## residual energy

$\Delta S = \frac{q_{rev}}{T}$

Joanna Pham - 2D
Posts: 113
Joined: Fri Apr 06, 2018 11:04 am

### residual energy

Today in lecture, Professor Lavelle talked about residual energy. Could someone please explain what it is? I'm still a bit confused.

He also mentioned that CH4 had no residual energy, but CH3Cl had residual energy. Could someone explain how to determine if a molecule has residual energy please?

Beatrice Petelo 1F
Posts: 62
Joined: Fri Sep 28, 2018 12:17 am

### Re: residual energy

I think you meant residual entropy (idk if there is a difference between residual energy and residual entropy haha). Residual entropy is the entropy at T=0 K. You can solve for it by using S=Kb*lnw (s=entropy, kb=boltzmann constant, w=degeneracy which is # of orientations^# of molecules).

Degeneracy (w) of CH4 is 1 (only 1 b/c the rearrangement of hydrogen atoms around carbon atom is the same orientation regardless). You can plug this value into the equation (--> your equation would end up as R*lnw) and you end up with s=0, meaning entropy of CH4 at T=0K is 0.

For CH3Cl, there are four possible arrangements of the hydrogen and chlorine atoms around the carbon, thus w=4. Plug this into the equation and your entropy of CH3Cl at T=0K is 11.5, so this molecule has some residual entropy.

Jake Gordon 1A
Posts: 61
Joined: Fri Sep 28, 2018 12:15 am

### Re: residual energy

As another way to look at it, there are 4 types of energies in compounds: vibrational energy(how much the atoms or molecules vibrate), translational energy(energy from heat), rotational energy(how free the molecule is to rotate in space), and positional energy(the location of each atom in relation to the total molecular structure)

When we cool the compound to near absolute 0 (0K) essentially only positional energy remains (that's why it is called residual energy) if there is only one option for the molecule ex ch4 when this is plugged into the equation mentioned in the previous answer, entropy is 0, but with CH3Cl we can put the Cl at any of 4 positions, this adds to the degeneracy of CH3Cl and when plugged into the S equation we get a non zero number

I hope this offers another perspective on you question

LedaKnowles2E
Posts: 62
Joined: Fri Sep 28, 2018 12:27 am

### Re: residual energy

Residual entropy or positional entropy is the entropy that a sample has when you disregard thermal entropy. This residual/positional entropy results from the different positions the atoms can be found in.