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I have a year-long research project next year in my senior year of high school, in which we have to make some product or prototype to solve some issue.

My interest was in the Liquid Fluoride Thorium Reactor but considering that I do not have the access I need, I opted to invest in the heat it produces.

One use as proposed by Kirk Sorensen proposed using the heat from the reactor to fuel the sulfur-iodine cycle to split water into $\ce{H2}$ and $\ce{O2}$. Then use those combined with carbon collected from the waste of coal and fossil fuel plants and nitrogen from the atmosphere to make methanol dimethyl-ether and ammonia.

My teacher and I have ruled out the first two, but decided that we might be able to make ammonia. My question is whether it would be feasible and practical to use the sulfur-iodine cycle in combination with the Haber process to split water and make ammonia at a much lower temperature and pressure to ensure safety.

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Yes this is possible but you must remember it is a reversible reaction so if more pressure creates ammonia, applying less will cause the reaction to reverse creating some of the reactants again.

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