Entropy and Disorder (Crystallization)

[roam]

To show that entropy is not the same thing as disorder (what people intuitively accept as disorder) my textbook gives an example of crystallization in a supersaturated solution. And it argues that since both temprature and disorder decrease the entropy must decrease also, but it does not. Hence giving a contradiction to the disorder interpretation:

Consider an isolated supersaturated solution a liquid in which a solid has been dissolved to a concentration greater than it would be for equilibrium. Such a solution is unstable. A crystal suddenly and spontaneously forms in the solution. The entropy of the system cannot decrease. Yet the appearance of the crystal certainly would be regarded as an increase in order. But in this example the temperature of the system could decrease. How on Earth can we retain the disorder interpretation of entropy when the system has undergone a partial transition from liquid to solid and its temperature has also decreased?

Unlike what the book says, in reality the entropy must decrease because no such system is truly isolated. Right?

Also, doesn't the 2^nd law say that entropy only tends to increase in an isolated system (it can decrease locally within an isolated system)? So, wouldn't stacking some coins would have sufficed as example? So why give this example in particular?

 

[Andrew Mason]

To show that entropy is not the same thing as disorder (what people intuitively accept as disorder) my textbook gives an example of crystallization in a supersaturated solution. And it argues that since both temprature and disorder decrease the entropy must decrease also, but it does not. Hence giving a contradiction to the disorder interpretation:

It is not necessarily wrong, but it is misleading to equate entropy with disorder. One has to define disorder in a particular way.

Suppose I have a thimble full of boiling water at 100C and a large block of ice at -10C in a vacuum and I pour the water on the ice and end up with a a solid block of ice at -9.9C. Entropy has increased. Whether disorder has increased depends on how I define disorder.

Unlike what the book says, in reality the entropy must decrease because no such system is truly isolated. Right?

Entropy of the system + surroundings must increase but that does not mean the entropy of the crystal cannot decrease.

Also, doesn't the 2^nd law say that entropy only tends to increase in an isolated system (it can decrease locally within an isolated system)?

Entropy cannot decrease in an isolated system. Ever. If that were to occur, the second law would be violated. The second law is never violated.

AM

 

[Andy Resnick]

Entropy is used as a driving 'force' for some colloidal crystallization experiments- arranging "large" colloid particles in a crystalline array increases the available volume for "smaller" particles.

http://www.google.com/url?sa=t&rct=...-KG0Dw&usg=AFQjCNHuY7XE3XgHAhbxbDjbENGJLIuVbQ

http://www.google.com/url?sa=t&rct=...-KG0Dw&usg=AFQjCNFomfWQgz0qG_aQriQzoc8mf0RAcA

http://www.google.com/url?sa=t&rct=...-KG0Dw&usg=AFQjCNFRGTgf219HgibRh1_yaj1aZo7V-Q

 

[haruspex]

Can you find an example where the crystallisation is accompanied by a temperature drop (or, at least, no increase)? I can't.

 

[Andy Resnick]

It depends on what you mean by 'temperature'- seriously. For example, hard sphere colloids experience phase transitions between fluid and crystal even when the system is isothermal. The 'temperature' of a hard-sphere colloid is a measure of the volume fraction of spheres, not the thermal energy.

 

[DrDu]

Can you find an example where the crystallisation is accompanied by a temperature drop (or, at least, no increase)? I can't.

http://webserver.dmt.upm.es/~isidoro/dat1/Heat%20of%20solution%20data.htm

 

[DrDu]

It depends on what you mean by 'temperature'- seriously. For example, hard sphere colloids experience phase transitions between fluid and crystal even when the system is isothermal. The 'temperature' of a hard-sphere colloid is a measure of the volume fraction of spheres, not the thermal energy.

Ok, so Delta H=0 in the phase transition. I don't see how you conclude from that that you need a new definition of temperature.

 

[haruspex]

http://webserver.dmt.upm.es/~isidoro/dat1/Heat%20of%20solution%20data.htm

Sorry, I should have qualified that with "and supersaturation is possible". I'm not saying it doesn't happen, just can't find any info on it.

 

[Andy Resnick]

Ok, so Delta H=0 in the phase transition. I don't see how you conclude from that that you need a new definition of temperature.

I'm not sure what you mean- I simply pointed out that for hard-sphere colloids, the parameter 'T' is a function of volume fraction.

