AP Chem; Calculating energy released

[Misteh]

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?

 

[chemisttree]

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.

 

[Blueshift5]

Hello! It's great to hear that you have started AP Chemistry and are already seeking help and resources. It shows dedication and determination, which are important qualities for success in this course.

Now, let's talk about the problem at hand. The first thing to note is that the equation you have written is not a fusion reaction, it is a neutron capture reaction. In a fusion reaction, two smaller nuclei combine to form a larger one, releasing energy in the process. In a neutron capture reaction, a nucleus absorbs a neutron, producing a larger nucleus and possibly releasing energy.

Assuming that the question is asking for the energy released in a fusion reaction, we can use the equation provided to calculate the energy released per mole of (4,2)He produced. The key here is to use the correct mass values for the reactants and products. The correct equation for a fusion reaction between (2,1)H and (3,1)H is:

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

Using the atomic masses given, we can calculate the change in mass (∆m) as:

∆m = (4.00260 + 1.00866) - (2.01410 + 3.01605) = 0.98111 amu

Now, to convert this to kilograms, we can use the conversion factor 1 amu = 1.66054 x 10^-27 kg. This gives us a mass change of:

0.98111 amu x (1.66054 x 10^-27 kg/amu) = 1.628 x 10^-27 kg

Using the equation E = mc^2, we can calculate the energy released:

E = (1.628 x 10^-27 kg) x (2.997 x 10^8 m/s)^2 = 4.62 x 10^-12 J

To calculate the energy released per mole of (4,2)He produced, we need to know the number of (4,2)He nuclei produced per mole. This is given by the coefficients in the balanced equation, which in this case is 1. So, the energy released per mole of (4,2)He produced is:

4.62 x 10^-12 J/1 mole = 4.62 x 10^-12 J/mol