Mass to Energy Transformation for ordinary Chemical reaction

[Dr. Who]

Hi,

My Modern Physics lecturer is of the opinion that the energy dissipated during exothermic reactions is due to infinitesimally small change in mass of the reactants. Similarly, he said that an infinitesimally small part of the food we eat gets converted into the energy using which we perform mechanical actions. The amount of mass transformed into energy can be calculated using E=Mc².

I argued that this is not possible for ordinary Chemical/ Biological reactions to exhibit Mass to Energy conversion phenomenon governed by E=Mc². I said that the energy dissipated in these reactions is because of enthalpy change, so the bond energy is converted into heat and other forms. I also said that in such reactions mass of the reactants is equal to the mass of products. I maintained that the only reaction by which we can convert Mass directly into Energy is the Fusion reaction.How valid is either mine or my instructor's argument?

 

[PeterDonis]

I argued that this is not possible for ordinary Chemical/ Biological reactions to exhibit Mass to Energy conversion phenomenon governed by E=Mc2.

Why not? The equivalence of mass and energy applies to all kinds of energy.

I said that the energy dissipated in these reactions is because of enthalpy change, so the bond energy is converted into heat and other forms.

The bond energy of a chemical compound is part of its mass, according to relativity, just as any other kind of energy contained in the compound.

I maintained that the only reaction by which we can convert Mass directly into Energy is the Fusion reaction.

Even setting aside the above for a moment, I think you forgot about fission reactions, didn't you?

But in any case, nuclear reactions are not the only kinds of reactions that convert mass to energy, as noted above. So your instructor is right. The reason we don't notice this for normal chemical reactions is that the change in mass is too small to detect without highly specialized apparatus. You might try estimating the mass equivalent of a typical chemical reaction energy and see how it compares to the rest masses of the reactants.

 

[Dale]

Your instructor is essentially correct. In an exothermic chemical reaction the sum of the masses of the products is (according to theory) slightly smaller than the sum of the masses of the reactants.

However, I don't think it is a good idea to speak of mass being "converted" to energy. I think that it is better to say that mass "has" energy, or even better, that a system that has mass also has energy.

 

[Dr. Who]

Why not? The equivalence of mass and energy applies to all kinds of energy.

Okay. My instructor also said that if I am running then my mass would also increase. How is that? My body is utilizing the chemical energy stored within my body to convert it into Kinetic energy. No external energy is provided, so how come the mass is not conserved?

The bond energy of a chemical compound is part of its mass, according to relativity, just as any other kind of energy contained in the compound.

Can you please cite this comment with a credible book/Author? I accept your theory but I only want to read this in detail that how is the bond energy part of the mass of molecules?

 

[PeterDonis]

My instructor also said that if I am running then my mass would also increase. How is that?

Here he is referring to the fact that your energy while moving, relative to a fixed inertial frame, is greater than when you are at rest in that frame. But this issue isn't as clear cut as the last one. See below.

My body is utilizing the chemical energy stored within my body to convert it into Kinetic energy. No external energy is provided

This isn't quite true; you are breathing oxygen and exhaling carbon dioxide, and in between your body is extracting chemical energy from the oxygen (in the process of converting it into carbon dioxide). So at least a part of the chemical energy that your body is converting into kinetic energy is coming from outside your body. But you are correct that the part that comes from inside your body does not change your total energy when it gets converted to kinetic energy--it's just energy that's part of your body getting converted from one form to another.

(There is one wrinkle here: considering kinetic energy as equivalent to mass is connected with the concept of "relativistic mass", which is not really used any more in relativity physics since it's just a synonym for "total energy". But for the purposes of this discussion, it's ok to consider kinetic energy as equivalent to mass, since all kinds of energy are equivalent to mass.)

However, in the short term your body is not necessarily in mass balance anyway; the mass of the CO2 you exhale in a given breath is not necessarily the same as the mass of the O2 you inhale in the same breath. Not to mention the fact that you also exhale water, and sweat water. The potential mass imbalances from these effects while you are running are orders of magnitude larger than the mass equivalent of your kinetic energy while running. So even if all of the chemical energy you used for running came from outside, its effect on your mass would be negligible compared to these other effects.

 

[PeterDonis]

Can you please cite this comment with a credible book/Author?

You probably won't find it in any books on chemistry, because the mass equivalent of chemical bond energies is so small. (Once again, I recommend that you try running some numbers to see how small.) If you look in relativity textbooks, you won't find chemical bond energies mentioned specifically; but you also won't find them saying that only nuclear reactions convert mass to energy. (Pop science sources might say something like that, but they're not credible sources.) You will find relativity textbooks making the general statement that mass and energy are equivalent--or they're different forms of the same thing, or something like that. They just say "mass" and "energy"--meaning any kind of mass and any kind of energy, no restrictions.

 

[Dr. Who]

First of all, many thanks for undoing many knots in my mind. It's wonderful the way you people deal with newbies (I know my questions would be a real nuisance for you).

