I am really lost with this.
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).
I know you have to subtract the product amu from the reactant amu to find the mass change before using E=mc^2
I do not know why they gave me the atomic mass of 3He or how to use E=mc^2. If someone could show me step by step that would be great but know its a long problem so I'd appreciate any help you can give.
To calculate the amount of energy released in kJ/mol for the fusion reaction, we need to follow a few steps.
Step 1: Determine the reactant and product masses.
Given:
Reactants: 1/1H + 1/1H
Products: 2/1H + 0/1e
The atomic masses are:
0/1e (0.0005486 u)
1H (1.00783 u)
2H (2.01410 u)
3He (3.01603 u)
Step 2: Calculate the mass difference.
To find the mass change, subtract the total mass of the reactants from the total mass of the products.
Reactant mass:
(1/1H) + (1/1H) = 1.00783 u + 1.00783 u = 2.01566 u
Product mass:
(2/1H) + (0/1e) = 2.01410 u + 0.0005486 u = 2.0146486 u
Mass difference:
2.0146486 u - 2.01566 u = -0.0010114 u
Step 3: Convert mass to kilograms.
To use the equation E=mc^2, we need to convert the mass difference from atomic mass units (u) to kilograms (kg).
Using the atomic mass unit conversion:
1 u = 1.66053906660 × 10^-27 kg
Mass difference in kg:
-0.0010114 u × (1.66053906660 × 10^-27 kg/u) = -1.678 × 10^-30 kg
Step 4: Calculate the energy released.
The equation E=mc^2 can be used to calculate the energy released. The speed of light, c, is approximately 2.998 × 10^8 m/s.
E = (mass difference) × c^2
E = -1.678 × 10^-30 kg × (2.998 × 10^8 m/s)^2
E = -1.678 × 10^-30 kg × 8.988 × 10^16 m^2/s^2
Finally, we can convert the energy to kilojoules per mole (kJ/mol). To do this, we need to determine the number of moles involved in the reaction.
Step 5: Determine the number of moles.
Since the reaction is between two 1H atoms, the number of moles is 2 (1 mole of 1H atoms + 1 mole of 1H atoms = 2 moles).
Step 6: Convert energy to kJ/mol.
Multiply the energy by Avogadro's number (6.022 × 10^23) to convert it to kilojoules per mole.
E(kJ/mol) = -1.678 × 10^-30 kg × 8.988 × 10^16 m^2/s^2 × (6.022 × 10^23 mol^-1)
The final calculation will give you the amount of energy released in kJ/mol for the fusion reaction of two 1H atoms to yield a 2H atom and an electron.
To calculate the amount of energy released in kilojoules per mole (kJ/mol) for the fusion reaction, you need to follow these steps:
Step 1: Determine the mass change
In this reaction, you are given the atomic masses of the involved atoms: 0/1e (0.0005486 u), 1H (1.00783 u), 2H (2.01410 u), and 3He (3.01603 u). To find the mass change, you need to subtract the sum of the masses of the reactants from the sum of the masses of the products.
Reactants: 1/1H + 1/1H
Products: 2/1H + 0/1e
Mass of reactants: (1.00783 u) + (1.00783 u) = 2.01566 u
Mass of products: (2.01410 u) + (0.0005486 u) = 2.01465 u
Mass change: (Mass of reactants) - (Mass of products) = 2.01566 u - 2.01465 u = 0.00101 u
Step 2: Convert mass change to kilograms
To use the equation E=mc^2, you need to express the mass change in kilograms. To convert atomic mass units (u) to kilograms (kg), you can use the conversion factor 1 u = 1.66054 x 10^-27 kg.
Mass change in kilograms: 0.00101 u * (1.66054 x 10^-27 kg/u) = 1.67770 x 10^-30 kg
Step 3: Calculate the energy released
Now that you have the mass change in kilograms, you can use the equation E=mc^2 to calculate the energy released.
First, you need to determine the speed of light (c), which is approximately 2.998 x 10^8 m/s.
Energy released (E) = (mass change) * (speed of light)^2
E = (1.67770 x 10^-30 kg) * (2.998 x 10^8 m/s)^2
Step 4: Convert energy to kilojoules per mole
The answer you obtained in Step 3 is the energy released in joules. To convert it to kilojoules per mole, you need to divide by Avogadro's number (6.022 x 10^23). This conversion allows you to determine the amount of energy released in kJ/mol.
Energy released (kJ/mol) = (Energy released in joules) / Avogadro's number
E (kJ/mol) = [(1.67770 x 10^-30 kg) * (2.998 x 10^8 m/s)^2] / (6.022 x 10^23 mol^-1)
By following these steps, you should be able to calculate the amount of energy released in kJ/mol for the given fusion reaction.