Figure 3: Nitrous Oxide. Figure 4: All Greenhouse Gases. Global Warming. Elmhurst College. Carbon Dioxide - Fossil Fuels. Chemistry Department. Carbon Dioxide - Atmosphere. Virtual ChemBook. Click for larger image. Greenhouse Gases Absorb Infrared Radiation Radiation from the sun is absorbed by the earth as radiant visible light. Greenhouse Gas Molecules: The greenhouse gas molecules are shown in the next series of figures along with the IR spectra and the bending and vibrations caused by absorbing the IR radiation.
The graphic on the left is carbon dioxide. HCl does have a dipole moment. Stretching the HCl bond leads to a change in the dipole moment. If we stretched the bond so far as to break the bond and produce the two original neutral atoms, there would be no dipole moment.
Therefore, as we lengthen the bond in HCl, the dipole moment gets smaller. Because the dipole moment of HCl changes during a stretching vibration, it absorbs infrared radiation. The number of possible vibrations for a molecule is determined by the degrees of freedom of the molecule.
The degrees of freedom for most molecules are 3N — 6 where N is the number of atoms. The degrees of freedom for a linear molecule are 3N — 5. Carbon dioxide is a linear molecule so it has four degrees of freedom and four possible vibrations. Each bond dipole, which is represented by the arrows, does change on stretching, but the overall molecular dipole is zero throughout. Since there is no net change in the molecular dipole, this vibration is not IR active.
Each bond dipole does change on stretching and the molecule now has a net dipole. Since the molecular dipole changes during an asymmetrical stretch, this vibration is IR active. There are two bending vibrations that occur in two different planes. Both are identical so both have the same energy and are degenerate. The bending motion does lead to a net molecular dipole. Since the molecular dipole changes during the bending motion, these vibrations are IR active. This causes the atom not to be stationary and to fluctuate continuously.
Vibrational motions are defined by stretching and bending modes. These movements are easily defined for diatomic or triatomic molecules. This is not the case for large molecules due to several vibrational motions and interactions that will be experienced. When there is a continuous change in the interatomic distance along the axis of the bond between two atoms, this process is known as a stretching vibration.
A change in the angle occurring between two bonds is known as a bending vibration. Four bending vibrations exist namely, wagging, twisting, rocking and scissoring. A CH 2 group is used as an example to illustrate stretching and bending vibrations below.
Wagging Scissoring Rocking. Figure 3: Types of Vibrational Modes. To ensure that no center of mass motion occurs, the center atom yellow ball will also move. Figure from Wikipedia. As stated earlier, molecular vibrations consist of stretching and bending modes. A molecule consisting of N number of atoms has a total of 3N degrees of freedom, corresponding to the Cartesian coordinates of each atom in the molecule.
In a non-linear molecule, 3 of these degrees of freedom are rotational, 3 are translational and the remainder is fundamental vibrations. In a linear molecule, there are 3 translational degrees of freedom and 2 are rotational.
This is because in a linear molecule, all of the atoms lie on a single straight line and hence rotation about the bond axis is not possible. Mathematically the normal modes for a linear and non linear can be expressed as. H 2 O molecule is a non-linear molecule due to the uneven distribution of the electron density. O 2 is more electronegative than H 2 and carries a negative charge, while H has a partial positive charge.
The vibrational modes are illustrated below:. CO 2 is a linear molecule and thus has the formula 3N It has 4 modes of vibration 3 3 CO 2 has 2 stretching modes, symmetric and asymmetric. The CO 2 symmetric stretch is not IR active because there is no change in dipole moment because the net dipole moments are in opposite directions and as a result, they cancel each other. In the asymmetric stretch, O atom moves away from the C atom and generates a net change in dipole moments and hence absorbs IR radiation at cm The other IR absorption occurs at cm Two of its bands are degenerate and one of the vibration modes is symmetric hence it does not cause a dipole moment change because the polar directions cancel each other.
Thus "a" can be written as. On differentiating a second time the equation becomes. Using the harmonic oscillator and wave equations of quantum mechanics, the energy can be written as.
Transitions in vibrational energy levels can be brought about by absorption of radiation, provided the energy of the radiation exactly matches the difference in energy levels between the vibrational quantum states and provided the vibration causes a change in dipole moment. This can be expressed as. The frequency of radiation v that will bring about this change is identical to the classical vibrational frequency of the bond v m and it can be expressed as.
Molecular vibrational frequencies lie in the IR region of the electromagnetic spectrum, and they can be measured using the IR technique. In IR, polychromatic light light having different frequencies is passed through a sample and the intensity of the transmitted light is measured at each frequency. When molecules absorb IR radiation, transitions occur from a ground vibrational state to an excited vibrational state Figure 1.
For a molecule to be IR active there must be a change in dipole moment as a result of the vibration that occurs when IR radiation is absorbed.
Dipole moment is a vector quantity and depends on the orientation of the molecule and the photon electric vector. The dipole moment changes as the bond expands and contracts. When all molecules are aligned as in a crystal and the photon vector points along a molecular axis such as z. Absorption occurs for the vibrations that displace the dipole along z. Vibrations that are totally x or y polarized would be absent. Dipole moment in a heteronuclear diatomic molecule can be described as uneven distribution of electron density between the atoms.
One atom is more electronegative than the other and has a net negative charge. The transition moment integral, that gives information about the probability of a transition occurring, for IR can also be written as. Relating this to IR intensity we have. In order for a transition to occur by dipole selection rules , at least one of the integrals must be non zero. Most of the IR used originates from the mid IR region. The table below indicates the IR spectral regions.
IR deals with the interaction between a molecule and radiation from the electromagnetic region ranging 40 cm A linear wavenumber is often used due to its direct relationship with both frequency and energy.
The frequency of the absorbed radiation causes the molecular vibrational frequency for the absorption process. The relationship is given below. IR spectroscopy is a great method for identification of compounds, especially for identification of functional groups.
Therefore, we can use group frequencies for structural analysis. Group frequencies are vibrations that are associated with certain functional groups. It is possible to identify a functional group of a molecule by comparing its vibrational frequency on an IR spectrum to an IR stored data bank. Here, we take the IR spectrum of Formaldehyde for an example.
The value obtained from the following graph can be compared to those in reference data banks stored for Formaldehyde. It's important to note that this value is dependent on other functional groups present on the molecule. The higher cm -1 indicates a large dipole moment change. It is easier to bend a molecule than stretch it, hence stretching vibrations have higher frequencies and require higher energies than bending modes.
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