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Nitrogen into ammonia
The nitrogen is free, the hydrogen is the cost, and an iron catalyst joins them into the fertiliser the gardens need.
See it in the tour: chapter garden, shot 6.3.
Free, but not usable
About 95% of Titan's air is nitrogen physics. Plants cannot use it as nitrogen gas, because its two atoms are held by a triple bond. The gardens need it bound to hydrogen, as ammonia, NH₃. Ammonia is 82% nitrogen by mass physics.
The Garden Hall's trees are civic. Food grows in sealed agricultural modules out of sight, and those are the customers fiction.
Getting the nitrogen
Titan's air is 93.65 K and carries 5.65% methane physics. Methane freezes at 90.6 K and nitrogen boils at 77.3 K physics. Cooling the air to between the two freezes the methane out and leaves nitrogen gas design. The sea gives more: nitrogen flashes out of the barge load before the methane is sorted. See Sorting the sea.
Getting the hydrogen
Hydrogen is the expensive half. Two routes feed the plant design.
From ice. Electrolysis splits water, and it makes eight times as much oxygen as hydrogen by mass physics. It takes at least 285.8 kJ per mole of hydrogen physics. See Water, oxygen and electrolysis.
From methane. Heat alone cracks methane into hydrogen and solid carbon, and no oxygen is needed physics:
CH₄ → C + 2 H₂
Bonds broken: 4 C–H. Bonds formed: 2 H–H.
- 10⁰ m The hot reactor
- 10⁻⁹ m Bonds break and re-form
It takes 37.3 kJ per mole of hydrogen, 7.7 times less than electrolysis physics. The cost is solid carbon, 0.53 t for every tonne of ammonia physics.
The synthesis loop
Nitrogen and hydrogen go in at three to one, are compressed to 100 atmospheres or more, and run over iron at 400 to 450 °C physics. Carl Bosch described that loop in his Nobel lecture in 1932, and it is still the loop.
N₂ + 3 H₂ → 2 NH₃
Bonds broken: 1 N≡N, 3 H–H. Bonds formed: 6 N–H.
- 10⁰ m The synthesis loop
- 10⁻⁹ m Bonds break and re-form
Only part of the gas turns to ammonia on each pass. The ammonia is condensed out and the rest goes round again physics. The reaction gives off 91.9 kJ per mole of nitrogen, about 2.7 GJ for every tonne of ammonia physics. At 94 K that heat is not waste. It is kept design.
Ammonia boils at 239.8 K and melts at 195 K physics. On Titan's open ground it would be a solid, so it is stored warm.
What a tonne costs
For each tonne of ammonia the plant takes 0.82 t of nitrogen and 0.18 t of hydrogen physics. Via ice that means 1.59 t of water, at least 25 GJ, and 1.41 t of oxygen left over physics. Via methane it means 0.71 t of methane and at least 3.3 GJ physics. The oxygen is not a waste. See Fire on Titan for what it is worth.
Key numbers
| Quantity | Value | Basis |
|---|---|---|
| Reaction | N₂ + 3 H₂ → 2 NH₃ | physics |
| Heat released | 91.9 kJ per mole of nitrogen | physics |
| Loop conditions | 100 atm or more, 400 to 450 °C, iron | physics |
| Nitrogen / hydrogen per tonne of ammonia | 0.82 t / 0.18 t | physics |
| Hydrogen from ice: water, oxygen, energy per tonne of ammonia | 1.59 t, 1.41 t, at least 25 GJ | physics |
| Hydrogen from methane: methane, carbon, energy per tonne of ammonia | 0.71 t, 0.53 t, at least 3.3 GJ | physics |
| Ammonia boiling / melting point | 239.8 K / 195 K | physics |
Sources
- Carl Bosch, Nobel lecture 1932, The development of the chemical high pressure method during the establishment of the new ammonia industry
- NIST Chemistry WebBook, ammonia (enthalpy of formation, phase change data)
- NIST Chemistry WebBook, methane (enthalpy of formation, phase change data)
- NIST Chemistry WebBook, nitrogen, phase change data
- NIST Chemistry WebBook, water (enthalpy of formation, liquid)