The other day, I was wondering, if cheap and easy nuclear fusion were developed tomorrow and fossil fuels disappeared, would there be a way to fuel all the gas-powered cars out there? After all, we have the Haber-Bosch process for producing ammonia. But then gasoline is not a chemical but a mixture of different organic compounds. So, let me structure a question to get at the heart of my curiosity:
How might we produce gasoline from electricity on an industrial scale without the use of fossil fuels as input?
Assume the electrical power came from an unlimited source, such as nuclear fusion, solar arrays in space, or very specific magic.
You may also assume that the gasoline doesn't need to be replicated perfectly -- that which can fuel anything that uses gasoline, or which satisfies an industry definition of gasoline, is sufficient. Ethanol does not count, since most cars cannot use it solely.
Feel free to comment on the environmental friendliness of the solution, excepting the electricity generation itself.
This basic question was originally asked here, and where it was suggested to migrate to chemistry SE.
Answer
Historically, this sort of process has been done with the Fischer–Tropsch process.
The core of this process is to use "syngas" (a mixture of $\ce{CO}$ and $\ce{H2}$) in the presence of a catalyst to make higher molecular weight hydrocarbons:
$$\ce{(2n + 1) H2 + n CO → C_{n}H_{2+2n} + n H2O}$$
Under normal conditions, this will actually make mostly straight-chained hydrocarbons, which are great for diesel fuel, but not so great for gasoline/petrol engines. However, there are standard catalytic cracking techniques in the petrochemical industry which can adjust the branchedness of hydrocarbons, making them more "gasoline like".
Now, the only question is where to get the $\ce{CO}$ and $\ce{H2}$ from? The $\ce{H2}$ is easy, as it is readily obtained from the hydrolysis of water.
The $\ce{CO}$ can be obtained from $\ce{H2}$ and $\ce{CO2}$ by the water-gas shift reaction (here technically run in reverse):
$$\ce{CO2 + H2 \rightleftharpoons CO + H2O }$$
As I mentioned, the Fischer–Tropsch process was actually used during WWII by the Germans to produce motor fuel, as conventional sources were blocked off by the Allies. Their syngas didn't come from $\ce{CO2}$ and water, though, but from reformed coal, which they had a ready supply of.
This process is not done much because it's hugely inefficient, compared to just digging oil out of the ground. But if you have a "too cheap to meter" supply of electricity, the efficiency concerns go away. The main issue is getting a ready supply of $\ce{CO2}$, and there are a number of techniques being proposed at the moment for scrubbing $\ce{CO2}$ from the atmosphere - either by capturing it from point-source generators like power plants and cement manufacturers, or from "artificial trees" which capture $\ce{CO2}$ directly from standard atmospheric concentrations.
These "artificial trees" tend not to use normal photosynthesis for carbon capture, but instead often use something like a (strong) base in aqeous solution or $\ce{CaO}$. In these systems the base or the $\ce{CaO}$ reacts with dissolved $\ce{CO2}$ to form a carbonate salt, which either stays in solution or precipitates out. This carbonate salt formation is favorable, and happens spontaneously. The energy intensive portion of the process is the regeneration of the basic solution/$\ce{CaO}$. This normally happens by heating the carbonate salt, which causes $\ce{CO2}$ release. If done correctly, this can produce a stream of relatively pure carbon dioxide. But again, the regeneration step is quite energy intensive, and so would not be feasible without a cheap source of power.
Other environmental considerations would be minimal, aside from the land needed for the $\ce{CO2}$ devices (you would need a fair number to get a suitable steady volume of $\ce{CO2}$), and any disposal concerns about the process catalysts (which shouldn't be any more onerous than dealing with the catalysts now used in the petrochemical industry).
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