The binding energy in kJ/mol for bromine-79 is approximately -6.35169169 x 10^10 kJ/mol.
The binding energy in kJ/mol for bromine-79 can be calculated using the equation E = mc², where E is the energy, m is the mass, and c is the speed of light.
To find the binding energy, we need to determine the mass defect, which is the difference between the actual mass of the nucleus and the sum of the masses of its individual nucleons (protons and neutrons).
The mass of bromine-79 is given as 78.91830 g/mol. To calculate the mass defect, we need to sum the masses of the individual nucleons. The masses given are: proton (1.00783 g/mol), neutron (1.00867 g/mol), and electron (0.00055 g/mol).
Step 1: Calculate the total mass of the individual nucleons:
(35 protons x 1.00783 g/mol) + (44 neutrons x 1.00867 g/mol) = 35.27405 g/mol + 44.35148 g/mol = 79.62553 g/mol
Step 2: Calculate the mass defect:
Mass defect = Actual mass - Total mass of nucleons
Mass defect = 78.91830 g/mol - 79.62553 g/mol = -0.70723 g/mol
Step 3: Convert the mass defect to kilograms:
Mass defect = -0.70723 g/mol x (1 kg / 1000 g) = -0.00070723 kg/mol
Step 4: Calculate the binding energy using E = mc²:
Binding energy = (-0.00070723 kg/mol) x (299,792,458 m/s)²
Binding energy = -0.00070723 kg/mol x 8.9875517923 x 10¹⁶ m²/s²
Binding energy = -6.35169169 x 10¹³ J/mol
To convert the binding energy to kJ/mol, divide by 1000:
Binding energy = -6.35169169 x 10¹³ J/mol / 1000
Binding energy = -6.35169169 x 10¹⁰ kJ/mol
Therefore, the binding energy in kJ/mol for bromine-79 is approximately -6.35169169 x 10^10 kJ/mol.
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