# Explain exceptions to Conservation of Matter to me?

1. Feb 20, 2014

### maximiliano

Matter can not be created nor destroyed....."in a closed system" ....and except where "energy transfers" are present. So, in a fusion reaction, energy is released; but mass is also lost. ?

Can someone/s just square this more a layman (me) so I can understand exactly what's going on? Thanks!!

Max

2. Feb 20, 2014

### dauto

The mass of a substance is just a measure of it's total energy content. If energy is removed the mass is reduced. BTW that's true for all forms of energy, not just fusion energy.

3. Feb 20, 2014

### maximiliano

But....isn't it correct that exactly the same amount of mass and energy in the universe today as there was in the instant after the big bang?

So are you saying that, as the sun "burns" (fusing H into He) and releasing energy, the mass of the sun is reduced, and in fact, that missing mass is now energy with no mass?????

When you burn a piece of wood, no matter is lost as the energy is released. It's just converted to other forms of matter (CO2, H2O, C, etc.). Obviously fusion and fission are releasing energy from the strong force.....but I can't see how matter has been destroyed.

4. Feb 20, 2014

### Staff: Mentor

No, the missing matter is now energy that does have mass, according to the famous $E=mc^2$. It's not matter that is conserved, it's energy, and matter is just one especially dense form of stored energy.

Not so. When you burn a piece of wood, the mass of the combustion products (ash, smoke, hot gas) is very slightly less than the mass of the oxygen and wood that you started with. The difference is in the energy (in the form of heat and light) that was released, and again you can calculate it according to $E=mc^2$.

This is true of all energy-releasing reactions, not just combustion. For example, a battery weighs very slightly more when it is fully charged that when it is discharged and the difference comes from the electrical energy that is released as the battery discharges.

We don't usually pay attention to this effect because it is so small. For a 20 kg lead-acid battery, we're talking a difference of a few nanograms (I seem to remember from the last time I calculated it). To get a sense of the scale involved... this is like the change in weight of a diesel locomotive if a mosquito lands on it.

5. Feb 20, 2014

### Agrasin

Also a layman here. I have a little extension of the OPs question.

I read somewhere that matter pops in and out of existence in vacuums. That clearly defies the conservation law. I also read that vacuums have a lot of energy (vacuum energy). Does this vacuum energy (which I don't understand) turn into mass, thus conserving mass-energy? Or is this an exception?

6. Feb 20, 2014

### maximiliano

So, If I take X mass of fuel and burn it in an enclosed glass sphere containing Y mass of oxygen.....and assuming x+y=Z......after the burn (and the energy is released)....the net mass inside the sphere will now be slightly less than Z?

7. Feb 20, 2014

### Agrasin

@maximiliano

I think that mass-energy conversion only occurs in nuclear reactions. Burning fuel is a simple chemical reaction, and stoichiometry says that the net mass will be the same. The heat given off is accounted for by new chemical bonds. When bonds are formed, heat is released.

8. Feb 20, 2014

### ZapperZ

Staff Emeritus
Please read one of our FAQ entry in the General Physics forum:

Zz.

9. Feb 20, 2014

### Bandersnatch

Only if you allow the released energy to escape. I.e., if light and heat produced in the reaction get radiated away. If you were to take a perfectly isolated box, from which nothing can escape, then no matter what would happen inside, its mass as measured from the outside wouldn't change.

@Agrasin, read Nurgatory's post. There is a mass deficit in chemical reactions.
In general, any system that gets bound in an attractive force field releases energy in the process, and the more strongly it becomes bound(the greater the binding energy), the more energy is released.

In nuclear reactions the energy of the strong force bonds between protons and neutrons is much higher than in chemical reactions(electromagnetic force is much weaker), so the binding in the latter case releases less energy, is easier to break, and harder to detect.

It's the same with gravitational force - any two masses brought close together have less total mass(gravitational mass) than if they were further apart, or isolated. Due to the relative weakness of the gravitational force, it is even less pronounced an effect than with chemical binding. However, in the case of very strong gravitational fields, like that of a neutron star, the gravitational mass can be as much as 20% lower than the total baryonic mass of its components.

10. Feb 20, 2014

### Agrasin

@Bandersnatch @Nugatory this changes everything. Why did my teachers never mention that E = mc^2 applies to all forces, not just in nuclear reactions?

This is difficult to grasp for me. Let's take the chemical bonding scenario. I've always been taught that creating chemical bonds makes atoms more stable, thus lower energy, thus they give off energy. However, you're saying that forming chemical bonds detracts from an atom's overall mass and releases energy?

Is the opposite true? When we break chemical bonds, is the input energy condensed into mass that is added to the atoms?

