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Name:  CraigC
Status: other
Grade: other
Location:AR
Country: N/A
Date: 10/12/2005


Question:
I read the answer to the question about whether or not mass is converted to energy in a normal chemical reaction. The answer was very unsatisfying to my students because there did not seem to be a consensus. My question is twofold.

In an exothermic chemical reaction is mass converted to energy according to E=MC^2? If I had a sealed glass container floating isolated in a vacuum and inside I initiated an exothermic reaction and then let the excess heat radiate out would the whole thing (container and reaction products) weigh a minuscule amount less?

If so, what happens in an endothermic reaction? Does the extra energy needed for the reaction convert to mass in the reaction products? If I had a sealed glass container floating isolated in a vacuum and inside I initiated an endothermic reaction and then added energy in the form of infrared light would the whole thing (container and reaction products) weigh a minuscule amount more when the reaction was complete?

This would seem to me to be a very important basic physics question. Has it ever been answered or is it impossible to answer because the resulting mass change is too small?


Replies:
The lack of "consensus" is a matter of a difference in "significantly measurable" vs. "in principle". In principle, in an exothermic reaction there is a small loss of mass. The reaction CH4 + O2---> CO2+2H2O has a heat of reaction -890 kJ. This is equivalent to a loss in mass of ~ 10^-11 kg. So it is not "significantly measurable. The factor of c^2 in Einstein's equation E=mc^2 is a large lever -- a very small loss in mass results in a very large liberation of energy. Only in nuclear reactions and/or matter -- anti-matter is the mass change large enough to be conveniently measured. And this conservation of mass-energy has been confirmed millions of times (provided of course all factors such as the generation of neutrinos) are taken into account. In the case of endothermic reactions the addition of energy in the form of radiation is an addition of a minuscule amount of the equivalent amount of mass. There are two other "complications" that need to be recognized. First, it is assumed that the reaction vessel is not moving at speeds approaching the speed of light, for then relativistic corrections to the mass would have to be taken into account. Second, it is assumed that the time and energy scale of the observations, delta time and delta energy, is not of the order of Plank's constant: h=6.6x10^-34 J*sec. That is the lower limit of precision that time and energy can be measured as a result of the Heisenberg uncertainty principle: dt*dE ~ h. At smaller scales the conservation laws do not apply. You might add another question (hypothetical). If mass and/or energy is lost/gained in a chemical reaction, which particles lose/gain the energy? I do not know the answer to that question. Only in nuclear and high energy "reactions" are the changes large enough to be accessible experimentally. The citations below give you some details (probably more than you want).

http://www.newton.dep.anl.gov/askasci/chem03/chem03534.htm

http://www2.yk.psu.edu/~jhb3/cotw06.htm

Treptow, Richard S. J. Chem. Educ. 2005 82 1636

http://en.wikipedia.org/wiki/Antimatter

Vince Calder


First, you must make sure that your students do not confuse "chemical reactions" with "nuclear reactions". It is only in nuclear reactions that there is a mass discrepancy and where a measurable mass is converted to energy and vice-versa. You need to clarify that bonds are not objects, they do not have mass, and that exothermic/endothermic chemical reactions are the result of the difference in the bond energies of bonds broken and bonds formed, not mass conversion.

Secondly, it is useful to do the calculations in class. If you want consensus, ask your students to define a lower limit of what they would consider a measurable mass loss (a milligram? a thousandth of a milligram?) within a normal lab setting. And then do the calculation on how much energy that would provide if in fact that energy was completely converted to energy. Then show what that energy loss would mean in terms of powering a light bulb (or a city!).

Greg (Roberto Gregorius)


Craig,

I looked up the answers that were given to this question originally, including my own answer. I gave a very simple answer aimed at a K-12 audience (which is what NEWTON is for), since the original questioner gave no details as to his/her background or knowledge other than "other" (this is also true of your current question).

As I look at all three responses, I agree with all of three responses (including my own) at different levels of sophistication and I see no substantial disagreement between them. My own response ("no") was very cut-and-dried because the change of mass that would be involved is so small as to be unmeasurable by any apparatus I can conceive of (which is what Vince Calder very correctly said). Therefore, to me this is a moot question.

