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Name: Bob
Status: educator
Grade: 9-12
Location: MD
Country: N/A
Date: 3/15/2005

A student showed me a reference book that stated the number of tons of coal burned per year in the US. It stated the number of tons of products produced from the combustion reaction. It went on to state that the products of the reaction weighed less than the original coal due to the energy removed. I've never heard of this. Mass is lost in nuclear reactions....but is it also true that mass is lost (in small amounts) in regular chemical reactions? Regular reactions manipulate energy stored in bonds, rather than the nucleus. If a reaction releases energy, do the products weigh less? Is the weight loss related to the weight of electrons?

In order to be "cute" some textbook authors incorporate Einstein's mass/energy equivalence, given by E = m x c^2, to convert the heat energy given off in an exothermic reaction to show that there is a loss of mass. Rigorously speaking that is true; however, let us look at the numbers because the Devil's in the details. Let us suppose a chemical reaction produces 10 kcal = 41840 joules (We want this conversion to use MKS units.). c = 3 x 10^8 m/sec, so c^2 = 9 x 10^16 (m^2 / sec^2), rounding off this is 10^17(m^2 / sec^2). Plugging in: E / c^2 = m gives: 41840 / 9 x 10^16 = 4.7 x 10^-13 kg or 4.7 x 10^-10 gm. Further, assuming that this hypothetical involves a substance with a molecular weight of 100 gm / mol. Then the mass "defect" (as it is called) 4.7 x 10^-12 mol, or multiplying by Avogadro's number = 6.023 x 10 ^23 yields 3 x 10 ^12 atoms or molecules of the substance.

Negligible in any mass balance in chemical reactions. But it does show how the transformation of small amounts of matter in a nuclear bomb produces an enormous amount of energy. Although it would be technologically possible to measure the mass defect using high resolution, high precision mass spectrometry, no one really cares except in some very specific areas of nuclear physics.

So you are correct in any practical circumstances involving "chemical reactions". I would be looking for a new text. The author of your present one is "puffing a lot of smoke" without making the point. That only confuses students.

Vince Calder

More likely than anything else is that what the define as products does not truly cover everything from the combustion- water vapor and carbon dioxide and other gases would be major products of combustion. Assuming that the coal is nothing but hydrocarbon, the net mass of the products would exceed that of the coal, just by addition of oxygen atoms into the products. However, to be correct in the mass balance, the mass of oxygen reacted should be counted, in which case the mass of reactants = mass of products. Even if accounting for all these, often the numbers are just estimates, so there will be discrepancies that are not truly "lost mass", unless "lost" means not properly accounted for.

Don Yee

Surprise, Bob. This is believed to be true. The products weigh less. Energy has this much mass: E=mc2 <==> m = E/c2. Does not matter what kind of bonds it is stored in.

It sounds like you understand that for chemical reactions, the mass of the energy is so small, compared with the mass of the reactants or products, that nobody can have measured it ("actually seen it") yet. But it is very strongly in our theories, so it is assumed to be quite true.

You can presume some tiny mass flow goes with every accountable work flow; such as mechanical work done on an object, or energy coming out of a system.

I suppose this means that:

- a satellite gains some billionths of 1% in mass as you raise it from LEO to GEO using solar sails...

- a gamma ray photon has orders of magnitude more mass than a light wave photon. (both are photons, rest_mass=0, pure energy). Gamma rays often kick atoms out of place; light doesn't.

- an electric field has mass which will seem to be stuck to the object holding the charges that originated it.

A large metal sphere in very empty space, charged up to +600,000 volts with respect to the space some distance around it, would actually get heavier instead of lighter if you gently pulled more electrons from it.

Jim Swenson PS- what reference book mentions estimates of U.S. coal consumption and predictions of special relativity in the same page? It has nothing to do with electrons, except that electrons are the easiest way to check your conversion units, prove the math actually works for you. You may remember that an electron's annihilation/creation energy E is 511 KeV. Converting to metric: 5e5 eV * 1.6e-19 Coulomb/e * 1 J/Coul.Volt = 8e-14 Joules. A mole of Protons masses about 1 gram: 1/(6.02e23) grams = 1.66e-27kg/Proton An electron masses roughly 1/2000 of a proton: M=~8e-31kg. (looking it up: Me = 9.1e-31kg) Speed of light c = 3e8 meter/sec; c^2 = 9e16 (m/s)^2 mc2= 9e-31kg*9e16 (m/s)^2 = 8e-14 Joules, a match to the E value above.

Hi Bob! You are correct. In combustion or in any other chemical reaction the Conservation of Mass Law holds. I can only think as a "justification" of what the book you quote says has to do with the cool utilization, the efficiency of the reaction that in industrial basis, certainly is not 100%. Thanks for asking NEWTON!

(Dr. Mabel Rodrigues)

Bob, Your instincts are correct. There is no measurable mass loss in chemical reactions. The energy that is produced in chemical reactions is due only to the change in the enthalpy of the system -- which is related to bond energy. I think that reference book is trying to make a connection between two different process: the burning of coal which produces energy, and the mass of the commercial products that are produced (via various processes) from that energy. --And that is more of a coincidence then a statement of science. While it is true that there should be an energy loss in every process (2nd Law of Thermodynamics), the connection between energy and mass can only be made in nuclear processes and not chemical processes. There is no connection between chemical bond energy and the mass of the substance or chemical forming that bond.

Greg (Roberto Gregorius)

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