Learning #4

            The end of the semester is now upon us. Two more days of classes remain and I still can’t believe how fast it has all gone by. I have learned so many things this semester it is really hard to fit them all into four two-page responses.

            I know most of you aren’t well versed in the realm of physical chemistry and thermodynamics. It’s probably not a topic that most would find “fun.” Words like torturous and excruciating probably come to mind. The reason I am talking about this is because it’s a perfect example and summation of what I wrote in my first learning response. In that entry I wrote about how I was learning new ways to learn as well as putting the pieces of the puzzle together. In the last lecture of physical chemistry this afternoon we finally derived an equation that brought the class full circle. It was an equation that we used almost all the time in general chemistry and never knew what it was for.

            After years of just accepting it, an entire semester of deriving and working up to it we finally saw where the equation came from. I am talking, of course, about the equilibrium constants of a reaction and how they relate to concentrations of the various reactants and products present in the solution. We also explained why you never take the solvent into account when calculating the equilibrium constant.

            This is only true for dilute solutions, which is a pretty good approximation when talking about a solute in a solvent. Unless the solution is very concentrated, the solvent will be the majority of the solution. As it turns out this number as a function of reaction extent (or how far the reaction has proceeded) is RTln(conc solvent+reaction extent/conc solvent). The reaction extent has to be between zero and one therefore it becomes approximately RTln(1), which, of course, is zero because the natural log of one is always zero. This value therefore drops out of the equation and no longer needs to be accounted for. This is why the solvent never shows up in the equilibrium constant expression.

            Another part of this derivation yielded a huge mess of partial derivatives with respect to the reaction extent that were a result of taking the derivative of the Gibbs free energy per mole as a function of reaction extent. As complicated as it may sound or may look the derivative of that whole mess ends up summing to zero. That leaves the classic equation .

            It may not seem like much but it was a lot of time waiting and wondering where it actually came from. This is a prime example why I love taking my upper-level major courses. I’m finally learning why and where things come from as opposed to just learning how to plug numbers into these magical equations that give you the right answers on tests.

            I have also learned that understanding where things come from and deriving them from scratch has increased my knowledge on the subject immensely. I can now answer questions about thermodynamic equilibrium that I wouldn’t even have known how to start previously. I cannot only explain that the equation works but how it works. Call me crazy but I find that incredibly exciting and fascinating.

            Seeing my learning experiences this semester come full circle is one of the most satisfying feelings. I may have not learned as much material this semester as I have in previous ones, but the depth that I’ve been able to learn in incredible.