The mass of a molecule is the mass of its constituent atoms plus the mass of the bonds between them. When those bonds are broken, the system loses the amount of mass one would expect given e = mc^2.
Note: this amount of mass is very small and so is typically left out of introductory chemistry courses.
The mass is almost almost almost conserved in chemical reactions. By special relativity, the energy/heat that produces the reaction should come from a extremely slightly difference of mass between the reagents and the products. The difference is so small that in any chemical class and chemical application you just assume that they are equal. (http://en.wikipedia.org/wiki/Conservation_of_mass#The_mass_a... )
For example, a person consumes approximately 2000 kcal/day of food. The calculation is more complicated, because not all the energy is used. But for the sake of the argument, let's assume that the person just use all the 2000 kcal and they are lost as heat, work (lifting a heavy object , moving the air, moving the water while swimming, ... )
Using the famous E=mc^2 equation we have that m=2000 kcal/c^2 = 9E-8 grams = 3E-9 ounces. That's very small and is not useful for a diet, but it's not zero.
There are several ways that "mass" can be converted into energy. In this case we are not talking about e=mc^2. The conversion of fat cells to energy for brain and muscles should involve at the end of the day: urine (lactic acid etc.) and exhaled H2O and CO2.
Edit:
Notice I put mass in quotation marks. I am not trying to break the law of conservation of mass. Fat cells consumed will produce energy through some kind of biological process.
...isn't that just re-arranging atoms and electrons into lower energy states? The mass of those atoms and electrons doesn't change. A block of steel has the same mass at the top and bottom of a hill.
Does converting chemical bond energy into kinetic energy somehow remove energy (i.e. mass) from the system?
Does a block at rest sitting on the top of a hill have more mass than a spinning block at the bottom of a hill (assuming the rotational kinetic energy equals the difference in potential energy)?
Whether the energy leaves a system depends on the particulars. If you burn some hydrogen in a bomb calorimeter, the energy will stay inside the calorimeter. This is a "closed system". If you burn it with an open flame, the kinetic energy will warm the atmosphere. This is an "open system". The energy could end up anywhere... you can use hydrogen to launch rockets into space.
Since the energy can end up anywhere and the energy has mass, the mass can end up anywhere, too.
I don't follow how that explains why two identical objects with the same energy content should be expected to have different masses. It seems like this whole thread is trying to argue that chemical reactions destroy mass through examples of open systems that leak energy. A leaky water balloon loses mass, too but that doesn't constitute evidence that atmospheric pressure/tension/etc destroys mass, does it?
If you take a block of steel from the top of a hill to the bottom of the hill and convert all the potential energy to kinetic energy (without loss), why would the mass of the block be altered? It may well be true, but arguments based on applying the mass-energy equivalence is not the answer.
Likewise, if you start with some pool of molecules and rearrange the constituent atoms and bonds, energy must be balanced via kinetics (i.e. translational and rotational energy of and within molecules on both sides of the reaction)--why should anyone expect the overall mass to change from such chemical reactions?
Per E=mc^2, energy and mass are basically the same thing. Also, if you weight your substrates before and after and exothermic reaction, you'll see a (very tiny) loss of mass.
Yeah I know they're basically the same which is what makes this hard. And energy stored in chemical bonds has gravity just like some tiny amount of mass would. But if someone is asking for the difference between mass and energy, I wouldn't put that on the mass side.
Not technically correct. A small amount of mass is lost or gained in chemical reactions, just like when gravitational potential energy is gained or lost.
If you walk up a flight of stairs, you will be heavier at the top. If an electron changes orbital, its mass changes as well, making it heavier or lighter.
Let's calculate it. A 90 kilogram man walks up a flight of stairs, one story (3.3 meters). The expression "m * g * h" gives us the gravitational potential energy of mass "m" ascending height "h". Evaluating the formula we get 2910 joules. So how much heavier has the man become? Given E=mc^2, then m = E/c^2. As you can see, we'll be dividing by c^2, which is a very big number. The resulting increase of mass is 3.24 E-14 kg, or too small to be noticeable, but still very real: A 90 kg man ascending a 3.3 meters gains 0.00000000000003 kilograms of mass.
Chemical potential energy changes result in mass changes as well. These changes in mass are insignificant at the scale of chemical reasons, but are indeed taking place. So while it may be reasonable to simplify a discussion of chemistry by saying that chemical reactions don't change mass, in reality the changes do take place, just at a very small scale. A starting point for further research:
"Whenever any type of energy is removed from a system, the mass associated with the energy is also removed, and the system therefore loses mass. This mass defect in the system may be simply calculated as Δm = ΔE/c^2"
nit: "heavier" refers to weight, not mass. The man will actually be lighter at the top of the stairs due to decreased gravity. (R_earth / (3.3m+R_earth))² ≈ -0.0001 %
Someone else can calculate the decreased buoyancy in thinner air ;)
Q is the released energy. If you weigh the molecules before and after very carefully, you will notice that they lose weight (or mass if you are being pedantic about it). That mass loss corresponds exactly to the Q-value (through E=mc²).
