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A question that appeared on my last exam was :

Which of the following has greater entropy A) An atom B) A macromolecule

The question doesn't specify anything else(i.e. type/size of atom or macromolecule). The macromolecules we learned class were proteins, sugars, nucleic acids(DNA/RNA) or lipids. What is the correct answer and why(hypothetical calculation, if possible) ?

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closed as off-topic by WYSIWYG, Chris, Bez, Amory, J. Musser Jul 20 at 3:23

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "General chemistry questions are off-topic here, but can be asked on Chemistry Stack Exchange." – WYSIWYG, Chris, Bez, Amory, J. Musser
If this question can be reworded to fit the rules in the help center, please edit the question.

I see the close vote is for off-topic. I think this question is safely in the intersection of chemistry/physics and biology. Entropy is very important in biology and I think this standard question is not off-topic. –  daniel Jul 19 at 13:15
This is an exact duplicate of a recent question on chemistry SE, though by different users. Don't know if that's allowed or not. chemistry.stackexchange.com/questions/14438/… –  canadianer Jul 19 at 19:16
The OP should have indicated the question was cross-posted. Otherwise it is allowed. The answer at the other SE points out a weakness of the question but cross-pollination is good. It looks like I will be making my case on Meta again. –  daniel Jul 19 at 23:48
Link to Meta question: (meta.biology.stackexchange.com/questions/640/…) –  daniel Jul 20 at 1:07
@daniel.. i dont think this is on-topic even if it was not cross posted.. this is a very general question and general principles of physical chemistry are applicable everywhere.. this doesn't make it a biological question.. it is not that we cannot answer it.. it is better suited in chemistry se. –  WYSIWYG Jul 20 at 6:12

3 Answers 3

Ahh entropy. The bane of many undergraduates. You won't need a lot of mathematical rigor needed to solve for absolute entropies in most biological fields so it's best to think of it abstractly.

Consider the atom. What can it do? Well if you remember from chemistry class, it can bounce around a process we call translate, and the electrons can basically switch spins. For the most part, if you had a single atom alone in the universe, that's all it could do. Move around and have its electrons switch states. It's best to think of these as "states" of the atom.

Let's see, the atom can move in the X direction and be in spin up. It can move in the x and y direction and be spin down...etc. But the point is, there is not a whole lot the single atom all by it's lonesome can do.

On the other hand, if we start adding other atoms to the mix, say across chemical bonds, then they can start to do more. If two atoms are bonded, they can stretch and contract (vibrational states), they can rotate around each other, and they can do everything the atom can do as well.

As you can see, there a lot more "things" or "states" that the two atoms can be defined in at any one time. They can be rotating one direction, vibrating in one way, moving in another... etc etc...even this sentence seems to be getting more chaotic! And that is really all entropy is. Adding up more and more ways for matter to get into all these possible configurations.

So the answer to your question is the macromolecule. It has tons of atoms and bonds. An uncountable number of ways to rotate, translate and vibrate, and be struck with photons, and emit light, and do all kinds of chaotic "stuff" (you can count it actually, it's just really hard).

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Being struck by photons and emitting light have nothing to do with entropy in this setting. –  daniel Jul 19 at 13:17
sure it does. if you have a bond in molecular orbital theory that has a ton of states that can an excited electron can sit in, they are microstates –  jwillis0720 Jul 19 at 17:34
Number of microstates, yes. Being struck (or not) by photons, no. Incoming photons may affect the entropy of a system but the entropy is defined in terms of possible microstates (restrictions on freedom of rotation, etc.). I think the language is confusing. –  daniel Jul 20 at 1:51
Ok first off, this is a biology forum and I said to think in abstract. Second off yes it does, because the same photon can be strike an N number of microstates. Oh my god!!! what is with trolls on SE. –  jwillis0720 Jul 21 at 10:48

Entropy is a measure for the number of states accessible to a system. The more states available, the higher the entropy.

If you think of an atom confined in a volume V, then, without further restrictions, the atom can be anywhere inside that volume, i.e. the number of states will be a function of the volume V. The bigger the volume, the bigger the entropy. Now, if you add another atom to that volume so that the two atoms form a gas, i.e. they do not bind, then these atoms can access states individually. The number of states for the system will be the number of states of atom1 times the number of states of atom2. Thus, in a gas, the number of states, and therefore the entropy, increases with the number of atoms.

What happens now, if the two atoms bind together. They now can't access states individually, so the total number of states, and thus the entropy, will be smaller than that for a gas of the same atoms. But the two atoms can still access states similar to the one atom gas, plus they can do new things like rotating around each other. So the number of states of a molecule of two atoms will be bigger than the number of states of just one atom.

Thus, if you compare the entropy of a single atom to the entropy of a molecule of N atoms, the entropy of the molecule will be larger.
If you compare the entropy of a gas of N atoms to the entropy of a molecule build from these N atoms, the entropy of the gas will be larger.

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As this table shows, the more complex a molecule is (in general) the more entropy it has.

Entropy is an absolute quantity which is zero at $0^o K.$ When an atom or molecule has no way to rotate (is 'frozen') there is only one state in which it can exist. An atom of a gas or a molecule of a diatomic gas at $25^oC$ is also somewhat constrained compared to a complex molecule like sugar at the same temperature and pressure. The carbons and hydrogens in sugar have more possible states in which to exist. So, for example, chlorine gas, $Cl_2 (g),$ has lower entropy than propane, $C_3H_8.$

Trends for $S$ for various atoms and molecules generally reflect the idea that S is determined by molecular mass and restriction of motion.

A typical calculation.

If you want to measure the entropy of a simple molecule you assume the entropy is 0 at $0^o K$ and measure changes in entropy as the molecule is heated. In practice this might mean measuring the decrease in entropy of the surroundings as a substance heats up. By measuring the changes carefully up to a standard temperature (25$^oC)$ you get a number that is characteristic for each substance.

The equation used in chemistry courses is usually given as

$$\Delta S = \frac{\Delta H}{T}$$

In English, the change in entropy equals the change in heat (per mass or per mole), usually at some phase change, divided by the temperature in degrees Kelvin.

As a simple example, if liquid benzene is converted to vapor at its boiling point $80.1^o C$ and the heat of vaporization for benzene is 394 J/g then for 50 g of liquid benzene ($C_6H_6$) the entropy change is

$$\Delta S = \frac{(50 g)\cdot(394 J/g)}{(80.1+273.15)^oK} = 55.7 J/^oK$$

Chemists have created tables that measure entropy changes for states of various molecules. With the exception of very simple molecules predictions of entropy based on structure are difficult and the tables are empirically derived.

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