Question

The infrared absorption spectrum of gas-phase HCl can be analyzed to gain information about both rotation and vibration of the molecule. The absorption lines shown involve transitions from the ground (v = 0) to first excited vibrational state (v = 1) of HCl, but also involve changes in the rational state with a change Delta j = +1 (right branch) and Delta j = -1 (left branch). The splitting of the lines shows the difference in vibrational frequencies between the two chlorine isotopes 35Cl and 37Cl. Why there is a missing line in the middle? Determine the force constant for HCl from this spectrum Determine the bond length for HCl from the spectrum. How does your result compare to the standard value?

IR absorption soectrum of gasphase hcl question

Answer 1

Answer:

a. Missing line in the middle is shows the difference in rotational inertia of two chlorine isotopes.

b . The bond force constant can be calculated by involving the vibrational transition in spectrum of HCl from the ground state to the first excited state as quantum harmonic oscillator.

Since transition frequency does not involved in the observed spectrum, as there is no transitions between j = 0, v = 0 to j = 0, v = 1, rotational quantum number must has to change by one.

Take approximately the mid-value of j = 1, v = 0 > j = 0, v = 1 and the j = 0,v = 0 > j = 1,v = 1 transitions. This provides information that difference between j = 0 and j = 1 levels is same for the ground state as well as first excited state, which gives that the first excited vibrational state does not stretch the bond.