## 4G.5

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

AKhanna_3H
Posts: 104
Joined: Wed Sep 18, 2019 12:19 am

### 4G.5

How would you explain why the cis crystal would have a higher entropy than the trans isomer? Also what does residual entropy mean and is it different than entropy? Thank you!

Jeremy_Guiman2E
Posts: 82
Joined: Fri Sep 28, 2018 12:29 am

### Re: 4G.5

The cis form would have the higher residual entropy because it has many more possible orientations than the trans form.
If we used the Boltzmann entropy equations, we can see that the cis form would have a greater entropy.

Residual entropy is a particular type of entropy - it is "the nonzero entropy at T = 0 in certain systems, which is due to a surviving disorder in the
orientation of molecules." Basically, it's the entropy that still exists in a molecule after it's been reduced to T=0.

Posts: 81
Joined: Fri Aug 09, 2019 12:17 am

### Re: 4G.5

According to the textbook, the cis compound has 12 different orientations while the trans compound only has three different orientations, decreasing the entropy due to the fact that there is less uncertainty in its orientations. In regards to entropy, residual entropy is the measure of how many different arrangements a molecule can have while molar entropy is a measure of a molecule's chaos. Residual is the amount of entropy left once it is cooled to 0 kelvin.

Delaney Smith 1C
Posts: 52
Joined: Thu Feb 28, 2019 12:15 am

### Re: 4G.5

madawy wrote:According to the textbook, the cis compound has 12 different orientations while the trans compound only has three different orientations, decreasing the entropy due to the fact that there is less uncertainty in its orientations. In regards to entropy, residual entropy is the measure of how many different arrangements a molecule can have while molar entropy is a measure of a molecule's chaos. Residual is the amount of entropy left once it is cooled to 0 kelvin.

I'm having a hard time seeing why the cis compound has 12 different orientations while the trans only has 3. Can anyone explain this? It really just looks like they would have the same amount of orientations.

Alice Chang 2H
Posts: 101
Joined: Fri Aug 30, 2019 12:18 am

### Re: 4G.5

Delaney Smith 1C wrote:
madawy wrote:According to the textbook, the cis compound has 12 different orientations while the trans compound only has three different orientations, decreasing the entropy due to the fact that there is less uncertainty in its orientations. In regards to entropy, residual entropy is the measure of how many different arrangements a molecule can have while molar entropy is a measure of a molecule's chaos. Residual is the amount of entropy left once it is cooled to 0 kelvin.

I'm having a hard time seeing why the cis compound has 12 different orientations while the trans only has 3. Can anyone explain this? It really just looks like they would have the same amount of orientations.

It's kind of hard to visualize it, but if you look at the VSPER model and try to imagine it rotate in 3-d, you'll notice that the cis model has 12 orientations. If it helps, look at a single red dot, and rotate it around into the different positions in comparison to the other red dot. It's hard to explain in words, but if you map it out visually (draw it out helps!), you'll see that there is 12 for cis, and only 3 for trans.

Trans is a bit easier to explain its 3 orientations, since the 2 red dots have to be across from each other at all times. Thus, there are only 3 orientations that it can take if the red dots have to be across each other, along the x-, y-, and z-plane (thinking about it mathematically).

Hope this helps somehow??

Return to “Third Law of Thermodynamics (For a Unique Ground State (W=1): S -> 0 as T -> 0) and Calculations Using Boltzmann Equation for Entropy”

### Who is online

Users browsing this forum: No registered users and 1 guest