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Since approximately WWI, humanity has been able to fix nitrogen gas from the atmosphere ($\ce{N2}$) into compounds that are much more bio-available, like ammonia and nitrate. The first (hard) step is the Haber-Bosch process $\ce{N2 + 3H2 -> 2NH3}$, which has to be carried out under elevated pressure, temperature and highly anoxic conditions.

Given that our atmosphere is 80% $\ce{N2}$, 20% $\ce{O2}$ and therefore naturally quite oxic, given that nitrate seems to have a much lower enthalpy of fusion(*), given also that typical fertilizer prescriptions are overweight on $\ce{NO3}$ compared to $\ce{NH3}$ (in ratios like 4/1)... why did humanity not develop an industrial process emulating e.g. fixation in lightning and thus synthesizing useful $\ce{NO_x}$ for its fertilizer needs as opposed to $\ce{NH3}$?

(*) In effect, if the Haber-Bosch process is followed by the Ostwald process to make nitric acid, it seems there's going to be a massive loss of exergy (not least because the extraction of $\ce{NH3}$ from the reaction mixture in the Haber-Bosch plant seems to involve a massively wasteful cooling-down step). As an illustration I looked up the standard enthalpy of formation of a mixture (1 mol $\ce{NH3}$ + 1 mol $\ce{KHCO3}$ + 2 mol $\ce{O2}$) vs a stoichiometrically equivalent mixture (1 mol $KNO_3$ + 2 mol $H_2O$ + 1 mol $\ce{CO2}$) and the former contains $\pu{448.5 kJ}$ more than the latter mixture!

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    – Buck Thorn
    Jan 23 at 16:06

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I do not address agriculture application, but extreme energetic demand and inefficiency of direct synthesis of nitrogen oxides by the Birkeland–Eyde process, or the Frank–Caro process of thermal capture using $\ce{CaC2}$. Synthesis of nitric acid via ammonia by H-B process is the most cost and energy efficient process,

There is always long way from labs to industry. Consider how many revolutionary new designs of rechargable cells have been announced during decades.

That quote of the abstract of your linked resource;

This analysis shows that the energy consumption for NOX synthesis with plasma technology is almost competitive with the commercial process with its current best value of 2.4 MJ mol N−1, which is required to decrease further to about 0.7 MJ mol N−1 in order to become fully competitive.

Industry has to first see the decisive advantage to change the technology, as aside energy demand there would be new technology challenges and extra investments.

Much more energy than needed for endothermic reaction $\ce{N2+O2 -> 2NO}$ is wasted, because of creating condition where such reaction can provide sufficient yield by sufficient rate.

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Because the capital investment and energy consumption if the Haber + Ostwald process is still far lower than the alternatives

The reason why specific industrial processes are chosen are usually economics and practicality. While some chemical reactions look, in principle, to be better alternatives (surely direct routes to nitrate are better than making ammonia first and then oxidising it?) they may not be practical or economic.

We also know that some plants can fix nitrogen using enzymatic reactions at normal temperatures and pressures. Every chemist wishes there were a way to industrialise that. It is clearly possible but nobody has ever demonstrated it on an industrial scale. And industrial routes to nitrate were known before the Haber process was developed. But those direct processes (using plasma reactions) were far more expensive in both capital and energy inputs than the, apparently, indirect, combination of Haber and Ostwald processes. 100 years later this is still true. The linked paper shows that the energy cost of plasma processes to nitrate is still about five times higher than the the Haber Ostwald process (per mol of fixed nitrogen). Plus, the capital and maintenance costs are higher.

In short, the choice of which processes are used is based on accessible known reactions when the processes is adopted and the overall economics of the competing processes. Plasma processes were and are still far from competitive despite the theoretical advantages of a direct route to nitrate.

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