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${CO_2}$ is plentiful in Martian atmosphere. $H_2$ can be produced on Mars using sunlight and can be reacted with $CO_2$ to form $H_2O+C$, or $CH_4+H_2O$.

Is it a feasible chemical reaction?

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Is production of methane possible on Mars?

Yes, via the Sabatier process. This has been proposed multiple times as a type of in-situ resource utilization on Mars. All that's needed is energy (e.g., sunlight), CO2, and hydrogen. The first two are easily obtainable. Except near the poles, the last is a bit of a challenge.

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