Generating 500g hydrogen requires 25kWh (and a perfectly-efficient electrolyser would require 20kWh). One gallon of fuel has about 40kWh of energy available.
To put it another way - by this proposed system, assuming 35mpg, an annual personal mileage of 5000 miles would need a dedicated installed solar capacity of 2kW nominal, assuming a 20% capacity factor. This takes up 15sq. meters. Mutiplied by the population of the US, that's 4,500sq km of solar, just for fuel for driving.
The majority of the energy content of the "sustainable" fuels in your scenario would have to come from sources other than the biomass feedstock. Sure solar generates more power per acre than photosysntheis, but it's very expensive - especially in a sustainable world where the solar panel factories are powered by solar panels, and not by coal.
To put it another way - by this proposed system, assuming 35mpg, an annual personal mileage of 5000 miles would need a dedicated installed solar capacity of 2kW nominal, assuming a 20% capacity factor. This takes up 15sq. meters. Mutiplied by the population of the US, that's 4,500sq km of solar, just for fuel for driving.
The majority of the energy content of the "sustainable" fuels in your scenario would have to come from sources other than the biomass feedstock. Sure solar generates more power per acre than photosysntheis, but it's very expensive - especially in a sustainable world where the solar panel factories are powered by solar panels, and not by coal.