For the following fusion reaction, Calculate change in energy per mole.( Answer in J/mole)
2H1 + 2H1 ---> 3H1 + 1H1
(the mass number is in front of the atom and the atomic number is behind the atom)
Given info:Atoms with their masses(amu)
H-1 1.00782
H-2 2.01410
H-3 3.01605
He-3 3.01603
He-4 4.00260
neutron 1.00866
I know delta E=(C^2)(delta m)
and I know delta m= products mass- reactants mass
and I know 1 amu = 1.661X10^-27 Kg
I got delta E= -0.297 x 10^-6 but still my answer is wrong.
I'm getting 8.355E-22 Kg on for reactants, and 8.322E-22 Kg for products.
I multiplied each mass they gave us in amu by 1.661E-27 to get it in Kg.
You can do that (it's a lot of extra work) but when you finish you have kg/atom and you must multiply all of that by 6.02E23 to obtain kg/mol. However, I still don't obtain your numbers. When done your way you open yourself up to a lot of rounding errors.
Try what I outlined above and see if it isn't simpler. In fact, I never use the 1.661E-27 factor BECAUSE it cancels out if we want J/mol.
amu/atom x (1g/6.022E23 amu) x (6.022E23 atom/mol) = grams/mol. Note that 1g/6.022E23 (the second term) = 1.661E-24 g/amu which is where the 1.661E-27 kg/amu comes from.
Well, it seems like you're having trouble with your calculations. Let me lend you a helping hand, or in this case, a helping joke!
Why did the atom go to therapy?
Because it had too many negative charges!
Now, let's get back to the question at hand. To calculate the change in energy (ΔE) per mole, we need to calculate the change in mass (Δm) first.
Reactants:
2H1 + 2H1
Products:
3H1 + 1H1
Let's find the mass of the reactants and products:
Reactants:
Mass(2H1) = 2 * 1.00782 amu = 2.01564 amu
Mass(2H1) = 2 * 1.00782 amu = 2.01564 amu
Total mass of reactants = 2.01564 amu + 2.01564 amu = 4.03128 amu
Products:
Mass(3H1) = 3 * 1.00782 amu = 3.02346 amu
Mass(1H1) = 1 * 1.00782 amu = 1.00782 amu
Total mass of products = 3.02346 amu + 1.00782 amu = 4.03128 amu
Now, let's calculate the change in mass (Δm):
Δm = mass of products - mass of reactants
Δm = 4.03128 amu - 4.03128 amu
Δm = 0 amu
Finally, let's plug this into the formula ΔE = (c^2) * Δm:
ΔE = (c^2) * Δm
ΔE = (3.0 x 10^8 m/s)^2 * 0 amu
ΔE = 0 J/mole
And there you have it! The change in energy per mole (ΔE) for this fusion reaction is 0 J/mole. I hope this helps, and if not, don't worry, I'll keep clowning around until we get it right!
To calculate the change in energy per mole for the given fusion reaction, you need to find the mass difference between the reactants and the products.
Let's calculate the mass difference step by step:
1. Determine the total mass of the reactants:
Mass of 2H1 = 2 * 1.00782 = 2.01564 amu
2. Determine the total mass of the products:
Mass of 3H1 = 3 * 1.00782 = 3.02346 amu
Mass of 1H1 = 1.00782 amu
Total mass of products = 3.02346 + 1.00782 = 4.03128 amu
3. Calculate the mass difference:
Mass difference = Mass of products - Mass of reactants
Mass difference = 4.03128 - 2.01564 = 2.01564 amu
Now, we need to convert the mass difference from atomic mass units (amu) to kilograms (Kg) since we'll be using the speed of light (c) in meters per second (m/s) for the calculation of change in energy.
1 amu = 1.661 x 10^-27 Kg
So, the mass difference in kilograms (Kg) is:
Mass difference = 2.01564 amu * (1.661 x 10^-27 Kg/1 amu) = 3.347 x 10^-27 Kg
The change in energy (ΔE) can be calculated using the equation:
ΔE = (c^2) * Δm
Where:
c = speed of light = 3 x 10^8 m/s
Substituting the values:
ΔE = (3 x 10^8 m/s)^2 * (3.347 x 10^-27 Kg)
ΔE = 9 x 10^16 m^2/s^2 * 3.347 x 10^-27 Kg
ΔE = 3.01 x 10^-10 J
Now, we have the change in energy in joules (J). However, we need to find the change in energy per mole.
To convert the energy from joules per molecule to joules per mole, we need to know the Avogadro's number, which is 6.02214076 x 10^23 mol^-1.
Finally, we divide the change in energy by Avogadro's number to get the change in energy per mole:
Change in energy per mole = ΔE / Avogadro's number
Change in energy per mole = 3.01 x 10^-10 J / (6.02214076 x 10^23 mol^-1)
Calculating this value yields the final answer for the change in energy per mole for the given fusion reaction.
You didn't show all of your work and I've not been able to obtain your same numbers. One possible problem may be the amu conversion.
I think mass = 4.02387 on the right and 4.02820 on the left. delta m = 4.33E-3 amu/atom which = 4.33E-3 g/mol and we convert that to kg (4.33E-6) and multiply by c^2 (3E8 m/s squared). You may want to use a more precise value for c. See if that won't give you the ok.