem. The boundary conditions are at 151, with answers to objections on a couple subthreads from there (160 and such). Shouldn't be too hard to follow.
Not sure where you are going with the mol question, nor its relevance. Here's a corollary that might speed the process:
Given about 1078atoms in the universe, a generous estimate of 1055 atoms composing earth, and focusing on fluid dynamics of the boundary layer of lithosphere - atmosphere, what are the numbers for the critical organic builders C and H?
We are talking on the order of about 1045 hydrogen atoms and 1044 carbon atoms. Both estimates >> Avogadro’s constant.
Recall that we are working with a large sphere, and very small things. When you consider it all, turns out that the average density is 10-3 Angstrom-3 for H and 10-4 Angstrom-3 for C. This means an average separation of about 3000 angstroms (quite a chasm) between the critical organic atoms C and H. Since most primordial investigators propose the stable molecules H2O, H2, CH4, and CO2 as the most common sources of H and C, thus the distances are probably even larger by maybe an order of magnitude or two.
The following posts I got from you to make a conclusion.
"I made, what I think are very generous assumptions to the anti-ID crowd,..."
"crowd" a very eloquent scientific term.
"... and considered this as a simple probability problem."
You still lack to show me your simple calculations and tell me which factors you assumed as stochastically dependent and independent. It's not only pencil work.
"We are talking on the order of about 1045 hydrogen atoms and 1044 carbon atoms. Both estimates >> Avogadro’s constant."
That assumption you never mentioned before.
"Recall that we are working with a large sphere, and very small things. When you consider it all, turns out that the average density is 10-3 Angstrom-3 for H and 10-4 Angstrom-3 for C. This means an average separation of about 3000 angstroms (quite a chasm) between the critical organic atoms C and H. "
Density is 10-3 Angstrom-3 for H, pardon? What do you want to say? An H-atom size is about 0.3 Angström or 30 pm so... that was just a joke but is this estimation for aerially or fluid environment?
Your assumptions are in #151:
"The rest is statistical mechanics..."
As I remember statistical mechanics is about gas pressure. So what consistence and pressure you assume for your atmosphere?
Some more at #160:
"You still can't produce a probability that isn't zero."
You too.
My conclusion:
You try to hide your estimations and calculations.
It doesn't bother me what kind of degree you got even if it is something in natural science, you don't act as a natural scientist.
Play your games with someone less capable in science. Try it at some Sunday Schools.
To all others:
I want to mention what we even don't know what kind of molecules we got before earth even existed. A probe from a comet will help to answer this question. Until then results of probability calculations like the above one are just a nice waste of time.
Just to remember:
According to scientific theories all atoms heavier than Hydrogen were produced inside of stars. Therefore the earth is made out of stardust. Therefore we are stardust.