Kaplan MCAT General Chemistry Review

• For any value of l, there are 2l + 1 values of m_l (number of orbitals); values themselves will range from -l to l.

Figure 3.8

When l = 1, this indicates the p-subshell, which has three orbitals shaped like barbells along the x, y, and z axes at right angles to each other. The p-orbitals are plotted in Figure 3.9.

Figure 3.9

Although well beyond the scope of the MCAT, mathematical analyses of the wave function of the orbitals are used to determine and assign plus and minus signs to each lobe of the p-orbitals. The shapes of the five d-orbitals and the seven f-orbitals are more complex and need not be memorized for the MCAT. When two atoms bond to form a compound, the atomic orbitals interact to form a molecular orbital that describes the probability of finding the bonding electrons. Molecular orbitals are obtained by combining the wave functions of the atomic orbitals. Qualitatively, the overlap of two atomic orbitals describes this. If the signs of the two atomic orbitals are the same, a bonding orbital forms. If the signs are different, an antibonding orbital forms.

Two different patterns of overlap are observed in the formation of molecular bonds. When orbitals overlap head-to-head, the resulting bond is called a sigma ( ) bond. Sigma bonds allow for relatively free rotation, because the electron density of the bonding orbital is a single linear accumulation between the atomic nuclei. When the orbitals overlap in such a way that there are two parallel electron cloud densities, a pi () bond is formed. Pi bonds do not allow for free rotation because the electron densities of the orbital are parallel. To picture this difference, imagine pushing your fists together and rotating them as they touch—this is a sigma bond. Now imagine putting your arms out in front of you, holding them parallel to each other with your elbows bent at about right angles while another person slips two rubber bands around your forearms, one near the elbows and the second closer to the wrists. With the rubber bands on, try bringing one forearm up toward you while you extend your other forearm out away from you. The parallel tension provided by the rubber bands makes it quite difficult to rotate your forearms in opposite directions. This is a pi bond.

Bridge

The pi bonds of alkenes, alkynes, aromatic compounds, and carboxylic acid derivates are what lend the ever-important functionalities in organic chemistry.

The Intermolecular Forces

Like guests at a cocktail party who mingle but ultimately have little to say to each other, atoms and compounds participate in weak electrostatic interactions. The strength of these intermolecular interactions can impact certain physical properties of the compounds, such as melting and boiling point. The weakest of the intermolecular interactions are the dispersion forces, also known as London forces. Next, are the dipole–dipole interactions, which are of intermediate strength. Finally, we have the strongest type of interaction, the hydrogen bond, which is a misnomer because there is no sharing or transfer of electrons, and consequently, it is not a true bond. We must keep in mind, however, that even hydrogen bonds, the strongest of these interactions, have only about 10 percent the strength of a covalent bond, so these electrostatic interactions can be overcome with additions of small or moderate amounts of energy.

Bridge

These intermolecular forces are the binding forces that keep a substance together in its solid or liquid state (see Chapter 8). These same forces determine whether two substances are miscible or immiscible in the solution phase (see Chapter 9).

LONDON FORCES

The bonding electrons in nonpolar covalent bonds may appear, on paper, to be shared equally between two atoms, but at any point in time, they will be located randomly throughout the orbital. For these instantaneous moments, then, the electron density may be unequally distributed between the two atoms. This results in rapid polarization and counterpolarization of the electron cloud and the formation of short-lived dipole moments. These dipoles interact with the electron clouds of neighboring compounds, inducing the formation of more dipoles. The momentarily negative end of one molecule will cause the closest region in any neighboring molecule to become temporarily positive itself, thus causing the other end of this neighboring molecule to become temporarily negative, which in turn induces other molecules to become temporarily polarized, and the entire process begins all over again. The attractive interactions of these short-lived and rapidly shifting dipoles are called dispersion forces or London forces.

Real World

While London forces (a type of van der Waals force) are the weakest of the intermolecular attractions, when there are millions of these interactions, as there are on the bottom of a gecko’s foot, there is an amazing power of adhesion, which is demonstrated by the animal’s ability to climb smooth vertical, even inverted, surfaces.

Dispersion forces are the weakest of all the intermolecular interactions because they are the result of induced dipoles that change and shift moment by moment. They do not extend over long distances and are, therefore, significant only when molecules are close together. The strength of the London force also depends on the degree to which and the ease by which the molecules can be polarized (that is to say, how easily the electrons can be shifted around). Large molecules in which the electrons are far from the nucleus are relatively easy to polarize and, thus, possess greater dispersion forces. Think about two plates—a big dinner plate and a small teacup saucer—with nearly equal numbers of marbles on each. The marbles will roll around more, and may be distributed more unequally, on the bigger plate than on the smaller saucer. Nevertheless, don’t underestimate the importance of the dispersion forces. If it weren’t for them, the noble gases would not liquefy at any temperature because no other intermolecular forces exist between the noble gas atoms. The low temperatures at which the noble gases liquefy is to some extent indicative of the magnitude of the dispersion forces between the atoms.

DIPOLE–DIPOLE INTERACTIONS

Polar molecules tend to orient themselves in such a way that the opposite ends of the respective molecular dipoles are closest to each other: The positive region of one molecule is close to the negative region of another molecule. This arrangement is energetically favorable because an attractive electrostatic force is formed between the two molecules.

Dipole–dipole interactions are present in the solid and liquid phases but become negligible in the gas phase because of the significantly increased distance between gas particles. Polar species tend to have higher melting and boiling points than those of nonpolar species of comparable molecular weight. You should realize that London forces and dipole–dipole interactions are different not in kind but in degree. Both are electrostatic forces between opposite partial charges; the difference is only in the strength and in the permanence of the molecular dipole.

HYDROGEN BONDS