 

[DrDu]

I'm not sure what you mean- I simply pointed out that for hard-sphere colloids, the parameter 'T' is a function of volume fraction.

I was referring to your statement "For example, hard sphere colloids experience phase transitions between fluid and crystal even when the system is isothermal". Freezing of water is also isothermal, so this statement is trivial. I assumed that you were talking about a phase transition which is both isothermal and adiabatic. That means that Delta H must be zero, if not the heat created in the phase transition would lead to an increase of temperature in an adiabatic system.

 

[DrDu]

Sorry, I should have qualified that with "and supersaturation is possible". I'm not saying it doesn't happen, just can't find any info on it.

From
http://en.wikipedia.org/wiki/Solubility
it can be seen that solubility increases for most substances with temperature. By van't Hoff equation, it can be infered that the reaction is endothermic. On the other hand crystallization will be exothermic.
Exceptions are e.g. Na2SO4 at elevated temperatures or cerium sulfate for which cyrstallization is endothermic.
In equilibrium, Delta H=T Delta S, so that in this case entropy really increases in crystallization.
At least in the case of Cerium I would speculate that this is due to the highly ordered structure of the water molecules around a highly charged ion like Cerium IV in solution.

 

[Andy Resnick]

I was referring to your statement "For example, hard sphere colloids experience phase transitions between fluid and crystal even when the system is isothermal". Freezing of water is also isothermal, so this statement is trivial. I assumed that you were talking about a phase transition which is both isothermal and adiabatic. That means that Delta H must be zero, if not the heat created in the phase transition would lead to an increase of temperature in an adiabatic system.

The hard-sphere model is athermal (Carnahan and Starling, J. Chem. Phys)- phase transitions are only associated with changes in the packing fraction. Water can't be modeled this way, but sterically stabilized colloids can. Since the system is athermal, there's no latent heat or specific heat- although Pusey (Les Houches, vol. LI) only says the latent heat associated with structural transitions is 'too small to measure'. Presumably, the phase transition is then both isothermal and adiabatic. However, I can't find much on the way of a reference for that right now.

 

[DrDu]

The hard-sphere model is athermal (Carnahan and Starling, J. Chem. Phys)- phase transitions are only associated with changes in the packing fraction. Water can't be modeled this way, but sterically stabilized colloids can. Since the system is athermal, there's no latent heat or specific heat- although Pusey (Les Houches, vol. LI) only says the latent heat associated with structural transitions is 'too small to measure'. Presumably, the phase transition is then both isothermal and adiabatic. However, I can't find much on the way of a reference for that right now.

Yes, that's what I wanted to say, the phase transition is athermal, but I still have no clue what you mean in your post #5 and how this shall be related to the fact that a phase transition is athermal.

If the process is athermal then the slope dp/dT of the transition line is 0 or the phase transition allways occurs at the same pressure. I think this is all we can infer from this fact.

 

[Andy Resnick]

Regarding my post #5, all I intended to say was that for certain systems (colloidal suspensions, sandpiles, nonequilibrium systems), the concept of 'temperature' no longer coincides with the common-sense use of the term. Other examples: protein folding, receptor-ligand binding, and cytoskeletal dynamics. Although it's straightforward to analyze the energetics of these processes, I would avoid use of 'temperature' and 'heat'.

 

[haruspex]

From
http://en.wikipedia.org/wiki/Solubility
it can be seen that solubility increases for most substances with temperature. By van't Hoff equation, it can be infered that the reaction is endothermic. On the other hand crystallization will be exothermic.
Exceptions are e.g. Na2SO4 at elevated temperatures or cerium sulfate for which cyrstallization is endothermic.
In equilibrium, Delta H=T Delta S, so that in this case entropy really increases in crystallization.
At least in the case of Cerium I would speculate that this is due to the highly ordered structure of the water molecules around a highly charged ion like Cerium IV in solution.

If your speculation is correct, this example does not support the textbook's argument that entropy is not just disorder, right? It would have been more defensible to say that the crystallised form is not necessarily more ordered than the dissolved form.

 

[roam]

The question then is how should one define "disorder"? The kind of disorder the book is talking about is the intuitive meaning (i.e. a crystalline solid is more ordered than its liquid, which is more ordered than its vapor).