Hello dear prof stuart. at the 2:14 moment why none of the boxes are left empty. is it impossible to be some empty boxes as Free Volume? however there must be some free volumes which can be thought as empty boxes.thanks alot for your explanation in advance 🌹🌹🌹
A liquid sits on the bottom of the container, and any free (gas) space is above the liquid. So the lattice, in this case, just represents the sites at the bottom of the container, which are occupied by the solution. It is certainly possible to develop a lattice model that includes empty boxes, representing free space. See this video, for example: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-cS_Pdia7myA.html But if the model allows molecules to occupy all boxes, with empty space below them, it's a model of a gas, rather than a liquid.
@@PhysicalChemistry Thanks alot. but i have a problem because it seems be a solid without having empty boxes between liquid molecules.empty cells can provide moving probablity for molecules
This model doesn't specify any mechanism for *how* the molecules can change places. We just assume that they can. Remember that it is the *ideal* solution model. In other words, the simplest model possible, like the ideal gas model is the simplest model possible for a gas. You could certainly complain that real gas molecules aren't infinitely small with no interactions, like the ideal gas model claims they are. And you'd be right. But that's not the point of the ideal gas model. You could develop a more complicated model for gases, which would be more accurate, but would also be more difficult to solve. The simple model is good enough for some purposes, and explains *why* gases expand, etc. Similarly, you could design a more accurate model of solutions, that includes mechanisms for diffusion, etc. It might be more accurate, but the ideal solution model is good enough for explaining the energy and entropy of mixing similar solvents. "Make your models as simple as possible, but not simpler."
proffesor wouldn't it be change in entropy is zero because changing arrangements or microsystems would be changing entropy so changing microsystems in this case would mean the change in entropy is zero in the ideal solution sytem.
Your questions are subtle ones: I like them Entropy is often tricky because you have to specify clearly which micro/macro state you're discussing. You're right that each *micro*state in an ideal fluid is equally likely. But we can't really discuss the entropy of a single microstate. Entropy is used to discuss macrostates, or collections of microstates. If we're distinguishing between "unmixed" and "mixed" fluids, then there a lot more microstates that we would describe as "mixed" than microstates that we would describe as "unmixed". So the entropy of mixing is positive. For a concrete example of ideal fluids mixing on a lattice model, see this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-v7UzSsbHAmw.html
