Could we seed Earth's atmosphere with hydrogen?

Suppose the chemical reaction:

3 C O_{2} + 2 H_{2} \to 2 H_{2} O + 2 O_{2} + 3 C

This reaction could be used to filter out

C O_{2}

from the atmosphere, slowing down or reversing climate change. The solar system is rich in hydrogen.

There's a problem though, for this reaction to take place requires the catalyst of iron in the form of an aerosol.

Though this might work on a planet without life, it would most certainly kill off all life on earth.

What kind of future technology could make this a possible method taking

C O_{2}

out of the atmosphere at a global scale with or without iron aerosol?

Or is there another realistic way of taking

C O_{2}

out of the atmosphere with technology within the span of a few decades? Assuming carbon neutral energy generation of no more than an order of magnitude higher than earth currently has.

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Could we seed Earth's atmosphere with hydrogen?

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