AP Chem; Calculating energy released

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SUMMARY

The discussion focuses on calculating the energy released during the fusion of deuterium and tritium to form helium-4 in AP Chemistry. Using the 7th edition Chemistry textbook by Zumdahl, the participant calculates the mass defect (∆m) as -1.02755 amu, leading to an energy release of 49,289 Joules per mole of helium-4 produced. The participant also discusses the conversion of energy from Joules to MeV, emphasizing the need to express energy per helium nucleus and per mole of helium nucleus using Avogadro's number.

PREREQUISITES
  • Understanding of nuclear fusion reactions
  • Familiarity with mass-energy equivalence (E=mc²)
  • Knowledge of atomic mass units (amu) and their conversions
  • Basic proficiency in using Avogadro's number for mole calculations
NEXT STEPS
  • Learn about nuclear fusion processes and their applications in energy production
  • Study the conversion of energy units from Joules to MeV
  • Explore advanced topics in thermodynamics related to nuclear reactions
  • Investigate the role of mass defect in nuclear stability and reactions
USEFUL FOR

High school students enrolled in AP Chemistry, educators teaching nuclear chemistry concepts, and anyone interested in the principles of energy release in nuclear fusion reactions.

Misteh
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I have just started AP Chemistry this year as a junior at my high school despite all peer protests against it. And I admit so far the course has lived up to it's reputation of being very difficult. I was rather ecstatic to come across this site where I may obtain the help I /know/ I will need all year. So expect to see me often. ^_^
We use the 7th edition Chemistry textbook by Zumdahl, so I believe my source is familiar to at least some.

Homework Statement



Calculate the energy released per (4 mass #, 2 Protons)He nucleus produced and per moles of (4 mass #, 2 Protons)He produced. The atomic masses are (2,1)H, 2.01410; (3,1)H, 3.01605; and (4,2)He, 4.00260. The masses of the electron and neutron are 5.4858 x 10 raised to the -4 and 1.00866 amu, respectively.


Homework Equations



The easiest fusion reaction to initiate is


(2,1) H + (3,1) H ---> (4,2) He + (0,1) n


The Attempt at a Solution



∆m = (4.00260 + 1.00866) - (2.01410 + 3.01605) = -1.02755 amu
(Originally I had the two enclosed equations swapped which would give a positive result instead. Would this matter? If so, why?)

For Mole;
-1.02755 amu = 1.6005 x 10 to the -27 Kg / 1 amu
= -1.6446 Kg

E= mc squared, so: -1.6446 Kg x (2.997 x 10 to the 8) Squared
= 49289 J

For Nucleus;
I was unsure how to find this, but I found that
1 mol = 6.0221 x 10 to the 23 nuclei
So do I need to convert Kg into mol and then into nuclei?
 
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You can express the energy in terms of MeV. 931.5 MeV/amu is the conversion factor I believe. To convert that to joules, use the equality 1 electron volt = 1.602 X 10^-19 Joule and MeV is million electron volts. The question asks you to give the energy in terms of 'per He nucleus' and in terms of 'per mole of He nucleus'. Find the energy per nucleus of He and then multiply that by Avogadro's number to get it in terms of energy per mole.
 

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