Endothermic reaction: where has the energy disapeared?

[coquelicot]

Assume a thermodynamic system S entirely isolated from the rest of the world, consisting in a block of salt inside in a tube containing water at some initial temperature. The total calorific energy of S is E. Now, after a time T, the bloc of salt has dissolved itself completely or partially in the water, and this reaction is endothermic, so it goes with a loss of temperature. Finally, the calorific energy of S is E'<E.
First question: where has the energy disapeared?
Second question: I guess that you will answer that it is stored in some form of chemical energy, but if this were true, let us consider the second following problem: suppose that the system now consist in two tubes, one containing the water with the salt, and the second containing only water, at the same initial temperature; again, after a time T, the block of salt has dissolved itself in the water and the temperature of the first tube has decreased, as well as its calorific energy. On the other hand, the temperature of the second tube remains approximately the same. But then, from the difference of temperature, it is possible to create energy, so a part of the calorific energy has been transformed into potential energy. At the same time, "you said" that the energy was transformed into chemical energy, so I have now more energy than was lost!
Well, I believe that all of this is stupid and that there is a simple answer, so, I won't call this a paradox.
I will appreciate some hint.

thx.

 

[Drakkith]

The energy hasn't disappeared or been created or lost, it has simply been transferred from the temperature of the water/salt to cause the salt to disolve and bond with the molecules in the water.

 

[coquelicot]

The energy hasn't disappeared or been created or lost, it has simply been transferred from the temperature of the water/salt to cause the salt to disolve and bond with the molecules in the water.

This is close to say that the energy has been transformed into chemical energy, so my second question still holds.
Furthermore, you say that the energy has been transferred from the temperature of the water to cause the salt to bond with the molecules of the water; but this is strange, because I know no mean to extract energy from salted water: the contrary is true, you have to spend energy to separate salt and water. I feel uncomfortable with these questions. Maybe am I missing a basical point.

 

[hologramANDY]

My guess is that it has somthing to do with the entropy of the system. Entropy always increases or is contstant in a closed system.

 

[coquelicot]

My guess is that it has somthing to do with the entropy of the system. Entropy always increases or is contstant in a closed system.

hummm. Doesn't help very much.

 

[Cleonis]

a block of salt inside in a tube containing water at some initial temperature. The total calorific energy of S is E. Now, after a time T, the bloc of salt has dissolved itself completely or partially in the water, and this reaction is endothermic, so it goes with a loss of temperature. Finally, the calorific energy of S is E'<E.
First question: where has the energy disapeared?

I think you have raised a valid question, probing the nature of conservation of energy.

The starting situation is a volume of salt, and a volume of water, with the potential to mix them.


Recapitulating:
When you bring the salt and water in contact with each other then the salt dissolves in the water. The state of being dissolved is more probable than the state of being unmixed.

As we know, temperature is kinetic energy, so it is tempting to take an analogy with, say, the swing of a pendulum. During the upswing kinetic energy converts to potential energy. This implies that if a process is endothermic, it must somehow be driving towards a state of higher potential energy.

In the case of pendulum the potential energy is available energy, in the sense that the swinging converts once again to kinetic energy. The thing to notice is that the energy conversions are reversible, it's a two-way process


Now another example of an endothermic process.
Stack two containers for holding gas on top of each other. (A couple of cilinders for example.) The bottom one filled with a high density gas (say, Nitrogen) the top one one filled with a low density gas. Then allow mixing of the gases. A uniform distribution of molecules is more probable, so some of the nitrogen will migrate upwards, against the pull of gravity. This means that the process of getting mixed will be endothermic.

Contrary to the case of the pendulum it's an irreversible process. The nitrogen molecules have gained gravitational potential energy allright, but there is no way to "harvest" that potential energy. The gases have become mixed, and to unmix them requires more energy than can be harvested.


Back to dissolution of salt in water.
The water molecules tend to form hydrogen bonds, and with salt dissolved in the water there is less opportunity for those hydrogen bonds. Overall that means there is an energy cost to dissolution, rather analogous to the energy cost for migrating gas molecules that move against the pull of gravity.

The salt dissolves against that energy cost. The salt solution does have a potential energy correlated with that energy cost, but there is no way to "harvest" that potential energy. The necessary unmixing will cost more than can be harvested.

 

[Drakkith]

This is close to say that the energy has been transformed into chemical energy, so my second question still holds.
Furthermore, you say that the energy has been transferred from the temperature of the water to cause the salt to bond with the molecules of the water; but this is strange, because I know no mean to extract energy from salted water: the contrary is true, you have to spend energy to separate salt and water. I feel uncomfortable with these questions. Maybe am I missing a basical point.

If the reaction of the salt drops the temperature, you could get work out of the system by transferring heat to the solution. Why exactly do you think you need to extract energy from the solution though?

 

[coquelicot]

Now another example of an endothermic process.
Stack two containers for holding gas on top of each other. (A couple of cilinders for example.) The bottom one filled with a high density gas (say, Nitrogen) the top one one filled with a low density gas. Then allow mixing of the gases. A uniform distribution of molecules is more probable, so some of the nitrogen will migrate upwards, against the pull of gravity. This means that the process of getting mixed will be endothermic.

