Hello Dr. Stuart! This might be a minor quibble, but starting at 6:50 you switch from partial differential notation to total differential notation and I was wondering how and why that happened. Is this mathematically rigorous? Thanks!
Good question, and good eye. The math is fine, though. The partial derivative just specifies what direction the derivative is taken in: ∂/∂T means you are changing T while holding other variables constant. Once you break the derivative down into differentials, then the dT on the right side is just describing how much the T is changing, and the d(ln a) on the other side describes how much the log activity changes in response. These are just infinitesimally small changes in a single variable, so we don't use ∂ notation to describe them.
Hi, my final is on friday, may you please explain why the freezing point depression will stop being effective at a certain temperature? Example, why salt won't melt ice when it gets too cold? Thank you!!
Keep in mind that the freezing point depression doesn't prevent the solution from freezing under all conditions. It just shifts (depresses) the freezing point by some amount. If you want an analogy, perhaps you could think of training for exercise. Maybe today I can run 1 km in 5 minutes. (This is like the pure solvent.) Next, I train for a few months. Now I can run 1 km in 4:30 (This is like the solution.) More training = more decrease in my time. But just because I trained doesn't mean I get to run as fast as I want. It's the same with solutions. A little bit of solute lowers the freezing by a little bit. More solute lowers it by more. The reason *why* this happens is hiding in the math described in this video. Adding solute to a solution lowers the chemical potential of the solution. Cooling it down raises the chemical potential. So a solution can be cooled below the freezing point and still have the same chemical potential as the solid at the pure-solvent freezing point. This is why it can stay liquid to colder temperatures.
