Intuitively it seems that doing electrolysis to produce gasses under higher pressure must take more energy, because in addition to the chemical energy of the products you also have to account for the potential energy of the compressed gas that you're creating. However, the Nernst equation doesn't seem to take pressure into account. Also, it's conceptually difficult for me to imagine exactly how the presence of high-pressure gas above a solution would translate into more energy being consumed during electrolysis. If I'm doing electrolysis at a given voltage in a closed container, would I see a gradual current drop for a given voltage as pressure builds up?
I too have pondered this as it would seem to be low capital cost way to get tank of high pressure Hydrogen (or other gases that can be electrolytically produced from a liquid. Chlorine being one of economic importance from strong brine solutions.) Low capital as no pump required. The lack of any significant weight pump is especially beneficial in a hydrogen powered car as the weight of a hydrogen gas compression pump is also avoided. (The H2 compression pump cannot be left in your garage as you may need to recharge the H2 storage tanks when at friend house in another city, etc. -It must be in the car, if the system needs one.) The water in the "gravity well" of the hydrogen fuel tank would need to be replenished periodically but the work done to inject, via a tiny water pump, would not be great as the H2O volume is relative small. It would be easy to calculate the work required as one can imagine a cylindrical "gravity well" with the water level in it rising like a piston pushing against the gas pressure resistance above the water surface. This pressure can even be assumed to be constant with little error as the gas volume would large compared to the reduction (compression) of the gas volume. Likewise one could calculate with ease the work done on the entire gas volume by compressing it a small fraction. I agree with the OP - It will take more energy to due electrolysis under pressure by exactly the work done plus the heat produced during the compression of the gas above the "water piston." I note that the products are the two gases, H2 & O2 but as water is H2O the number of oxygen molecules is exactly half as many as hydrogen produced. In practice to keep the H2 & O2 separate the water well would be "U" shaped with rather tall vertical arms connecting the H2 to its separate tank and the O2to its separate tank which has half the volume of that H2 tank. This 2:1 volume ratio would tend to keep the pressure in both tanks equal. That is important as the water in the bottom of the U tube is the barrier that prevents the mixing of the two gases. However, if one vertical arm is on one side of the car and sun is shining on that side then the vertical height of the water in that warmer of the two vertical arms will be lower due to the extra pressure the higher temperature produces, Thus a clever design for the two arms connecting the produced gases to their separate storage tanks is concentric vertical tubes. (Oxygen tube inside the hydrogen tube with inner radius such that when the volume of the outer radius of the oxygen tube is subtracted from the volume of the larger inner radius of the hydrogen tube the 2:1 volume ratio is achieved. If the wall of the smaller inner tube is thin and metallic then the volumes of both vertical arms will tend to maintain the same temperature, even if there is sun on one side of the car only. For the same "thermal / pressure" reasons the two gas storage tanks should be concentric, or at least in good thermal contact and insulated from external temperature changes, but they need not be vertical. If you consider the wall stress in a gas storage tank (neglecting minor end closure costs) the cost of storing volume V of gas is essentially independent of the choice between one big tank vs. two or more smaller tanks.(You may have noticed that trucks transporting compressed gases normally have many small tanks, instead of one big one. - in part this is because the volume of steel pipe produced with say 10 inch diameter is much greater than pipe with 60 inch diameter. Thus in practice, it is cheaper to by 36 thinner walled steel pipes than one thick walled 60 inch diameter pipe. Thus in the car application, a multitude of relatively small diameter parallel tubes would be the "under body" floor board of the vehicle. There could be very simple design automatic shut off values in each, which close IFF that tube has a sudden loss of pressure (was ruptured by some idiot owner placing the jack on it when starting to change a flat tire, etc.). These tube would be basically just thin sheet metal rolled up in to cylinders as keeping the weight of the storage tank as small as possible is important. So important that probably the O2 tube is not within the H2 tube "stealing" volume from it. Instead there are twice as many H2 tubes as O2 tubes, all the same size in good thermal contact under the car and with some light weight insulation over the assembly of tubes. For example a cross section cut thru the under body of the car, between the wheels might look like" HOHHOHHOHHOHHOHHOHHOHHOHHOHHOH where each letter represents a gas storage cylinder. I have illustrated 10 oxygen storage tube and 20 hydrogen storages tubes but when volume produced, they are probably extruded, not welded together individual cylinders - this greatly reduces the cost of the gas storage tank. Also in this case they would not be round cylinders but more like: ____________ UUUUUUUUUU but of course the top bar is closing the "U"s and each of the vertical parts except for the extreme left and right vertical is very quite thin (normally has the same pressure on both sides of that "division wall.") Thus, within the limitations of "typed drawing" the cross section is more like: ______________ lLLLLLLLLLLLLLll However, all surfaces exposed to the one atmosphere air pressure are with at least a slight bulge outward to the air side. Now a few words more about the vertical concentric tube: They of course can be curved, so will easily fit in the structural roof support column between the two doors of a four door car (or at the rear of door if only a two door car) As the gas evolving electrodes are easily divided into two each and as already discussed two gas pressure tubes are as cheap as one larger one, there should be a concentric H2/O2 quasi-vertical slightly curved unit in both