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well, of course you can make methane from carbon dioxide and hydrogen, liberating oxygen in the process. Burn petrol and you get energy (heat) and carbon dioxide and water (among other things). To get the reaction to go in the reverse direction, you have to add the same amount of energy, and replace the hydrogen (probably getting it from water, which costs even more energy). What's the use if the stuff ends up costing 1000s of pounds per gallon? Ok, let's say all the energy for this process comes from, say, solar cells, and is 'free'. First point: nothing is free. You have to build that large solar energy facility first. Second point: Wouldn't it be better (more efficient, that is), just to use the electricity you produced directly in a vehicle? It's true that you wouldn't remove carbon dioxide from the atmosphere doing this, but the earth's systems do this nicely, if we leave them alone to get on with it (tho' it does happen quite slowly, and takes a while) and stop adding more than the earth can cope with. Which is precisely what happens if we used that electricity from solar instead of 'petrol'.
Posted by RHambeau