[Rutherford]

Which substance in each pair will have a higher absolute entropy:
a) 1 mol HCl(g) or 1 mol Ar(g) on 25°C;
b) 1 mol CH₃Cl (g) or 1 mol CHCl₃(g) on 25°C?

I thought that HCl and CHCl₃ have bigger dipole moments and therefore these will stick more closely than Ar and CH₃Cl, but actually HCl and CHCl₃ have bigger entropy. I need some advices here.

[Big-Daddy]

Which substance in each pair will have a higher absolute entropy:
a) 1 mol HCl(g) or 1 mol Ar(g) on 25°C;
b) 1 mol CH₃Cl (g) or 1 mol CHCl₃(g) on 25°C?

I thought that HCl and CHCl₃ have bigger dipole moments and therefore these will stick more closely than Ar and CH₃Cl, but actually HCl and CHCl₃ have bigger entropy. I need some advices here.

I can explain CH₃Cl having lower entropy than CHCl₃: the trend is that as M_r of a molecule increases, the entropy does as well. So then it's obvious that CHCl₃ (Mr=119.37) will have higher entropy than CH₃Cl (Mr=50.48). Actually we're looking at mass but mass=moles*mr=1*M_r for both your cases here.

Ar(g) vs HCl (g) is close enough that mass shouldn't make a difference, so my initial feeling is that it has something to do with there being 2 atoms in HCl and 1 atom in Ar, but we need expert help on this one.

[Rutherford]

How did you know for case b)? Do you know a relation between mass and entropy?

[Corribus]

Think about heat capacity and its relation to entropy.  That's where I'd begin my explanation.

[Rutherford]

Don't have an idea how to relate it.

[Big-Daddy]

OK all I had previously was the knowledge that state is the primary factor for S° (all are gaseous here), mass is the second factor (all 1 mole here so Mass=Mr, so for b) we can work out the answer) and the number of molecules might be the third factor, not sure.

Now though we can find out why that is the case.

To Corribus: like Raderford I cannot see the relationship of heat capacity to entropy. Maybe I can start us off though: by definition of the heat capacity, this is the amount of heat energy/energy which goes into enthalpy  required to raise the temperature of 1 mole of the substance by 1 K. So there in the "1 mole" might be the mass dependence we're looking for. But I don't know the relation to entropy either.

[Rutherford]

The trends I know and I found are:
1.temperature increase means increase in entropy;
2.pressure increase means decrease in entropy;
3.stronger bonds in molecule mean lower entropy;
4.bigger molecules have bigger entropy;
5.different states have different entropies that decrease in the sequence: gas-liquid-solid;
6.bigger amount of the substance means bigger entropy;
And all seem logic.

The substances are in same amounts, so I wouldn't compare them by trends 1., 2., 5. and 6.
According to 3., HCl should have lower entropy, but it isn't the case.
CHCl₃ is a bigger molecule but it exhibits stronger intermolecular bonds, so I am not able to decide. Again I am at the beginning  .

[Corribus]

Well my reasoning can be made from a statitical mechanical and classical point of view.  Both essentially boil down the same thing.

Entropy is basically a measure of how energy is distributed.  Temperature being the same, a higher energy system has energy distributed in more ways than a lower entropy system.  The primary difference between Ar and H-Cl is the fact that the latter has a chemical bond.  When you put heat energy into a sample of Ar, the only place it can go is kinetic energy: the Ar atoms move faster.  When you put heat energy into a sample of H-Cl, it goes into kinetic energy states and also vibrational and rotational energy states.  Thus for a given temperature, HCl has energy distributed in more ways than Ar.  HCl has greater total entropy.  The relationship with heat capacity should be fairly clear - a substance with higher heat capacity takes more energy to raise the temperature than a substance with lower heat capacity, and the reason is because in the former case there are lots more places that energy can go that don't necessarily change the sample temperature.

Note that this effect on entropy can be overrided by other considerations - using this explanation you might expect condensed phases to have higher entropy (they have all kinds of intermolecular interactions for energy to be distributed into).  However the freedom of motion of gasses (and the huge increase in volume) overrides the effect of energy distribution channels.

So in general, a substance with more degrees of freedom will have higher entropy.

[Rutherford]

Thanks for the explanation. I got now to the idea that there are also more possible space arrangements of the diatomic HCl molecule.

What about b)? Both molecules have 4 atoms. Does size decide here? But how can that be explained?

[Big-Daddy]

The trends I know and I found are:
1.temperature increase means increase in entropy;
2.pressure increase means decrease in entropy;
3.stronger bonds in molecule mean lower entropy;
4.bigger molecules have bigger entropy;
5.different states have different entropies that decrease in the sequence: gas-liquid-solid;
6.bigger amount of the substance means bigger entropy;
And all seem logic.

The substances are in same amounts, so I wouldn't compare them by trends 1., 2., 5. and 6.
According to 3., HCl should have lower entropy, but it isn't the case.
CHCl₃ is a bigger molecule but it exhibits stronger intermolecular bonds, so I am not able to decide. Again I am at the beginning  .

Correct me if I'm getting it wrong but I think the general trend is that the state is the biggest factor, followed by temperature/pressure, followed by amount (well if you have 2 moles instead of 1 then the entropy doubles whereas if you double the Kelvin temperature or half the pressure there will be a bigger change than x2), followed by number of atoms in molecule, followed by mass of molecules, followed by bond strength.

If anything, your original question is asking you to get these in the right order. I'm not sure I have but this is a decent guess (it seems to me).

[Rutherford]

The temperature, pressure, state and amount of substances are the same here. It is 3. vs 4.:
3.stronger bonds in molecule mean lower entropy;
4.bigger molecules have bigger entropy;
Somehow the 4. must have won because in the answer CHCl₃ has bigger entropy, but I don't understand how is it so.

[Corribus]

CHCl₃ has a higher entropy because it has a higher mass.  The reason mass impacts entropy is the essentially the same reason degrees of freedom does: there are more ways for temperature to distribute itself among the available vibrational and rotational states.  Mass affects this because in molecules with heavier mass, vibrational and rotational states are closer together (to see this, just look at the energy formulas for the vibrational/rotational states under simple models like harmonic oscillator and rigid rotor, and see their mass dependencies).  Because these states are closer together, for a given temperature there will be more states available for energy to be distributed into, hence a higher entropy.

EDIT: I looked around for a figure that illustrates this and found one here:  http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Dependence-of-S-on-Molecular-Structure-985.html

[Rutherford]

Many different factors affect entropy and they need to be taken in consideration and as I saw now, even classical mechanics isn't enough. Thank you for the help.

[Big-Daddy]

CHCl₃ has a higher entropy because it has a higher mass.  The reason mass impacts entropy is the essentially the same reason degrees of freedom does: there are more ways for temperature to distribute itself among the available vibrational and rotational states.  Mass affects this because in molecules with heavier mass, vibrational and rotational states are closer together (to see this, just look at the energy formulas for the vibrational/rotational states under simple models like harmonic oscillator and rigid rotor, and see their mass dependencies).  Because these states are closer together, for a given temperature there will be more states available for energy to be distributed into, hence a higher entropy.

EDIT: I looked around for a figure that illustrates this and found one here:  http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Dependence-of-S-on-Molecular-Structure-985.html

The data additionally suggests to me that bond strength is a less important factor than the rest, whereas mass is important if the difference is great but less important than number of atoms per molecule if the mass difference is small.

Thank you for the lesson

[Corribus]

yw

Btw earlier when I said "more ways for temperature to distribute itself", whatever I meant was "more ways for energy to distribute itself".  Sorry if there was confusion.