How much energy in KJ is release to form one mole of 123Sb from protons and neutrons if the atom has a mass of 122.90422 amu? Please remember to include the mass of electrons in calculations.
Havent been taught this yet so a step by step walkthrough would help me immensely.Thanks in advance
Can anyone help me with this question? Thanks
To calculate the energy released in forming one mole of 123Sb (antimony) from protons, neutrons, and electrons, you need to use the concept of mass defect and E=mc^2.
Let's break down the steps to calculate the energy released:
Step 1: Determine the mass defect
The mass defect is the difference between the mass of the individual particles (protons, neutrons, and electrons) and the mass of the atom. The mass defect (∆m) is given by:
∆m = (Z × mass of a proton) + (N × mass of a neutron) + (A - Z - N) × mass of an electron - mass of the atom
Here, Z is the atomic number (number of protons), N is the number of neutrons, and A is the mass number.
In this case, the atomic number (Z) of antimony is 51, and the mass number (A) is 123. Given the mass of the atom (122.90422 amu), we can substitute these values into the formula to find the mass defect.
Step 2: Convert the mass defect to kilograms
Since energy is typically measured in joules, we need to convert the mass defect from atomic mass units (amu) to kilograms (kg). The conversion factor is 1 amu = 1.66054 × 10^(-27) kg.
Step 3: Calculate the energy released
Using Einstein's equation E=mc^2, where E is the energy released, m is the mass defect in kilograms, and c is the speed of light (3 × 10^8 m/s), we can calculate the energy released in joules.
Step 4: Convert energy to kilojoules and mole basis
Lastly, we convert the energy from joules to kilojoules (1 kJ = 1000 J) and adjust it to the molar basis. Since we are interested in one mole of 123Sb, we divide the energy by Avogadro's number (6.022 × 10^23).
Now, let's put these steps into action:
Step 1: Determine the mass defect
∆m = (Z × mass of a proton) + (N × mass of a neutron) + (A - Z - N) × mass of an electron - mass of the atom
∆m = (51 × mass of a proton) + (N × mass of a neutron) + (123 - 51 - N) × mass of an electron - 122.90422
Step 2: Convert the mass defect to kilograms
The conversion factor is 1 amu = 1.66054 × 10^(-27) kg.
Step 3: Calculate the energy released
E = (∆m) × c^2
Step 4: Convert energy to kilojoules and mole basis
Energy (in kJ) = E / 1000
Energy / mole = Energy / (6.022 × 10^23)
By following these steps, you can calculate the energy released to form one mole of 123Sb from protons, neutrons, and electrons.