Contrary to the case of the pendulum it's an irreversible process. The nitrogen molecules have gained gravitational potential energy allright, but there is no way to "harvest" that potential energy. The gases have become mixed, and to unmix them requires more energy than can be harvested.

This example is very interresting: it means that entropy acts as an irreversible "pump" of energy, even if it is not transformed in heat. Furthermore, I have never seen in what I know of thermodynamics that this is taken into consideration: all the variables usually considered in thermodynamics are usually heat, temperature, volume, mass, work, etc., but not potential energy at the molecular level.

Back to dissolution of salt in water.
The water molecules tend to form hydrogen bonds, and with salt dissolved in the water there is less opportunity for those hydrogen bonds. Overall that means there is an energy cost to dissolution, rather analogous to the energy cost for migrating gas molecules that move against the pull of gravity.

The salt dissolves against that energy cost. The salt solution does have a potential energy correlated with that energy cost, but there is no way to "harvest" that potential energy. The necessary unmixing will cost more than can be harvested.

If I understand right, you say that there is some potential energy associated with the bonds at the molecular level.
Now suppose I furnish with an energy E to separate again salt and water: do you think the total heat energy contained in the system after that will be > E?

Back to my second question: according to your answer, if I get energy by heat transfer from one tube to the other, this means that the potential energy that was contained in the first tube has been transformed back into energy, say work. And this means that the molecular potential energy in a salted solution is proportional to the concentration of salt. Things begin to be more clear for me. Neverthless, I still don't understand what is this potential energy that depends on the concentration of salt, that is, what is this energy of bonds between molecules.

 

[Cleonis]

This example is very interresting: it means that entropy acts as an irreversible "pump" of energy, even if it is not transformed in heat.

Indeed entropy is recognized as a factor that will drive a process in a particular direction.

Another example (this example is very well known).

Plant cells of leaves and stems have an outer wall that will not stretch. Inside the plant cells there are socalled vacuoles. The plant cells spend energy to maintain a high concentration of dissolved molecules in the vacuoles. (That is, embedded in the membranes of the vacuoles there are special molecules that use energy to transport particular molecules from outside the vacuole to inside the vacuole. So the concentration inside is maintained at a higher level than outside.)

The concentration difference causes water to migrate into the vacuoles. The cell enlarges, pressing against the non-stretchable outer wall. That way the plant cells achieve rigidity.

The pressure that builds up in the vacuoles is called osmotic pressure. Osmotic pressure is an entropy based phenomenon.


Entropy driven processes are just about everywhere, and I have seen them described often in textbooks. I think in doing physics the concept of entropy driving processes is encountered pretty much daily.

 

[Cleonis]

If I understand right, you say that there is some potential energy associated with the bonds at the molecular level.

Yes.

Water molecules tend to form a type of bond that is called 'hydrogen bond'. (For instance, ice is formed in crystalline structures because the formation of the hydrogen bonds orients the water molecules with respect to each other.)

The potential to form hydrogen bonds is a potential energy. When the hydrogen bonds do form this energy is released. The process of water freezing is a big increase in the number of hydrogen bonds. Ice occupies more volume than water. This increase of volume is quite forceful. That is, the process of ice freezing is capable of doing work. That is how in thaw/freeze cycles rocks are cracked. Water seeps in tiny fissures, and when the water freezes the fissure is widened.

When salt goes out of solution then there is more opportunity to form hydrogen bonds between the water molecules. So energy-wise it is favorable for salt to go out of solution (or to not dissolve). But the state of being dissolved is more probable, and you end up with a balance between the two opposing tendencies.
In the case of salt and water there is a saturation point. There is an upper limit to the concentration that entropy can sustain. Above the critical concentration some of the salt will go out of solution.

 

[coquelicot]

Thank you very much Cleonis (and Drakkith) for your very enlighting answers. I would like to pose a last question: According to my second question I posted when opening this thread, it is possible to get back energy by transfering heat from one tube to another: that is, the salted solution will become more hot, and the non salted one will become colder. But this energy can come only from the potential energy accumulated in the salted solution as hydrogen bonds (according to your answer). So, this means that at the end of this process, the salted solution will contain less potential energy than at the beginning; it follows that this potential energy doesn't depend only on the concentration of salt, but also on the temperature (more precisely, it is a decreasing function of the temperature). Am I right?

 

[Cleonis]

I would like to pose a last question: According to my second question I posted when opening this thread, it is possible to get back energy by transfering heat from one tube to another [...]

Recapitulating (from memory) the setup you described:
At the start one tube contains water and a chunk of salt, the other tube contains just water. The endothermic dissolution of the salt causes the temperature of the tube with water/salt to drop.

As you pointed out, when there is a temperature difference then it's possible to get some work done. (In the process of harvesting that potential the temperature evens out of course.)

You question, I gather, is whether one can attribute that potential to a particular component. Well, no. You cannot.

The potential to get some work done from a system where different parts have different temperature is a property of that system as a whole. Getting the work done does not come from the temperature of either component, it comes from temperature difference between the constituent parts of the system as a whole.


The process of temperature evening out is a process towards a more probable state. A thermocouple, for example, channels that process. A thermocouple hastens the process of temperature evening out, but in such a way that a bit of electric energy is generated along the way.

The driving principle behind a thermocouple is entropy: the entropy of the system as a whole can only increase.