All that said: your present question (about an exothermic reaction in a glass container floating in vacuum) presupposes that all of the energy generated by the exothermic reaction is lost to the environment. In reality all of the energy generated by the reaction in your example will have to go into the glass walls of the container because "true" vacuum does not conduct heat at all. Now, if the glass gets hot enough it may start to glow and give off some energy in the form of radiation. I suppose that would very slowly decrease the mass, but without actually putting it on a balance to weigh it, who knows? However, a caveat: quantum mechanics limits what frequencies of energy can be liberated this way, and not all of the energy that could be liberated as heat will be converted into radiation. Some will remain as increased kinetic energy of the molecules in the glass. Basically, the system will not evolve in the manner you have suggested and give off all of the energy that is liberated during the reaction to the surroundings. In fact, keeping the system isolated in this fashion will inhibit the progress of an exothermic reaction by keeping it physically unable to release the heat it must generate in order to it to proceed.

Now, what if we set the glass container on a scale in an actual room? Well, some heat will go into the glass walls of the container, some will go into the balance used to weigh the apparatus during (or after) the reaction...some will even go back into the system itself if the room is warm enough!

The second law does not permit us to predict how much energy will go into each of these heat sinks, because the heat flow is an irreversible/spontaneous process. It therefore becomes impossible to answer the question of how much the mass would change because there is no way to predict the dynamics of how the energy will be disposed of as a result of the process.

I hope this helps....you have not asked a simple question...this is really beyond the scope of NEWTON...

Dr. Topper


Craig-

Sorry we did not answer it clearly before. Thanks for sending us questions so clear that our answers cannot be unclear!

*** In an exothermic chemical reaction is mass converted to energy according to E=MC^2

Yes.

***...sealed glass container ... exothermic reaction... excess heat radiate out would the whole thing (container and reaction products) weigh minuscule amount less?

Exactly So.

(It would not weigh less until the heat radiated out. Potential energy of under-satisfied molecular bonds weighs exactly as much (per joule) as kinetic energy of thermal motion. So the reaction itself would not change the weight of the container. Radiating the heat away would! Chemical reactions in a perfectly silvery thermal bottle would then never change the mass of the container and contents!)

*** If so, what happens in an endothermic reaction?

Pretty much the reverse. The reaction makes it cold, so energy is now allowed by laws of thermodynamics to flow inwards from the "normal" (warm) surroundings, and when it finally does so, the container weighs more. Of course, for this to happen requires that the surroundings to be well above absolute zero. Real deep space has a radiation temperature of 2.7Kelvin. If a container was in thermal equilibrium with that, it would be too cold to allow most chemical reactions to happen. So it seems you are imagining a Thermos bottle in a vacuum chamber whose opaque walls are at room temperature. The vacuum you specify has the effect of leaving only one path (radiation) for energy transport between the world and the container.

*** Does the extra energy needed for the reaction convert to mass in the reaction products?

Yes, but I think the right words, the meaningful distinction, is {matter vs. energy}, rather than {mass vs. energy}. Matter is a static, (un-moving), usually rather concentrated state of energy, and Energy itself has mass at all times, regardless of what form it is in. Try to adopt that concept, instead of deciding when it is matter and when it is energy.

(It bothers my mind a little trying to imagine how being weakly married to neighbors makes atoms heavier, and being tightly bonded makes them lighter, but that is the polarity of the E=mc^2 mass change. I would rather not assert that this potential energy situation is or is not part of the matter in the molecule. All I have to do is remember it is more energy, so it has more mass. I suppose, since potential energy is un-moving, it is plausible to call it part of the matter.)

*** If...sealed glass container...endothermic reaction....then added...infrared light would the whole thing ... weigh more ...?

Yes, exactly.

The mass picked up by the container would be exactly the mass previously owned by the free-flying IR (infra-red) photons that were absorbed in the container. There you have it: conservation of mass and energy, simultaneously. Which is less surprising if you believe that energy has mass and matter is merely a "bound" state of some more energy.

*** ...is it impossible to answer...?

Regrettably, we cannot at present satisfy our skepticism by measuring mass change after chemical reactions. But it is considered so consistent with everything we have been able to measure and think through, and its effects are so impossible to perceive anyway, that we adopt it as true and wrap our thinking around it. It is pretty much an Occam's razor situation: We have no demonstrative proof of this, but we do of larger energies than chemical, and of many related situations, so it has become simpler to believe it, until proven noticeably wrong.

Someday we will come across a way to do the experiment, I bet. Then we will see if the universe teaches us another curious exception to our "common sense", or whether the theory was boringly right all along. My guess, E=mc^2 will stand fine, but some other subtle fundamental thing might be noticed in the effort to do this extremely sensitive measurement.

Jim Swenson



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