# Solid diprotium saturated vapour density

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• snorkack

#### snorkack

What precisely is the equilibrium vapour density of bulk solid diprotium surface now, at 2,7 K?

The density of the world falls with some power of temperature (which one?). The density of saturated vapour falls exponentially.
At which temperature shall the world saturate with respect to bulk solid diprotium?

What has your research brought you so far ? Any reason you don't like hydrogen and focus on the isotope that's overwhelmingly dominant anyway ?
http://www.tvu.com/PEngPropsSH2Web.htm
https://www1.eere.energy.gov/hydrogenandfuelcells/tech_validation/pdfs/fcm01r0.pdf
https://en.wikipedia.org/wiki/Solid_hydrogen
https://nvlpubs.nist.gov/nistpubs/jres/47/jresv47n2p63_a1b.pdf

Can you give some more context ? What are you trying to find ? What, for example is the reason you want it 'precisely' (without giving a definition) ? In an age of global warming it might be good enough to use approximate values from physical property approximation expressions and equations of state ?

Anyway, why look at solid hydrogen when first the oceans freeze, then O2 and N2 condense etc etc ?
The density of the world falls with some power of temperature (which one?)
The temperature of the earth, of course But if the 'which' refers to the power, then I'd start with 1 (see iron/nickel or rock)

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• berkeman
What has your research brought you so far ?
Tables tend to break off at temperatures far above 2,7 K.
That one was useful.
Vapor pressure of the solid (20.4 K equilibrium hydrogen) follows the equation

log P (mm Hg) = A + B/T + CT,

where A = 4.62, B = -47.02, C = 0.02023, although the vapor pressures for a mixtures closer to normal hydrogen are somewhat lower 
For 2,7 K, I get log P at about -13.
Can you give some more context ? What are you trying to find ? What, for example is the reason you want it 'precisely' (without giving a definition) ? In an age of global warming it might be good enough to use approximate values from physical property approximation expressions and equations of state ?

Anyway, why look at solid hydrogen when first the oceans freeze, then O2 and N2 condense etc etc ?
The temperature of the earth, of course But if the 'which' refers to the power, then I'd start with 1 (see iron/nickel or rock)
Hydrogen and helium are as yet gases, even in molecular clouds.
How does that present equilibrium vapour pressure, of 10-13 mm Hg, compare with pressure in molecular clouds?

Dunno, but outer space is different from 'the world' . With a few H atoms per m3 there's no chance of solid formation.

For 2,7 K, I get log P at about -13
wouldn't trust those numbers: with those values in the Antoine eqn I can't even reproduce the pressures they mention ! and 2.7 K is extrapolating way out...

compare with pressure in molecular clouds
Those guys have funny 'standard units' P/kB of 104 to 107 cm-3 K, it seems (nice exercise: convert to mm Hg -- I get 10-15 to 10-12 , so perhaps a case of oops! -- but I may well be mistaken. It's past bedtime here )

But then again, when you google 'interstellar ice' or 'volatiles' ... Let me know if and how you find inroads for this diprotonium ice !

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wouldn't trust those numbers: with those values in the Antoine eqn I can't even reproduce the pressures they mention ! and 22.7 K is extrapolating way out...
Sure, but I could not find actual measurements for 2,7 K.
Do you expect that the pressure would be subject to some sort of Antoine equation?

Here's another (table 6) with eqn ##A + B/T + B'\ln T##
Perhaps you can sort out he references mentioned here (section 2.2.30) ; data are on P 6-288

Here's another (table 6) with eqn ##A + B/T + B'\ln T##
Page 17. For eH2, it gives A as 2,5 (for Torr), B as -85,3, B' as 2,9.
For 2,7 K, that would mean B/T=-31,6, ln T=1, B´/ln T=2,9
then ln Q=2,5-31,6+2,9=5,4-31,6=-26,2
log Q=ln Q/2,303=-11,5

Thus, two sources give P as 10-13 and 10-11,5 mm Hg respectively. Appreciable divergence, but not unreasonably big seeing how these are extrapolated out of the measurable range. Same ballpark.
How do these numbers - 10-13...10-11 mm Hg - compare to the present pressures in molecular clouds?