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Chemical Relativity (Posted on 2010-03-22) Difficulty: 2 of 5
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.

  Submitted by Charlie    
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Each mole of hydrogen produces one mole of water (only hald a mole of oxygen is used in the process, being half the chemical equation). So the heat produced in the formation if each molecule of water is 242 kiloJoules divided by Avogadro's number -- 6.0221415 * 1023. That result is 4.0185 * 10-19 Joules.

Google then tells us that (4.0185 * (10^(-19)) joules) / (c^2) = 2.69261042 * 10-9 atomic mass units, so indeed any change in the molecular weight is in the 9th place after the decimal, while water has a molecular weight of about 18 amu and atomic mass numbers are usually given only to 3 or 4 decimal places.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: solutionbroll2013-01-31 07:05:16
solutionJustin2010-03-23 22:26:56
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