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.
Add mass protons, neutrons, electrons and subtract from 122.90422. Then delta E = delta m x c^2 which is for one atom. Multiply by 6.022E23 to convert to 1 mole.
Thank you so much DrBob222
To calculate the energy released to form one mole of 123Sb, we need to use Einstein's mass-energy equivalence equation, E = mc^2.
First, we need to determine the mass of one mole of Sb. The atomic mass of 123Sb is approximately 122.90422 atomic mass units (amu). Since 1 mole is equal to the Avogadro constant (6.022 x 10^23) entities, the molar mass of 123Sb is 122.90422 g/mol.
Now, let's calculate the mass of 123Sb in kilograms.
Using the molar mass, we can convert it to kilograms by dividing by the Avogadro constant (6.022 x 10^23).
Mass of 123Sb = (122.90422 g/mol) / (6.022 x 10^23) = 2.045 x 10^-22 kg.
Next, we need to determine the mass of protons, neutrons, and electrons.
The mass of a proton is approximately 1.673 x 10^-27 kg.
The mass of a neutron is approximately 1.675 x 10^-27 kg.
The mass of an electron is approximately 9.109 x 10^-31 kg.
Since one mole of 123Sb contains 123 protons, 123 neutrons, and 123 electrons, we can calculate the total mass of the particles involved in the formation of one mole of Sb:
Total mass of particles = (123 protons x mass of a proton) + (123 neutrons x mass of a neutron) + (123 electrons x mass of an electron)
= (123 x 1.673 x 10^-27 kg) + (123 x 1.675 x 10^-27 kg) + (123 x 9.109 x 10^-31 kg)
= 3.484 x 10^-25 kg + 3.417 x 10^-25 kg + 1.121 x 10^-29 kg
= 6.921 x 10^-25 kg.
Now, we can calculate the energy released using Einstein's equation:
E = mc^2
E = (total mass of particles) x (speed of light)^2
E = (6.921 x 10^-25 kg) x (3 x 10^8 m/s)^2
E = (6.921 x 10^-25 kg) x (9 x 10^16 m^2/s^2)
E = 6.229 x 10^-8 J.
To convert the energy from joules to kilojoules, we divide by 1000:
Energy = 6.229 x 10^-8 J = 6.229 x 10^-11 kJ.
Therefore, approximately 6.229 x 10^-11 kilojoules (kJ) of energy is released to form one mole of 123Sb from protons and neutrons, considering the mass of electrons as well.