The vibrational frequencies of a CO molecule and a CO2 molecule can be calculated using the following formula: = 1/2 * k/ where is the vibrational frequency, k is the force constant, and is the reduced mass of the molecule. The reduced mass can be calculated using the formula: = m1 * m2 / m1 + m2 where m1 and m2 are the masses of the two atoms in the molecule.For CO molecule:m1 C = 12 amu, m2 O = 16 amu = 12 * 16 / 12 + 16 = 192 / 28 = 6.857 amuThe force constant k for CO is approximately 1857 N/m. Now, we can calculate the vibrational frequency: = 1/2 * 1857 / 6.857 * 1.66 * 10^-27 kg/amu 2143 cm^-1For CO2 molecule, there are two vibrational modes: symmetric stretching and asymmetric stretching.Symmetric stretching: = m1 * m2 / m1 + m2 = 12 * 16 / 12 + 16 = 6.857 amuk 534 N/m 667 cm^-1Asymmetric stretching: = m1 * m2 / m1 + m2 = 16 * 16 / 16 + 16 = 8 amuk 1900 N/m 2349 cm^-1To identify these frequencies experimentally, vibrational spectroscopy techniques such as Infrared IR spectroscopy or Raman spectroscopy can be used.Infrared IR spectroscopy:In this technique, a molecule is exposed to infrared radiation, and the absorption of the radiation is measured. Molecules absorb specific frequencies of IR radiation that correspond to their vibrational frequencies. By analyzing the absorption spectrum, the vibrational frequencies of the molecule can be determined.Raman spectroscopy:In Raman spectroscopy, a monochromatic light usually from a laser is scattered off a sample, and the frequency shift of the scattered light is measured. The frequency shift corresponds to the vibrational frequencies of the molecule. Raman spectroscopy is particularly useful for molecules that do not absorb IR radiation well or for samples that have strong IR absorption from other components.By using either of these techniques, the vibrational frequencies of CO and CO2 molecules can be identified experimentally.