Exercise 4G Question 5

[Vivian Leung 1C]

Hi, I was just wondering how you would determine the number of different orientations for the molecules in this problem (see attachment).

According to the Solution Manual, there are supposed to be 12 different orientations for the "cis" molecule and 3 different orientations for the "trans" molecule.

[Hannah_Butler_2E]

So the way I'm thinking about it is if you look at the two red dots as one structure, this is the structure that you have to figure out how many positions it can occupy. For the trans molecules, this structure can occupy three different orientations, you can think about them as the x y and z axes on this molecule. For the cis molecule, the red structure can occupy four spaces on the x axis alone (by rotating the red dots around the center yellow dot and stopping every 90 degrees). In fact, the red structure can fit into four positions each on the x, y, and z axes of this molecule. So you multiply 3 times 4 to get 12 total positions for the cis molecule.

What I don't understand is why you consider both red dots together when determining the microstates of this molecule. I guess it's because they are the only variable aspect of this molecule? If someone else could explain this part that would be helpful!

[Andersen Chu 2H]

^ I think it is because when you consider the possible positions of the red atoms, you are also considering the possible positions of the other atoms because they must move as the red atoms move. Therefore, you are basically considering all possibilities by just looking at how the red atoms can move

[Vivian Leung 1C]

Thank you everyone!

[David Jen 1J]

Why do we power W with avogadros constant? Is it because we are calculating the delta S in units of mol?