It keeps saying I am wrong!
Am I doing the math incorrectly?
Problem:
Calculate the amount of energy released in kJ/mol for the fusion reaction of two 1H atoms to yield a 2H atom and electron:
1/1H+1/1H→2/1H+0/1e
The atomic masses are
0/1e (0.0005486 u),
1H (1.00783 u),
2H (2.01410 u),
and 3He (3.01603 u).
....
2(1.00783u)= 2.01566u
2.01410 u + 0.0005486 u= 2.0146486u
Subtract for mass defect:
2.01566u-2.01566u=0.0010114u
Convert to kg:
(0.0010114u)(1.661e^-20kg) =3.46260494e^-12kg
E=mc^2:
E=(3.46260494e^-12kg)((2.998e^8m/s)^2)=
1699.19855J/atom
Convert to kJ/mol:
((1699.19855J/atom)(6.022e^23atoms/mol) /1000J)
=99714419144.9kJ/mol
or 9.971e^10kJ/mol
My answer:
E=9.971e^10kJ/mol
What did I do wrong?
I didn't look at all of it but 1 amu = 1.6605E-27 kg
It still says that I have the wrong answer.
Using 1 amu = 1.6605E-27 kg I got
(0.0010114u)(1.6605e^-27kg) =3.1565365e^-15kg
(3.1565365e^-15kg)((2.998e^8m/s)^2)
=77.1202723J
((77.1202723J/atoms)(6.022e^23atoms/mol) /1000J)
=4525664853.4
or 4.526e^-9
So then E=4.526e^-9
Right?
From this step,
Using 1 amu = 1.6605E-27 kg I got
(0.0010114u)(1.6605e^-27kg) =3.1565365e^-15kg
I don't believe this math is correct. Estimate 1E-3*1.7E-27 = about 1.7E-30
Based on the calculations you provided, it seems that you have made an error in the unit conversion from joules to kilojoules.
Let's go through the calculation step by step to identify the mistake:
1. You correctly calculated the mass defect as 0.0010114u.
2. Converting the mass defect to kilograms, you multiplied it by the conversion factor 1.661e^-20kg/u, resulting in 3.46260494e^-12kg. This step is correct.
3. Applying the equation E = mc^2, you multiplied the mass in kilograms by the speed of light squared, resulting in 1699.19855J/atom. This step is also correct.
4. To convert joules to kilojoules, you need to divide the energy value by 1000, which you did not do. That is where the error lies.
5. Multiplying the energy value by Avogadro's number (6.022e^23 atoms/mol) is the correct step to convert from per atom to per mole.
6. Finally, dividing the energy in joules/mole by 1000 will give you the energy in kilojoules per mole.
Therefore, your corrected calculation would be:
((1699.19855 J/atom) * (6.022e^23 atoms/mol))/1000 J = 10191.921 kJ/mol
Hence, the correct answer for the amount of energy released in kilojoules/mol is 10191.921 kJ/mol.