I hope that you can calculate it, if you’re teaching it? Well, then, there you go. That calculation is the definition. Really, this is the case for almost all quantities in physics: You can’t directly measure total energy, either. All you can do is calculate 1/2 mv[sup]2[/sup] for all objects, and qV, and mgh, and all the rest, and add all of those together. Then, define the result of that calculation to be “energy”. The only difference is that you’ve known about total energy for longer, so you’re more comfortable with it.
What determines whether something happens is that the entropy (disorder) of the universe has to increase. That is all. However entropy is very difficult to measure (obviously a stacked deck of playing cards has less entropy than one scattered on the table but there is no meter that will measure it. One can calculate it though)
However rather than try and define or measure the entropy of the universe, one breaks down the reaction into two main parts mainly for convenience
(i) entropy of reaction (in principle calculable, and is indirectly measurable)
(ii) entropy change in the rest of the universe (this usually is measured mainly as a heat gain, and what is known as the enthalpy. However, depending on the conditions (e.g. constant Pressure or Volume) the calculation of this term are slightly different. Hence the different types of free energy.
So Gibbs free energy is a theoretical concept, and involves hard to measure items such as entropy of reaction. It works and is used because many of the terms can in principle (though often not in practice) be calculated from first principles. The measured or calculated terms then become extremely useful as they do not change much when changing conditions, so know the entropy and enthalpy at one PTV or set of conditions allows one a good stab at calculating whether the reaction will go at another PTV. By using correction factors such as activities the accuracy can be improved even more.
So a reaction with a decrease in entropy can still be spontaneous if (Delta)H is more negative than -T*(Delta)S.
Now I am not a physical chemist, and I am having trouble locating a reference that proves I am right, but I beleive that this is one reason many reactions go at high pressure go, that would never go at atmospheric pressure. I am specifically thinking of things like the Haber-Bosch proces where several small molecules (H[sub]2[/sub] and N[sub]2[/sub]) are combined into one molecule (NH[sub]3[/sub]), indicating that there is a negative overall entropy.
I was talking about the entropy of the universe. When you are talking about entropy you are only referring about the entropy of reaction. Huge difference. Reread my post
actually my post was a little unclear and its not suprising someone took its meaning somewhat different than I intended.
Actually its not even clear that the entropy of the entire universe has to always increase (e.g if the universe contracts again). But if one takes any large closed system then the entropy must increase within, even though locally it may not appear to as you say.
