When energy is produced in nuclear reactions, we are reminded of the equation e=mc². However, since no energy can come from just nowhere, even in chemical reactions the energy released must come from some conversion of mass to energy. But the Wikipedia article on the Conservation of Mass mentions that "Einstein pointed out that the change in mass of systems for which the chemical amounts of energy were allowed in or out of systems, was predicted by his theory to be so small that it could not be measured with available instruments."

When hydrogen is burned it gives off 242 kiloJoules per mole of hydrogen (H₂ -- so it's Avogadro's number of molecules -- not atoms). How much does the molecular weight of water differ from half the total of the molecular weights of two molecules of hydrogen and one of oxygen?

The reaction is 2H₂ + O₂ → 2H₂O or H₂ + (1/2)O₂ → H₂O.

Based on the E=mc˛ equation, it would seem that the differences in molecular weights would be just that amount of mass being converted to energy when hydrogen is burned.

So, in our case, E=242kJ:

242 kJ = m * (299,792,458 m/s)˛, where m is in kilograms.

242,000 J = m * 89,875,517,873,681,764 (m/s)˛
 
m = 242,000 J / 89,875,517,873,681,764 (m/s)˛

m = 2.692613135649757 x 10^(-12) kg

Posted by Justin on 2010-03-23 22:26:56