Q: What is the conversion factor between wavenumber (cm-1) and joules per mole (J/mol)?

Solution

From E = hn and n' = n/c, we have that E = hn'c. Putting

• n' = 1 cm^-1
• C = 3*10¹⁰ cm*s^-1
• h = 6.63*10^-34 J*s

  E = (6.63*10^-34)*(3*10¹⁰) J

This is the answer for one molecule. For one mole, we multiply by Avogadro's number, N = 6.03*10^-23

E = (6.03*10²³)*(6.63*10^-34)*1*(3*10¹⁰) J*mol^-1

= 12 J*mol^-1

thus

1 cm^-1 = 12 J*mol^-1