Why is Q not part of the system anymore? Isn't the Q carried by the 2H₂O molecules (or the solution/matrix/whatever)? Doesn't it just represent that the energy is of a different form?
How does bond energy represent mass but kinetic energy does not represent mass? I realize Q is a different symbol in the formula, but that's just notation. The bond energies are implicit in the formula, but that doesn't mean they aren't there.
No mass is lost in this reaction. The mass of the atoms remains the same. The energy that is released is due to the difference in bond energies. To balance the equation you would need to add a Q to the other side, corresponding to the bond energies.
The molecules consist of Hydrogen and Oxygen that have equal atomic masses, either side of the equation, due to the identical numbers of protons, neutrons and electrons.
Any mass gained or lost will be due to changes in bond energies, and the corresponding emission or absorption of photons that change the energy states of the electrons in the bonds.
Putting a Q on the left hand side would be an error. Q indicates that the energy is not bound in the molecular configurations.
If you measure the mass of a quantity of water accurately enough, the mass will be lower than the mass of the equivalent amount of hydrogen and oxygen gas. The difference would be so small that our most sensitive instruments would not be able to detect it.
Likewise, in a nuclear reaction, the only thing changing is the nuclear binding energies of the protons and neutrons. However, since the energy involved is many orders of magnitude higher, our instruments are sensitive enough to detect the difference in mass.
Speaking in generalities yes, but TECHNICALLY stuff that contains more energy is heavier too. But given that most enthalpies are in the kJ/mole range and most moles of things are pretty heavy relative to 9e18 (the speed of light squared) that you might as well round it out and say "no mass is created or destroyed in an ordinary chemical reaction"
I just want to say as someone with a degree in physics that this commenter is correct. Mass and energy directly relate through E=mC^2. If you remove energy (and "just" energy) from a system, it now has E/C^2 less mass.
Example:
You have some fissible material that undergoes a nuclear reaction in a closed system and the reactants turn into products with lower mass.
The mass of the system doesn't actually go down until/unless the system cools down.
edit: The above commenter is still being pedantic though
Conservation of mass at the scale of biological reactions is true enough though. I also didn't like this phrasing, but it leads into talking about the byproducts of metabolism, which was the whole point.
And, it is contradicted just a few paragraphs later. Sugar (and fat once it has been broken down) is burned. The statement becomes much more sensible (and less of a straw man) if we say "mass is burned". Works for steam engines. Works for people.
I don't know why the parent thinks it's wrong, but I think it's wrong because it's a statement that works at the wrong level of abstraction.
Yes, it's quite true that in physics, mass cannot be turned into to energy. But the article's not talking about physics; it's talking about biology, and in biology, fat can be turned into energy --- that's why your body makes it.
Yes, of course it's not a nuclear process. The fat's metabolised into energy and waste products, which are excreted mostly through the lungs. Also via the skin, urine, faeces and any other bodily fluid --- one byproduct is water.
'It's turned into energy' is actually the right answer if you're thinking about biology. It's just not a complete one. The article would have done much better to have instead said 'you're right, but' and then gone on to explain, rather than just saying 'if you think this you suck'.
Also the idea that exercise has a huge affect on mass loss is also pretty wrong. If you've got a large amount of weight you need to lose, the only needle exercise is going to move is your willpower, downward. Making it difficult to stick to what works, which is eating less. Shedding mass is way more about building willpower and good habits than it is about playing metabolic tricks.
The picture changes when you're down to those last few pounds. To get those off, you have to keep up the reduced caloric intake, and you also have to exercise. If you slack off on the former, you'll gain weight back. If you don't exercise, you won't lose any fat.
Building habits and willpower is a journey that takes at least a year and involves changing your relationship with food. To a large extent, we see food as entertainment, it takes a long time before our subconscious minds' adjust to thinking about it as fuel. Inherent in this is replacing that hole left in our psyches where food entertainment used to be with something else as entertainment.
It was a whole year after I started dieting before I started looking at salads as a perfectly acceptable lunch, perfect for getting a feeling of fullness without blowing up the calorie meter. For a long time I played this game of trying to get the most value out of my calorie budget, still mind thinking of food as entertainment.
I did intermittent fasting, which was effective at helping me lose weight but not at keeping it off because it didn't solve the food-as-entertainment issue. Once I got down to a more reasonable weight I stopped, and before I knew it I was fat again, though not nearly as fat as before. I hadn't stopped thinking of food as something to cure boredom with.
I eat better than I ever have, and look more youthful at 31 than through most of my twenties. Ironically, I feel I also enjoy food a lot more than I used to. I taste it better, I find it more interesting. In a Buddhist non-attachment sort of way.
This is wrong enough to make me stop reading.