[jjkwest1]

Iron-56 (5626 Fe) has a binding energy per nucleon of 8.79 MeV.
   (1 MeV is 1.60 x 10^–13 J)
   72.   Determine the amount of energy needed to “decompose” one mole of iron-56 nuclei.
   a)   3.47 x10^11 J
   b)   8.47 x10^11 J
   c)   8.90 x10^11 J
   d)   1.13 x10^14 J
   e)   7.75 x10^13 J

I know that the answer to this questions is 8.47 j/mol by doing:

8.79MeV/nucleon * 6.022*10^23nucleon/mol * 1.6* 10^-12J/mol=  8.47*10^11J


however, when i looked at an example from my textbook it showed the conversion from 1.23*10^23 J/mol to 7.98 MeV/nucleon (binding energy for O-16) which was:

1.23*10^13 J/mol * mol/6.022 *10^23 nuclei * nucleus/16 nucleon * 1 MeV/ 1.6*10^-13J= 7.98 Mev/nucleon

When i tried to convert 7.98 MeV/nucleon back into J/mole

i did 7.98 MeV/nucleon * 6.022*10^23 nucleon/mol * 1.6 *10^-13 J/mol = 7.69 *10^11 J/mol, which doesn't match 1.23*10^23 J/mol

however, when i did:  7.98 MeV/nucleon* 16 nucleon/nucleus * 6.022*10^23 nuclei/mol * 1.6*10^-13 J/MeV = 1.23 *10^13 J/mol

My questions is, for the questions above shouln't you do:

8.79MeV/nucleon * 56 nucleon/nucleus * 6.022*10^23 nuclei/mol*  1.6* 10^-13J/mol= 4.74 * 10^13 J/mol

shouldn't the energy needed to “decompose” one mole of iron-56 nuclei be 4.74 * 10^13 J/mol? or am i missing something here.

Please help, i'm really confuse