Calculate the amount of energy evolved (in kJ) when 2.50 mg of 2H undergoes fusion according to the equation below. 2H + 3H = 4He + 1n ?

Ive calculated the mass defect through guidance of a video. The video calculates the energy for one mole of 4He. How do i calculate the energy for 2H?

1 Answer
Doc048
Feb 1, 2018

The energy change is for the 'overall' reaction, not just deuterium or tritium. For a 2.50 mg sample of Deuterium (H-2) #Delta E ~ -4.22xx10^6j#.

Explanation:

For the reaction #""_1^2H# + #""_1^3H# => #""_2^4He# + #""_0^1n# determine the nuclear masses ...

Nuclear mass of #""_1^2H# = Mass of #""_1^2H# - Mass of #1e^-#
= 2.01400 amu - 0.000549 amu = 2.013451 amu

Nuclear mass of #""_1^3H# = Mass of #""_1^3H# - Mass of #1e^-#
= 3.01605 amu - 0.000549 amu = 3.015501 amu

Nuclear mass of #""_2^4He# = Mass of #""_2^4He# - mass of 2#e^-#
= 4.00260 amu - 2(0.000549) amu = 4.001502 amu

Mass of 1 #""_1^on# = 1.00865 amu

Change in nuclear mass
#Delta m# = #Sigma(Product Masses)# - #Sigma(Reactant Masses)#
= #[4.001502"amu" + 1.008665"amu"]# - #[2.013451"amu" + 3.015501"amu"]# = #-0.018785 "amu"#
= #-1.8785xx10^-5Kg#

Energy Change for one mole #""_1^2H# ...
#DeltaE = mc^2# = #(-1.8785xx10^-5Kg)(3xx10^8"m/s")^2#
= #-1.68839xx10^12 Kgm^2/s^2# = #-1.68839xx10^12"joules"#

Energy Change for 2.50 mg #""_1^2H# = #2.5xx10^-6 "mole"""_1^2H#
= #2.5xx10^-6cancel("mole")# #(-1.68839xx10^12j/cancel("mole"))#
= #-4.22xx10^6j#

Energy Change in MeV per nucleon ...
= #((-4.22xx10^6cancel(j))/(2.5xx10^-6cancel("mole")))##((1cancel("mole"))/(6.023xx10^23"nuclei"))##((1"MeV")/(1.602xx10^-13cancel(j)))#
= #-17.5"MeV"/"nuclei"#

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