# Conversion of mass to energy in chemical/nuclear reactions

Is mass converted into energy in exothermic chemical / nuclear reactions?

My (A Level) knowledge of chemistry suggests that this isn't the case. In a simple burning reaction, e.g. $C+O_2\to \text{CO}_2$, energy is released by the CO bonds forming; the atoms lose potential energy when they pull themselves towards each other, in the same way that a falling object converts GPE to KE. There are the same number of protons, electrons etc. in both the reactants and products. I would have assumed that this reasoning extends to nuclear fission/fusion as well, but one physics textbook repeatedly references very small amounts of mass being converted into energy in nuclear reactions.

So I just wanted to know if I was wrong about either of these types of reactions, and if so, what mass is lost exactly?

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This is actually a more complex question than you might think, because the distinction between mass and energy kind of disappears once you start talking about small particles.

So what is mass exactly? There are two common definitions:

1. The quantity that determines an object's resistance to a change in motion, the $m$ in $\sum F = ma$
2. The quantity that determines an object's response to a gravitational field, the $m$ in $F_g = mg$ (or equivalently, in $F_g = GMm/r^2$)

The thing is, energy actually satisfies both of these definitions. An object that has more energy - of any form - will be harder to accelerate, and will also respond more strongly to a given gravitational field. So technically, when computing the value of $m$ to plug into $\sum F = ma$ or $F_g = mg$ or any other formula that involves mass, you do need to take into account the chemical potential energy, thermal energy, gravitational binding energy, and many other forms of energy. In this sense it turns out that "mass" is effectively just a word for the total energy of an object (well, divided by a constant factor: $m_\text{eff} = E/c^2$).

If mass is just another word for energy, why do we even talk about it? Well, for one thing, people got used to using the word "mass" before anyone knew about all its subtleties ;-) But seriously: if you really look into all the different forms of energy that exist, you'll find that figuring out how much energy an object actually has can be very difficult. For instance, consider a chemical compound - $\mathrm{CO}_2$ for example. You can't just figure out the energy of a $\mathrm{CO}_2$ molecule by adding up the energies of one carbon atom and two oxygen atoms; you also have to take into account the energy required to make the chemical bond, any thermal energy stored in vibrational modes of the molecule or nuclear excitations of the atoms, and even slight adjustments to the molecular structure due to the surrounding environment.

For most applications, though, you can safely ignore all those extra energy contributions because they're extremely small compared to the energies of the atoms. For example, the energy of the chemical bonds in carbon dioxide is one ten-billionth of the total energy of the molecule. Even if adding the energies of the atoms doesn't quite get you the exact energy of the molecule, it's often close enough. When we use the term "mass", it often signifies that we're working in a domain where those small energy corrections don't matter, so we can just add the masses of the parts to get the mass of the whole.

Obviously, whether the "extra" energies matter or not depends on what sort of process you're dealing with, and specifically what energies are actually affected by the process. In chemical reactions, the only changes in energy that really take place are those due to breaking and forming of chemical bonds, which as I said are a miniscule contribution to the total energy of the particles involved. But on the other hand, consider a particle accelerator like the LHC, which collides protons with each other. In the process, the chromodynamic "bonds" between the quarks inside the protons are broken, and the quarks then recombine to form different particles. In a sense, this is like a chemical reaction in which the quarks play the role of the atoms, and the protons (and other particles) are the compounds, but in this case the energy involved in the bonds (by this I mean the kinetic energy of the gluons, not what is normally called the "binding energy") is fully half of the energy of the complete system (the protons) - in other words, about half of what we normally consider the "mass" of the proton actually comes from the interactions between the quarks, rather than the quarks themselves. So when the protons "react" with each other, you could definitely say that the mass (of the proton) was converted to energy, even though if you look closely, that "mass" wasn't really mass in the first place.

