[technicalbard]

Except the reactions happen at 300C, and the FT reaction is exothermic between H2 and CO, not CO2. taking CO2 apart is endothermic. And then you need to refine the hydrocarbons (because they will look like diesel or wax, not gasoline).

[philipkglass]

Using the standard gas-phase enthalpies of formation, the production of 1 mole of n-octane and 16 moles of water from 8 moles of CO2 and 25 moles of hydrogen is exothermic by 923 kilojoules.

8 CO2 + 25 H2 -> C8H18 + 16 H2O

Energy of products minus energy of reactants:

(-208.7 + 16 * -241.83) - (8 * -393.52 + 25 * 0) = -923

Experimental values are from NIST WebBook.

The hydrogenation of CO2 to CO and water is endothermic and kinetically hindered. The hydrogenation of CO2 to saturated hydrocarbons and water is exothermic (though still kinetically hindered).

There are also hydrocarbon synthesis paths that involve less reforming and purification of high-boiling products than F-T, e.g. methanol synthesis starting from CO2 and H2 followed by Mobil methanol-to-gasoline.