the right and left roof support column. There will need to be two small ID tubes separately collecting the H2 & O2 from the top of these concentric "vertical" differential pressure compensation tubes leading down to the under floor distribution manifold that delivers the H2 & O2 separately to the thin under floor extruded storage unit, crudely illustrated in cross section by the typed drawings above. Now for the question of how these two gases are to be used: (1) Most of the time as the car even at 70mph on level road requires only about 30 or less HP from a small H2/O2 fuel cell producing H2O, but that water is NOT released as exhaust. (It is very pure and the electrolysis unit needs very pure water to avoid becoming "posioned." - Any the owner adds is triple distilled "battery water" now available in most gas stations, but probably the sealed system has a LifeTime supply in it from the factory and no connection for adding water even exists as it could be an impurity path into the sealed system.) Ideally, the water produced by the fuel cell flows thru a "counter flow" heat exchanger to warm the H2 & O2 separately coming to the fuel cell to make it more efficient and probably smaller, with less weight for the same HP (power) output; however economic consideration may cause it to just be pumped directly back into the electrolysis unit (bottom of the "vertical" tubes in the roof support columns). If it is still with some warmth, when car is connect to the electric plug, this also reduces the expenditure of electrical energy, but most of the warm water produced by driving on fuel cell power will become cool before returning for more electrolysis. (2) Sometimes more power that the fuel cell can produce is wanted, or even immediately needed to avoid an accident. Thus the car should be a hybrid with an IC engine also. The best currently practical fuel for this IC is sugar cane produced alcohol. Currently, alcohol is the dominate car fuel in Brazil by 17%* as it cost much less to drive with alcohol fuel and amazingly, in the same flex fuel motor, approximate 3% MORE power is produced than when gasoline is the fuel. This IC motor, IMHO, should always be running (for immediate emergency power boost, when needed) but as the wheels are driven by electric motors the IC always drives a generator. The power output of a generator is thermally limited - copper coils make heat that must get out to the air. However for 10 seconds or so the generator can be overloaded buy a factor of 6 or so. Let’s assume that the IC and the fuel cell both are small. With fuel cell peak power of 30HP and the "idling power" of the IC only2 HP and its max steady state of 30HP also. Then for brief emergency you can go from using 17HP (half from the fuel cell's 30 + 2 from the idling IC) to (180+30) = 210HP in small fraction of a second. Much more than a light weight car can handle without "burning rubber" even if all four wheels have electric motors in them (and of course they would be rated for much less steady state power total also, so briefly badly over loaded to, but not permanently damaged by saving your life.) PS, I am too old to worry about patent disclosure etc. so if anyone wants to use these ideas they can. -------------- * What comes out of the "gasoline" pump at the filling station is actually 25% alcohol, by volume, now. (When price of alcohol is high because demand for it from flex-fuel cars, the government can mandate a lower than 25% alcohol content in the "gasoline.") Currently for every 100 liters of gasoline sold, only 63L come out of the pure alcohol pump, but as >90% of all new cars made in Brazil sold are flex-fuel cars, next year the volume of alcohol sold will be more than 66% of the volume of "gasoline". Most of the gasoline cars now being sold in Brazil are bigger, imported, gas hogs, that the very rich buy as the cost of driving on pure alcohol is now only about 60% as much as if you buy "gasoline” at the pump. Currently when the alcohol in 100L of "gasoline" i.e. 25L is added to the 63L of pure alcohol and subtracted from the "gasoline" there are 88L of alcohol for every 75L of pure gasoline being sold in Brazil in mid 2009. I.e. 17+% more alcohol than gasoline is now being used by the Brazilian fleet of cars. Next year that will climb to at least 20% more alcohol than gasoline used in cars in Brazil (In the US, I think the use of alcohol is less than 5% of the gasoline volume. - Not very "green" yet in the USA - Brazil is at least two decades ahead of the USA in this area still. -It takes at least a decade to change your car fleet fuel used. Current "cash for clunkers" is portrayed as a "green measure" as well as a stimulus but in the long run it is "anti-green" as it lowering the average of the cars on the US roads, prolonging the time when they will be replace by alcohol or electric hybrids, etc.) PS As the storage tanks are below the water surface in the "vertical" roof post columns, and because there will be H2O vapor in both the gas storage units, on cold nights, liquid water will accumulate in the gas storage tanks. The tiny pump which re-injects the H2O produced by the fuel cell can also re-inject this water too, perhaps only periodically when the car is going downhill, or parked with front lower than the rear, so the condensed water is conveniently near the fuel cell, which I assume is in the front part of the car. (And thermally connected to the "always idling" IC motor for better efficiency. In fact, the "counter flow" heat exchanger could easily be part of the IC motor block. Those blocks usually have voids in them to make them lighter and larger than the old style VW, water flow passages also for cooling. I.e. If the block is aluminum (and that will not dissolve to poison the fuel cell or electrolysis units) then using the sealed system water for part or all of IC cooling can improve the system efficiency and even slight reduce the cars weight!)
I haven't studied chemistry for a while and I don't remember what the Nernst equation is, but from a purely intuitive point of view would not the increase in pressure increase the amount of gas dissolved in the solution and thus the rate of the back-reaction? Thus some equilibrium is reached eventually unless you crank up the voltage? Just a guess.
Chem class has been a long time ago for me as well, but iirc the pressure enters the Nernst equation as a concentration term of the products(which are then not at stp), raising the necessary cell voltage.
