All you need is napkin maths. We gain energy by turning carbon into carbon dioxide. Now, we need the same energy to reverse it, but with a loss factor. In addi

All you need is napkin maths. We gain energy by turning carbon into carbon dioxide. Now, we need the same energy to reverse it, but with a loss factor. In addition to the chemistry other people have mentioned -- if we burn hydrocarbons and then capture carbon we're still net positive H -> H2O, capturing carbon as carbonate rocks can be less expensive than splitting CO2 to C and O2, etc -- most serious proposals for carbon capture have involved using cheap electricity, e.g. solar power in the middle of the day. It's quite possible that using cheap midday electricity to generate methane (which can be easily stored in large quantities) which is then burned in gas "peakers" when power is expensive would be economically profitable despite not being thermodynamically profitable.