Finding binding energy from equilibrium bond length

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SUMMARY

The equilibrium bond length of the He dimer is established at 2.97 angstroms. The interaction potential is defined by the equation V(r) = (B/r^13) - (C/r^6), with constants B = 9.29 x 10^4 kJ(angstrom^13)(mol^-1) and C = 97.7 kJ(angstrom^6)(mol^-1). Calculating the binding energy using this potential at the given bond length is essential to determine the stability of the dimer at room temperature (300K). A negative binding energy indicates instability, as it suggests that the dimer cannot exist under these conditions.

PREREQUISITES
  • Understanding of potential energy equations in molecular physics
  • Familiarity with the concepts of binding energy and stability
  • Knowledge of thermodynamic principles, specifically kT calculations
  • Basic proficiency in unit conversions related to energy and distance
NEXT STEPS
  • Calculate the binding energy of the He dimer using the provided interaction potential
  • Research the implications of negative binding energy in molecular stability
  • Explore the concept of kT and its relevance in thermodynamic stability assessments
  • Investigate other molecular interactions and their potential energy equations
USEFUL FOR

Students and researchers in physical chemistry, molecular physics, and anyone studying intermolecular forces and stability in dimers.

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1. The equilibrium bond length of the He dimer is 2.97 angstroms. What is the binding energy in kJ/mol for this dimer? Would be dimer be stable at room temperature T= 300K (Hint: compare the binding energy to kT)



2. interaction potential for the dimer:

V(r) = (B/r^13)-(C/r^6), where B= 9.29 x 10^4 kJ(angstrom^13)(mol^-1) and C= 97.7 kJ (angstrom^6)(mol^-1)




3. I didn't know what to do. My guess was to plug the equilibrium bond length into the interaction potential equation, but this gave me a negative answer. I figured that my answer couldn't be negative if I had to compare the binding energy to kT. Any help would be greatly appreciated.

Thanks!
 
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Perhaps negative binding energy tells you something about stability?

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