Question

38. What is the nuclear binding energy of iron-56 in kJ/mol? The mass of the iron-56 nucleus is 55.92068 amu. A. 7.90 x 1011 kJ/mol B. 2.78 × 109 kJ/mol C. 4.76 x 1010 kJ/mol D. 8.78 x 10-28 kJ/mol E. 5.38 x 101 KJ/mol

The answer is C

Answer 1

Fe-56 has an atomic number of 26

therefore it has 26 protons

And number of neutrons = 56 - 26 = 30

Protons: 26 x 1.007825 g/mol= 26.20345 amu
Neutrons: 30 x 1.008665 g/mol= 30.25995 amu

The mass of Fe-56 is given as 55.92066 amu
so subtract the protons and neutrons from this
( 26.20345 + 30.25995)amu - 55.92068amu= 0.54272 amu

Convert the mass defect into kilograms (1 amu = 1.66 x 10-27 kg)

So, 0.54272 x 1.66 x 10^-27 = 9.009 x 10^-28 kg

Now we have to use E= mc^2
c= speed of light= 2.99 x 10^8 m/s

m = mass defect

Putting the respective values, we get

E = 9.009 x 10^-28 kg x (2.99 x 10^8)^2

E = 8.054 x 10^-11 J

Convert it into kJ/mol

E = 8.054 x 10^-11 J x ( 6.022 x 10^23 / mol) / 1000

E = 4.85 x 10^10 kJmol-1

Which is approx to 4.76 x 10^10 kJmol-1.

So, option C is the correct choice.