Thermochemistry: Conservation of Mass and Energy
 Nuclear chemistry forces us to modify the Law of Conservation of Mass to include an energy term as well. The energy term is derived from Albert Einstein's famous E=mc2 equation. Actually this equation was rewritten for the layman, in its true form it is E = moc2, where E is the change in energy that takes place, mo is the change in rest mass, and c is the speed of light. Because the speed of light is very large and it's square even larger, even a very small change in mass would translate into an enormous change in energy. For example lets take a look at an ordinary chemical reaction.

The combustion of the gas methane.

CH4(g) + 2 O2(g) ---> CO2(g) + 2 H2O(g)      Ho = -890 kJ/mol

since E = moc2 then upon rearrangement we get mo = E
c2

Fact: 1 J = 1 kg m2 This a fact that should be memorized.
s2

therefore mo = ___890 kJ     X 1000 J  1 kg m2
(3.0 x 108 m)2       1 kJ              s2

= 9.89 x 10-12 kg

= 9.89 x 100 ng

The 890 kJ of energy released by the combustion of one mole of methane thus originates from the conversion of 9.89 ng of mass into energy. Such a small change, about 10 ng out of 80 g cannot be detected by balances. It amounts to the loss of 1.0 x 10-7% of the mass. So we ignore Einstein's equation when doing regular chemical stoichiometric calculations. However this equation is very useful in nuclear chemistry.

Nuclear Binding Energy
The sum of the rest masses of the nucleons of an atom does not equal the measured mass of any nucleus. The actual mass of an atomic nucleus is always a trifle smaller then the sum of the rest masses of all it's nucleons (p+ + no). This mass difference is changed into energy as the nucleus formed, and was emitted as high energy electromagnetic radiation. It would cost this much energy to break the nucleus apart into its nucleons again, so the energy is called the 'binding energy of the nucleus'.

Lets take a look at the manufacture of a Helium nucleus.

Binding energy of 42He - actual rest mass is 4.001506 amu.

The rest masses of the nucleons are:

p+ = 1.007277 amu no = 1.008665 amu You should include these numbers in your data book.

For 42He then 2 p+ = 2 x 1.007277 amu = 2.014554 amu
2 no = 2 x 1.008665 amu = 2.017330 amu
4.031884 amu

The difference in mass = calculated mass - actual mass
= 4.031884 amu - 4.001506 amu
= 0.030378 amu

1 kg = 1000 g          1 amu = 1.6606 x 10-24 g {Include these facts as well}

so

E = moc2

= (0.030378 amu X 1.6606 x 1024 g  1 kg    )(3.0 x 108 m)2
amu           1000 g                     s

= 4.54 x 10-12 kg m2
s2

= 4.54 x 10-12 J This is the energy release for 1 atom of 42He

A mole of He would be 6.02 x 1023 nuclei more, therefore,
6.02 x 1023 nuclei/mole * 4.54 x 10-12 J/nuclei

= 2.73 x 1012 J/mole (enough energy to power a 100 watt light bulb for 900 years)

How do I know this?

P=E/t from grade 11 chemistry class.

therefore t = E/P

= 2.73 x 1012 J
100 W

= 2.73 x 1012 J
100 J/s

= 2.73 x 1010 s (X 1 min/60 s)

= 4.55 x 108 min (X 1 hr/60 min)

= 7.583 x 106 h (X 1 day/24 h)

= 315972.2 days (X 1 y/365.25 days)

= 865.09 years

Go to the Nuclear Conservation of Energy Worksheet