If someone has the time to help with the following question it would be really helpful.
The problem is
209/83bi+64/28NI=272/111Rg+1/0n
How to calculate the energy change in J/mol reactants?
AMU amounts:
Bi=208.980384
Ni= 63.927969
Rg=272.1535
What I have done is
1. subtract products from reactants.
2. multiply the result by 1.66054x10^-27kg
3. multiply that by 8.98x10^16 (which is c^2 in e=mc^2
4. multiply that result by 6.022x10^23
The answer is 1.03x10^11. But I am not getting that.
can someone explain how to do this problem? I keep getting the following answer which by the book is wrong:
1. difference between reactant and products=.253807 amu
2. .253807 x 1.66054x10^-27=4.2145x10-28
3. 4.2145x10-28x8.98x10^16=3.784x10-11
4. 3.784x10-11 x6.022x10^23=2.279x10^13
The book has 1.03x10^11. Why??
I have looked at this problem (many times) and I don't see anything wrong with your answer. I have thought of dividing your final answer by 2 since the problem asks for J/mol REACTANTS and you have two mols reactants but that doesn't get close to the answer either. I have sent a link to my colleague Bob Pursley and asked him to take a look. He probably will post here.
You are almost correct on the mass difference, however it is negative (-.253807 amu) as the mass of products is greater than reactants, so high energy was required in the form of high KE in the Nickel atom.
Converting that to energy needed for the reaction, correct, -4.2145x10-28 kg then to energy
E=deltaM*c^2=-4.2145x10-28*(2.9979 x 108 m/s)2 = -3.784x10-11 Joules
then finally per mole reactant= yes, I would divide by two since Reactants was stated, however, I think they meant mole of Bi (then don't divide it).
So my truthometer rates the book answer in error. If you want to explore on this, calculate the nuclear binding energy of the product (including sign), and then look how unstable it is.
To calculate the energy change in J/mol of reactants, we need to use the formula E = mc^2, where E is the energy change, m is the mass difference, and c is the speed of light.
Let's go through the steps to solve this problem:
1. First, calculate the mass difference between the reactants and products.
Subtract the mass of the products (272/111 Rg + 1/0n) from the mass of the reactants (209/83 Bi + 64/28 Ni):
(209/83 Bi + 64/28 Ni) - (272/111 Rg + 1/0n)
2. Multiply the mass difference by the conversion factor.
The mass difference should be in atomic mass units (amu), so multiply it by the conversion factor 1.66054x10^-27 kg/amu to convert it to kilograms:
Mass difference (in kg) = Mass difference (in amu) x 1.66054x10^-27 kg/amu
3. Calculate the energy change (E) using E = mc^2.
Multiply the mass difference (in kg) by the speed of light squared (c^2), which is approximately 8.98x10^16 (m/s)^2:
E (in J) = Mass difference (in kg) x c^2
4. Convert the energy change to J/mol.
Since the energy change was calculated using the mass difference for the entire reaction, we need to convert it to J/mol. Multiply the energy change (in J) by Avogadro's number (6.022x10^23 mol^-1):
E (in J/mol) = E (in J) x 6.022x10^23 mol^-1
After following these steps, you should get the correct answer for the energy change in J/mol of reactants. Double-check your calculations to ensure accuracy.