|MadSci Network: Chemistry|
You are right that Henry's Law constants are empirically determined, but they don't have to be if you're willing to go through the complete thermochemical evaluation, and if you have all the information needed. Unfortunately, this is usually way too complicated. But let me explain basically what's involved. The Henry's Law constant is actually an equilibrium constant. Ultimately, equilibrium constants describe the change in enthalpy and entropy between two states. It is Le Chatelier's principle that "drives" the eventual approach to equilibrium in the system. But saying this is just hiding one mystery behind another. What's actually going on is the redistribution of energy into the lowest overall configuration. Nature likes to spread itself, make itself even. It's what drives diffusion and chemical reactions. Energy is bouncing around until a stable configuration is found. An interesting point here is that this stable configuration depends on knowing every single aspect of the system, including the temperature. Another important point is that the equilibrium constant has almost nothing to do with the rate at which the process takes place. It just tells you what the final states will be if conditions don't change, eventually. Determining the change in free energy of a molecule, say carbon dioxide, from air to dissolved liquid water requires understanding either the final thermochemical state (delta G) of carbon dioxide in air and liquid water, or, the difference of thermochemical states between all the intermediate steps in going from gas to liquid, or liquid to gas. The intermediate steps may include enthalpy of solution, enthalpy of vaporization, ... You also have to know the change in entropy. But even then, you're not done because carbon dioxide, once it's in a liquid form, has to go into equilibrium with other states such as carbonic acid and the various carbonates. And even after you know all the intricate chemical permutations and incorporate it all into an overall equilibrium constant, you have to consider things like how deep is the water? For example, a really thin layer of water has a high surface area to volume ratio. The thermochemical equilibrium will change near the surface because different things are affecting the solution (e.g. surface tension). So since it's all quite complicated, it's easier just to measure the value empirically. The empirical nature of the Henry's Law constant is a convenient way of glossing over all this complexity into a convenient and useful number. This is a really tough question if you want it answered properly. I only hope to have given you a peep into the kind of issues involved. As for the bottle of beer, the Henry's law constant is different for two compounds. I'm sure what was meant was that the partial pressure of carbon dioxide in the air inside the closed bottle was in thermochemical equilibrium with the concentration (mol/l) of carbon dioxide in the liquid. You can't of course, know this for sure, because maybe somebody picked up the bottle and shook it, or maybe it was taken out of the refrigerator and the temperature of the gas above the liquid is warming faster than the liquid. He probably was talking about some stale beer inside a dusty factory that's been untouched and untampered with for ages. Yuck. I like my beer cold and with a good head of foam. I'm sure you have other questions... pick up a book on thermochemical equilibrium or statistical thermodynamics. Paul Atkins has a good book on General Chemistry as well.
Try the links in the MadSci Library for more information on Chemistry.