The following is a high resolution IR transmission spectrum for gas phase HCL. F

Question

The following is a high resolution IR transmission spectrum for gas phase HCL. From the above spectrum, estimate the rigid rotor rotational coesiant B, and the bond length of HCI. Rotational constant (cm^-1) Bond length (A) 4a. Using the HO spectrum in the previous question, calculate the percentage of HC1 molecules in the lirst 3 (the lowest energy three) vibrational levels at 500 degreeC Assume a harmonic oscillator. vibrational level V = 0 1 2 Percent in level = 4b. Using the Ha spectrum above, calculate the force constant of the H-Cl bond Force constant (N m^-1)

Explanation / Answer

Solution,

From given IR spectrum of HCl we can calculate Rotational constant (B)=h2/2I ,

Where I=muR2­ (mu-reduced mass)

mu=m1m2/m1+m2   (m1 –mass of H, m2-mass of Cl)

mu=1*35/1+35

      =35/36

       =0.972 amu

Mu=0.972 amu

I=muR^2

R2 =2h2/h(.12*1013)

R2 =1.06*10-34J.s/(.972amu)(1.66*10-27kg/amu)pi(.12*1013)

R=0.13nm

Bond length of HCl=0.13 nm.

I=mu*R^2

=0.972*0.132

=0.972*0.0169

I=0.0164

Rotational constant (B)=h2/2I

                                           =(6.626*10-34)2J.s/2*0.0164

                                        B =1.38*10-65

Rotational constant (B)=1.38*10-65

4a)percent in level=Is/Ir*100

Since Is is intensity of sample beam, Ir is intensity of reference beam , but in spectrum transmittance is 100% so sample is nearly transparent.

4b) Force constant k=2piv-*mu*1.66*10^-27

                                   k=(2pi(8.66*10^13 Hz)^2 (0.972amu)(1.66*10^-27kg/amu

                        k=481 N/m

Force constant k=481N/m

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