Suppose we wanted to develop a new catalyst to solve our energy problems. All it needs to do is take water and split it into hydrogen and oxygen, then we can burn those products and use it to power things. This process is endothermic, so the energy will have to come from *somewhere*. Well, why can’t it come from the air around our system, for example? We just make the air colder, and with global warming, that is something we don’t mind at all!
Energy + 2 H2O(g) –> 2 H2 +O2
The reason for this ultimately doesn’t have anything to do with catalysis. A catalyst reduces the activation energy of the process, but it *cannot* make any non-spontaneous process into a spontaneous one, meaning a catalyst cannot affect the value of the equilibrium constant of a system. Catalysis affects nothing but the RATE of how quickly a system reaches equilibrium. (see http://en.wikipedia.org/wiki/Activation_energy for details)
Based on the concept of Gibbs free energy, the splitting of water into hydrogen and oxygen at 298K is a non-spontaneous process because the ΔGrxn is positive.
2 H2O(g) –> 2 H2 + O2
The Gibbs equation:
ΔGrxn = ΔHrxn – TΔSrxn
ΔHf for water = -241.8 kJ/mol
ΔHf for H2 = 0 kJ/mol
ΔHf for O2 = 0 kJ/mol
ΔSfor water = 188.7 J/mol·K
ΔS for H2 = 130.6J/mol·K
ΔS for O2 = 205J/mol·K
ΔGrxn = ΔHrxn – TΔSrxn
ΔGrxn = ((0+0)-(-483.6kJ/mol)) –298K·((205+2·130.6)-(188.7))J/mol·K
ΔGrxn = 400.9kJ/mol
Since ΔGrxn is positive, the reaction is not spontaneous under those conditions, meaning energy must be forced into the system. However, since the ΔSrxn component is positive, increasing the temperature will eventually cause the process to become spontaneous as the entropic effects become dominant over the enthalpic effects. For this process, one could expect to see that occur at around a temperature of 1740K. So, if we made an oven that hot, we could do this process, theoretically. The problem, however, is that we have to heat the oven, something which requires a lot of energy. At best, the efficiency of the process breaks even exactly (speaking theoretically, within the bounds of thermodynamics). Realistically, this would be insanely useless.
The ultimate answer to this question is then, there cannot be a catalyst which simply “makes” water turn into hydrogen and oxygen under these conditions because that process is thermodynamically unfavorable. The equilibrium is the controlling factor, not catalysis. It is this reason why the process cannot simply draw energy from the air to make it happen. In short, the answer for this question is basically the 2nd Law of Thermodynamics.
After writing this post, I feel it is safe to say: Science. It works, bitches.
Note: for any of you who don’t find your way here from Reddit, here is why I wrote this post: http://www.reddit.com/info/6nct8/comments/