Ask A Scientist Chemistry Archive

  
name         Bob
status       educator
grade        9-12
location     MD

Question -   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?
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   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
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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
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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.
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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!
Mabel
(Dr. Mabel Rodrigues)
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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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