Hydrogen is what your making, and for a car to run off from that, it needs a shit ton of it and compressed to like 5000psi in a tank and even then it pretty much blows as a car fuel.
Its Hydrogen and Oxygen. How is it any different than a browngas torch, lamp, or the like? It cant be a replacement for gasoline, but surely it can reduce the amount of gas you need for combustion.
as for the little bit you are releasing from a jar of water, and sucked into your intake.
Idk much about electrochemistry but from a pure spliting perspective
say you have 1 liter of water. that's about 1kilo of water at room temperature. 18 grams per mole, 1kilo has 55.55 moles of water. 55.55moles of H2, 27.2 moles of O2. not an ideal gas, but lets pretend. so V=nrt/P
665.4 Liters of O2
1358.977 liters of H2
of potential in a perfect system from a single liter of water. tote around a few liters on a system that pumps out 30-50 liters an hour to supplement the oxygen in the normal air intake and throwing some H2 in there...the mixture of which burns great at internal combustion temperatures... you cant tell me that it wont give you better milage.