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Question

The figure below is the plot of potential energy versus internuclear distance (š‘‘) of H2 molecule in the electronic ground state. What is the value of the net potential energy E0 (as indicated in the figure) in kJmol-1, for d=d0 at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As a reference, the potential energy of an atom is taken as zero when its electron and the nucleus are infinitely far apart. Use Avogadro constant as 6.023 Ɨ 1023 molāˆ’1.


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Solution

Step 1: Given data:

Avogadro constant as 6.023Ɨ1023mol-1

For d=d0 at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent.

The plot of potential energy versus internuclear distance (š‘‘) of H2 molecule

Step 2: Formula used:

P. E of 2 H-atoms

Total energy =PE2

Potential Energy =2TotalEnergyā€¦ā€¦ā€¦ā€¦1

Therefore, from the above equation, it is clear that potential energy is two times the total energy

Step 3: Calculation of the value of the net potential energy E0

Potential energy between two hydrogen atom is given by

E=kq1q2rwherekisconstant,risseperationbetweeenthem,qischarge

r can be calculate by sing

r=0.529Ɨn2zforgroundstaten=1forH-atomz=1r=0.529A

Where, z is the atomic number

n=1 is ground state

E=kq1q2rasq1,q2aresame(bothareelectron)E=kq2rE=9Ɨ109Ɨ1.6Ɨ10-1920.59Ɨ10-10

Total Energy = 2time potential energy of 1 H atom

TotalEnergy=2E

Potential energy per mole

E=9Ɨ109Ɨ1.6Ɨ10-1920.59Ɨ10-10Ɨ6.023Ɨ1023

Solving this we will get 5242.42KJ/mol

Hence, 5242.42KJ/mol is the value of the net potential energy E0 (as indicated in the figure) in kJmol-1


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