Question

Carbon monoxide binds strongly to the Fe2+ ion of the heme group of hemoglobin and myoglobin and thus prevents transport and storage of oxygen in blood. First consider free carbon monoxide. The bond in a 12C16O molecule has a force constant of 1860 N/m. For diatomic molecules the effective mass and vibrational frequency are defined in the following equations:
u = mAmB/(mA + mB) v = 1/(2pi) x (kf/u)1/2

A) Calculate the vibrational frequency of 12C16O.

B) What is the vibrational wavenumber for 12C16O?

C) Assuming that isotopic substitution does not affect the force constant of the C=O bond, calculate the vibrational wavenumbers for 13C16O, 12C18O, and 13C18O.

D) Next, assume that the atom that binds to the Fe2+ becomes immobilized and that the hemoglobin or myoglobin protein is infinitely more massive than either the carbon or oxygen atom. Also assume that the carbon monoxide peak is distinct in an infared spectrum of a C=O-myoglobin complex. Comparing the spectra of different isotopes of carbon monoxide can be used to identify whether the carbon or oxygen atom of the carbon monoxide molecule binds the Fe2+ ion. Use the following equation to predict what the force constant would be if the carbon atom binds the Fe2+ion and if the oxygen atom binds the Fe2+ ion.

kf = m(2pi c y?)2
where m is the mass of the atom not bound to Fe2+, c is the speed of light, y? is the wavenumber.