What is the binding energy in kj/mol?

Question

What is the binding energy (in kJ/mol) for Ag-107? The mass of a hydrogen atom is 1.00783 amu, the mass of a neutron is 1.00867 amu, and the atomic mass of this isotope is 106.90509 amu.

Answer 1

The binding energy of Ag-107 is determined as follows:

1. Determine Actual Mass: Mass of 61 protons and 46 neutrons = 61(1.00783 amu) + 46(1.00867 amu) = 107.90562 amu
2. Determine Mass Defect
3. Solve for E
4. Convert to kJ

Actual mass of Ag-107 = 106.90509 amu

Mass defect = (107.90562 amu - 106.90509 amu)

Mass defect = 0.00053 amu

The binding energy can be calculated using the equation:

E = Δmc₂

where;

1. Δm is the mass defect,
2. c is the speed of light, and
3. E is the binding energy.

Solving for E:

E = (0.00053)(1.66054 x 10⁻²⁷)(2.998 x 10⁸)²

E = 4.75 x 10⁻¹¹ J

Convert this value to kilojoules per mole:

E = (4.75 x 10⁻¹¹)(6.022 x 10²³) / 1000

E = 2.86 x 10¹² J/mol