So at least a part of the chemical energy that your body is converting into kinetic energy is coming from outside your body. But you are correct that the part that comes from inside your body does not change your total energy when it gets converted to kinetic energy--it's just energy that's part of your body getting converted from one form to another.

Alright. Now consider a capacitor powered toy car. Here no biological or chemical reactions are taking place to run the car, simply the electric potential energy stored in the charged plates is converted into Kinetic energy. How do you account for the change in mass here?

If your answer is same as below:

the part that comes from inside your body does not change your total energy when it gets converted to kinetic energy--it's just energy that's part of your body getting converted from one form to another.

Then, by analogy, would I not be correct in assuming that the energy/mass that comes from within a system is not responsible for changing the total energy of the system. "it's just energy that's part of your body (read system) getting converted from one form to another." And hence, surmising further, in a chemical reaction taking place in an isolated system, the masses of reactants and products should remain conserved. It is the bond energy or internal energy alone that gets converted into heat and other forms. Doesn't it?

 

[PeterDonis]

Now consider a capacitor powered toy car. Here no biological or chemical reactions are taking place to run the car, simply the electric potential energy stored in the charged plates is converted into Kinetic energy. How do you account for the change in mass here?

There isn't one. Stored electrical potential energy gets converted to kinetic energy. The total energy, with respect to a fixed frame, is constant; therefore so is the mass, by the definition of "mass" we are using here (where it is just another name for "total energy").

What does change in this process is the rest mass of the car. Before the car starts moving, the electrical potential energy stored in the capacitor is part of the rest mass of the car. After the car is moving, that energy is kinetic energy and is not part of the car's rest mass. So if the car were brought to rest again (for example, by pushing against a spring that slowed it to a stop and stored the energy in the compression of the spring), its mass would be smaller than before, by the amount of energy that was converted to kinetic energy.

would I not be correct in assuming that the energy/mass that comes from within a system is not responsible for changing the total energy of the system.

Yes, that's correct. But, as above, if the system changes its state of motion, its rest mass can change even if no external source of energy/mass is present.

in a chemical reaction taking place in an isolated system, the masses of reactants and products should remain conserved. It is the bond energy or internal energy alone that gets converted into heat and other forms. Doesn't it?

Now you're using "mass" in a different sense. In chemical reactions in an isolated system (say a closed reactor vessel with perfect thermal insulation that remains at rest throughout the reaction), the total mass/energy of the system as a whole never changes, and since we've ruled out changes in the system's state of motion, its rest mass never changes either. However, the same is not necessarily true of individual constituents of the system.

For example, suppose we start out with a reactor vessel filled with two moles of hydrogen gas and one mole of oxygen gas, and we end up with a reactor vessel filled with one mole of water. Two water molecules are formed from two H2 molecules and one O2 molecule. But the mass of the water molecule is not the same as the mass of two H2 molecules plus the mass of one O2 molecule; it is slightly less. The difference shows up as heat--the temperature inside the reactor vessel goes up.

Now, can we say that this extra heat comes only from the change in bond energy? Sort of, but not really. The problem is that the mass of one H2 molecule, say, is not the same as the mass of two H atoms; it is slightly less. (If it weren't, H2 molecules would not exist; hydrogen would occur in nature as a gas of H atoms, not a gas of H2 molecules.) And similarly for one O2 molecule vs. two O atoms. So the H2 and O2 molecules already, as bound systems, have less energy/mass than their constituent atoms. So if we had started with H and O atoms inside our reactor vessel, in a 2-to-1 ratio, we would end up with a larger change in temperature inside the reactor vessel than the case above, where we started with H2 and O2 molecules.

But, you say, how about the H and O atoms? Well, first of all, they are still composite systems. An H atom is composed of a proton and electron. If we take a proton and electron that are not bound, and make an H atom from them, energy is given off (13.6 electron volts of it); so the mass of the H atom is smaller by that amount than the mass of a proton + the mass of an electron.

Also, H and O nuclei can participate in nuclear reactions, so clearly there is some portion of their masses that is really binding energy. For example, if we took a quantity of H and O atoms and ran them through nuclear reactions to form a quantity of iron nuclei with the same total number of nucleons, a considerable amount of heat would be given off, orders of magnitude more than in the chemical reactions above (so the temperature inside our reactor vessel would go up a lot more).

And if we dig still deeper, we find that nucleons themselves are composite systems, made up of quarks; but much of the observed mass of nucleons is believed to be energy associated with the strong interaction between the quarks rather than the masses of the quarks themselves. So even at the most fundamental level, we really don't have a sharp dividing line between "mass" and "binding energy". The simplest thing is to just lump them all together as "energy" and keep track of how energy changes in different reactions, and not worry about what part of it is "mass" and what part is something else.

 

[Dr. Who]

Hi Peter,

No words of mine can be enough to adequately thank you for the detailed explanation you wrote.

Here, accept the Nobel prize for Physics for your services as a mentor to the budding Physicists of tomorrow!