When nugatory says after a combustion, the mass of the ash, wood, vapor, etc is very slightly less than the mass of the reactants, is he saying that the heat of enthalpy = mc^2, where m is the missing mass?

11. Feb 20, 2014

### Agrasin

Hold on, this all has some weird implications.

Take this reaction CH4 + 2 O2 → CO2 + 2 H2O + 891 kJ/mol

The extra energy on the products side means that some mass was converted to energy, meaning the product molecules are less massive than the reactant molecules. This is obviously odd because both sides have the same atoms.

So atomic weight changes for atoms? The carbon in CO2 is less massive than the carbon in CH4, for example??

How does that happen? Does the carbon lose a fraction of a proton? From where does this mass disappear?

And does this mean the mass of an atom depends on the molecule it is in?

12. Feb 20, 2014

### sophiecentaur

Before you allow yourself to be incredulous about this you need to consider the numerical difference in mass that corresponds to just a few electron Volts of energy (chemical energy changes). That formula E = mc2 tells you that there is a factor of 10^17 relating mass and energy. It's only when the energy transfer is of Nuclear proportions (gamma ray photons) that the mass change becomes relevant.

13. Feb 20, 2014

### Staff: Mentor

Let's look at water. 1 oxygen atom and 2 hydrogen atoms come together to form a water molecule and in the process they release energy. This energy comes from the the fact that the atoms are in a more stable and less energetic state when they are bound together through chemical bonds. This is obvious when you realize that to turn water back into its constituent atoms requires that you use energy to pull them apart. The energy given up when the atoms bond is exactly equal to the amount required to break their bonds and pull them apart.

When the atoms bind together and release energy, the mass of the molecule as a whole is less than the combined mass of the atoms prior to bonding. No particles are lost, there is an equal number of protons, neutrons, and electrons before and after the reaction.

14. Feb 20, 2014

### dauto

Why does any of that bother you? You knew about mass deficit in nuclear reactions didn't you? If the fact that a nucleus is lighter than the sum of the masses of its constituent protons and neutrons doesn't bother you why should the fact that the mass of a molecule is lighter than the sum of the masses of its constituent atoms bother you? It's exactly the same principle. In fact weird would be if such a principle applied to nuclear reactions but not to chemical reactions. That would require an explanation.

15. Feb 20, 2014

### Khashishi

Mass and energy aren't necessarily conserved on a cosmological scale, when gravity is included. According to some models, as the universe expands, the total radiation in the universe decreases, and the total dark energy increases. In Newtonian physics, there is a simple concept of gravitational potential energy, but I don't think that anyone has come up with a general relativity analog.

16. Feb 20, 2014

### Agrasin

You're right. I didn't think that through.

So in chemical/ nuclear reactions, where does mass disappear from? Can the neutrons and protons simply lose mass? And then gain it back in reverse reactions?

And, just wondering, is the heat of enthalpy (-891 kJ/mol in the case of the combustion of methane) = (missing mass)c^2?

17. Feb 20, 2014

### maximiliano

So.....both strong force and weak force have mass?

Then, would it be appropriate to say that energy (exclude "dark energy" for the moment) has mass....and when sufficiently concentrated in space and time, manifests itself as what we consider, at present, to be matter?

18. Feb 20, 2014

### Staff: Mentor

The neutrons and protons do not lose mass in nuclear reactions - they're neutrons and protons, and their mass is what it is. Likewise, in chemical reactions (which are reactions between atoms) the atoms don't lose or gain mass - they're whatever they are and that's how much mass they have.

However, the mass of two isolated oxygen atoms is very slightly greater than the mass of the same two oxygen atoms bound together in a molecule of O2. Likewise, the mass of two neutrons and two protons in isolation is (somewhat less slightly) greater than the mass of the the same four particles assembled into a helium nucleus. In both cases, the excess mass is stored in the energy fields between the particles, and that's greater when they're pulled apart than when they're allowed to bind together.

19. Feb 20, 2014

### Staff: Mentor

Careful with your terminology. Forces don't have mass, objects and systems of objects do.

Not really. Energy does have mass but the "concentration" of energy has little to do with matter.

20. Feb 20, 2014

### Staff: Mentor

One mole of methane has a mass of about 16 grams. Two moles of oxygen have a mass of about 64 grams. So 80 grams of reactants go into this reaction that yields less than 1000 kJ.

Plug 1000kJ into $E=mc^2$ and you come up with a mass deficit of .01 micrograms.

So, yes there is missing mass. But it's small enough so that we can forgive past generations of chemists for not noticing it and forgive current generations of chemistry teachers for telling us calculate as if mass is conserved in chemical reactions.

This might be a good time for a link to Asimov's classic essay: http://chem.tufts.edu/answersinscience/relativityofwrong.htm