The frequency and intensity of infrared IR radiation are directly related to the types of molecular vibrations observed in a given compound. Molecular vibrations can be classified into two main types: stretching and bending vibrations. Stretching vibrations involve a change in the bond length between two atoms, while bending vibrations involve a change in the bond angle between three atoms. These vibrations can be further classified as symmetric or asymmetric, depending on the displacement of the atoms involved.The frequency of a molecular vibration is determined by the force constant k of the bond and the reduced mass of the atoms involved in the vibration. The frequency can be calculated using the following equation: = 1/2 * k/ The force constant k is a measure of the bond strength, and the reduced mass is calculated as the product of the masses of the two atoms involved in the bond divided by their sum. As a result, stronger bonds and lighter atoms will have higher vibrational frequencies.The intensity of the IR radiation absorbed by a molecule is related to the change in the dipole moment of the molecule during the vibration. If a vibration causes a significant change in the dipole moment, the molecule will absorb IR radiation more strongly, resulting in a more intense absorption band in the IR spectrum.Now let's consider some specific examples:1. Carbon dioxide CO2 : CO2 has two types of vibrations: symmetric stretching, asymmetric stretching, and bending. The symmetric stretching vibration does not result in a change in the dipole moment, so it is not observed in the IR spectrum. However, the asymmetric stretching and bending vibrations do result in a change in the dipole moment, leading to strong absorption bands at around 2349 cm and 667 cm, respectively.2. Water H2O : Water has three types of vibrations: symmetric stretching, asymmetric stretching, and bending. All three vibrations result in a change in the dipole moment, leading to strong absorption bands in the IR spectrum. The symmetric stretching vibration occurs at around 3657 cm, the asymmetric stretching at around 3756 cm, and the bending vibration at around 1595 cm.3. Methane CH4 : Methane has four types of vibrations: symmetric stretching, asymmetric stretching, scissoring, and rocking. All of these vibrations do not result in a significant change in the dipole moment, so methane does not exhibit strong absorption bands in the IR spectrum. However, it does have weak absorption bands due to overtones and combination bands, which are the result of multiple vibrations occurring simultaneously.In summary, the frequency and intensity of infrared radiation absorbed by a given compound are directly related to the types of molecular vibrations present in the compound. The frequency is determined by the bond strength and the reduced mass of the atoms involved in the vibration, while the intensity is related to the change in the dipole moment during the vibration. By analyzing the IR spectrum of a compound, chemists can gain valuable information about the types of bonds and functional groups present in the molecule.