Nuclear reactions are kind of in the middle between the two extremes of chemical reactions and elementary particle reactions. In an atomic nucleus, the binding energy contributes anywhere from 0.1% up to about 1% of the total energy of the nucleus. This is a lot less than with the color force in the proton, but it's still enough that it needs to be counted as a contribution to the mass of the nucleus. So that's why we say that mass is converted to energy in nuclear reactions: the "mass" that is being converted is really just binding energy, but there's enough of this energy that when you look at the nucleus as a particle, you need to factor in the binding energy to get the right mass. That's not the case with chemical reactions; we can just ignore the binding energy when calculating masses, so we say that chemical reactions do not convert mass to energy.

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Thanks for this great answer. I had assumed that mass could somehow be converted, but you've made it clear that it's the other way round - mass is reduced because energy is released. –  myk Jun 23 '11 at 18:56

Chemical reactions of any kind ---> No conversion. All mass (and energy) is conserved.

Nuclear reactions ---> Yes, mass is converted to energy, in both fission and fusion reactions.

What mass? Well, going by my college instruction, I would have said that a neutron is lost (converted to energy). But a quick surf of the internet shows me that what I learned in college is now considered an old wives' tale. The new answer, though obviously not what I learned, defies my efforts to understand, let alone condense into easy reader format for you. Maybe someone else will give it a go.

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really, if you don't understand and know it, why answer? –  user2963 Jun 22 '11 at 22:57
@zephyr: not everyone knows everything. I don't think we need to discourage people from posting answers even if they aren't completely sure; the risk of getting downvoted should be enough to do that. –  David Z Jun 23 '11 at 0:11
@Vintage: just in case you didn't know, if you realize that an answer you posted is wrong, you should be able to delete it. Of course you're not obligated to do so. –  David Z Jun 23 '11 at 0:12
@David. Thank you for the tip. I'll stick with my answer, though, downrated as it is. I don't see anything in it that is untrue, in the classical mechanics sense. If someone were to tell me that mass is lost or gained in a chemical reaction, I'd respond, "How much mass?" If they tell me they are not sure, or can't even measure it, then I'd respond that my answer is perfectly fine in the practical world. Sort of reminds me of Pluto: It's not a planet anymore, but it was 10 years ago. Makes me wonder if it was really a planet when science said it was a planet. What changed on Pluto? –  Vintage Jun 23 '11 at 20:18
@Vintage - it is misleading because it ignores the universality of the process. There is a mass loss in a nuclear reaction and a chemical reaction, it is only the magnitude that differs. The physics is exactly the same. This is not a philosophical position, it is a straightforward application of our currently known laws of physics. There are many implications of these laws which can be neglected in the practical world, that does not make them any less real or true, and you do a disservice to learners by dismissing the truth rather than seeing the unified whole. –  user2963 Jun 28 '11 at 3:45
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The potential energy of the chemical bonds do correspond to an increase of mass proportionate to that energy.

So, for example the energy in a CO-O bond is 110 kcal / mol or about 7.6 x 10^-19 Joules per bond. Dividing by c^2 gives us a mass of about 8.5 x 10^-33 grams. In a mole of CO2, that amounts to 5.1 x 10^-9 grams. Since a mole of CO2 has a mass of about 44g, you're going to have a hard time measuring the mass difference.

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Theoretically, even chemical reactions do convert mass to energy or vice versa. But the amount of mass converted is so small that we are generally unable to detect it.

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First you have to understand, there are two definitions for mass: rest mass and motional mass. Rest mass is the mass measured in the frame where the object is stationary. Motional mass is $m_1=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$. The old school calls the motional mass mass, while the new school call rest mass mass.
Rest mass is not additive. The rest mass of a molecule is not the sum of its atoms, but the sum plus the bond energy divided by $c^2$. Therefore in a chemical reaction, though the number of atoms (or electrons, protons, neutrons) are conserved, the rest mass is not, since the bond energy is changed. And this can be called mass being converted into energy. In
Motional mass, however, is just another name for energy, and therefore always conserved. In combustion, the molecular bond energy is converted to the additional kinetic energy of $\mathrm{CO_2}$ molecules, so the mass(or energy) is conserved. In nuclear reaction, the electromagnetic and strong potential energy between nucleons are converted into the kinetic energy of new nuclei and (sometimes) flying neutrons. Sometimes the new nuclei are in excited state, and will soon emit gamma radiation, which are basically high energy photons with zero rest mass but nonzero motional mass.