Calculating Energy Released in Fusion: 21H + 31H -> 42He + 10n

[ProPatto16]

Homework Statement

A nuclear reaction being studied for its potential as a source of fusion power is:

²₁H + ³₁H -> ⁴₂He + ¹₀n

1) calculate energy in MeV released when two atoms fuse according to the reaction above.
2) calculate the energy in joules released per mole of reactants. (ie. one mole of H-2 and one mole of H-3)

The Attempt at a Solution

1) the answer is 17.59 Mev
and i don't know how to go about 2)

i know combined they release that energy found in part 1)... but I am not sure how to divide that energy up between them. is it done on a ratio of 2:3 by atomic mass? or is it done by mass in kg? i just don't know the connection there...

 

[rock.freak667]

Well if you know the masses of ²₁H and ³₁H, since they are both currently 1 mole, you can just add the atomic masses, which would be in the units kg/mol.

E=mc²

 

[ProPatto16]

the mass of 21H is 2.014102 so E is just 2.014102c^2?
same for 31H.

 

[rock.freak667]

the mass of 21H is 2.014102 so E is just 2.014102c^2?
same for 31H.

It is 2.014102u where u = 1.66053886 × 10^-27 kg.

 

[ProPatto16]

yeah, i used that conversion, just didnt clarify.

E of 21H = 3.01*10^-10J
E of 31H = 4.507*10^-10J

 

[rock.freak667]

yeah, i used that conversion, just didnt clarify.

E of 21H = 3.01*10^-10J
E of 31H = 4.507*10^-10J

Sorry, I thought your question was asking something else. Just convert the value you got to Joules, then you only have 2 moles of reactants so, that the energy per unit mole of reaction is just E_reactant/2.

 

[ProPatto16]

ohh... so the atomic masses and whatnot of the elements isn't even relevant? the energy is just half anf half?

 

[rock.freak667]

ohh... so the atomic masses and whatnot of the elements isn't even relevant? the energy is just half anf half?

Well you are finding per mole of reactant and not something like per mole of H-2 which I think would work out to be different, but my reasoning of the problem could be wrong.

 

[ProPatto16]

2) calculate the energy in joules released per mole of reactants. (ie. one mole of H-2 and one mole of H-3)


so its energy per H-3 and per H-2.