That 3 kWh/kg estimated by the poster above corresponds to an abysmal efficiency of an internal-combustion engine, of less than 25%.
Modern cars with good high-compression engines have efficiencies over 40%.
A fuel cell with hydrocarbons could reach efficiencies of 60% or more.
So no lithium battery can reach volumic energies or specific energies comparable to what can be achieved with hydrocarbons.
The reason to use lithium rechargeable batteries is to obtain a better total efficiency of using energy, not the hope that it is possible to match the densities achievable with energy stored in hydrocarbons.
Among lithium rechargeable batteries, the lithium-air batteries should achieve the best energy per mass, perhaps also per volume.
Usually the weak point of metal-air batteries is the power per mass or the power per volume, because the reaction with air is slow, therefore the electrical current density in the electrodes is low, so to obtain a given amount of power requires great areas for the electrodes.
Modern cars with good high-compression engines have efficiencies over 40%.
A fuel cell with hydrocarbons could reach efficiencies of 60% or more.
So no lithium battery can reach volumic energies or specific energies comparable to what can be achieved with hydrocarbons.
The reason to use lithium rechargeable batteries is to obtain a better total efficiency of using energy, not the hope that it is possible to match the densities achievable with energy stored in hydrocarbons.
Among lithium rechargeable batteries, the lithium-air batteries should achieve the best energy per mass, perhaps also per volume.
Usually the weak point of metal-air batteries is the power per mass or the power per volume, because the reaction with air is slow, therefore the electrical current density in the electrodes is low, so to obtain a given amount of power requires great areas for the electrodes.