Mass - Energy Conversion in Chemical Reactions
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
So you are correct in any practical circumstances involving "chemical
reactions". I would be looking for a new text. The author of your present
"puffing a lot of smoke" without making the point. That only confuses
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.
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
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
(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
with respect to the space some distance around it,
would actually get heavier instead of lighter if you gently pulled more
electrons from it.
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
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.
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)
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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Update: June 2012