MCAT Organic Chemistry Review
Answers and Explanations
The energies of the subshells within a principle quantum number are as follows: s < p < d < f
All single bonds are σ bonds; double and triple bonds each contain one σ bond and one or two π bonds, respectively. The compounds CH4, C2H2, and C2H4 all contain at least one single bond and therefore contain at least one σ bond.
In a carbon with one double bond, sp2 hybridization occurs—that is, one s-orbital hybridizes with two p-orbitals to form three sp2-hybridized orbitals. The third p-orbital of the carbon atom remains unhybridized and takes part in the formation of the π bond of the double bond.
The carbon and nitrogen atoms are connected by a triple bond in CN– (:C≡N:–). A triple-bonded atom is sp hybridized; one s-orbital hybridizes with one p-orbital to form two sp-hybridized orbitals. The two remaining unhybridized p-orbitals take part in the formation of two πbonds.
Beryllium has only two electrons in its valence shell. When it forms bonds to two hydrogens, it requires two hybridized orbitals, meaning that its hybridization must be sp. Note that the presence of only single bonds does not mean that the hybridization must be sp3; this is a useful assumption for carbon, but does not apply to beryllium because of its smaller number of valence electrons. The two unhybridized p-orbitals around beryllium are empty in BeH2, which takes on the linear geometry characteristic of sp-hybridized orbitals.
When atomic orbitals combine, they form molecular orbitals. When two atomic orbitals with the same sign are added head-to-head or tail-to-tail, they form bonding molecular orbitals. When two atomic orbitals with opposite signs are added head-to-head or tail-to-tail, they form antibonding molecular orbitals. Atomic orbitals can also hybridize, forming sp3, sp2 or sp orbitals.
Like atomic orbitals, molecular orbitals each can contain a maximum of two electrons with opposite spins. The 2n2 rule in choice (D) refers to the total number of electrons that can exist in a given energy shell, not in a molecular orbital.
π bonds are formed by the parallel overlap of unhybridized p-orbitals. The electron density is concentrated above and below the bonding axis. A σ bond, on the other hand, can be formed by the head-to-head overlap of two s-orbitals, two p-orbitals, one s- and one p-orbital, or hybridized orbitals. In a σ bond, the density of the electrons is concentrated between the two nuclei of the bonding atoms.
Each single bond has one σ bond, and each double bond has one σ and one π bond. In this question, there are five single bonds (five σ bonds) and one double bond (one σ bond and one π bond), which gives a total of six σ bonds and one π bond. Thus, the correct answer is choice(A).
The four bonds point to the vertices of a tetrahedron, which means that the angle between two bonds is 109.5°, a characteristic of sp3 orbitals. Hence, the carbon atom of CH4 is sp3-hybridized.
Bond strength is determined by the degree of orbital overlap; the greater the overlap, the greater the bond strength. A π bond is weaker than a single bond because there is significantly less overlap between the unhybridized p-orbitals of a π bond (due to their parallel orientation) than between the s-orbitals or hybrid orbitals of a σ bond. sp3-hybridized orbitals can be quite stable, as evidenced by the number of carbon atoms with this hybridization forming stable compounds.
The carbon bond in hydrogen cyanide (H–C≡N:) is triple-bonded, and because triple bonds require two unhybridized p-orbitals, the carbon must be sp-hybridized; sp-hybridized orbitals have 50% s character and 50% p character.
A resonance structure describes an arrangement of electrons in a molecule. Different resonance structures can be derived by moving electrons in unhybridized p-orbitals throughout a molecule containing conjugated bonds. In molecules that contain multiple resonance structures, some are usually more stable than others; however, each resonance structure is not necessarily the most common form a molecule takes, eliminating statement III. Statement I has reversed the terminology for resonance structures: the electron density in a molecule is the weighted average of all possible resonance structures, not the other way around.
An electron in the n = 4 shell and the l = 2 subshell can have five different values for ml: –2, –1, 0, 1, or 2. In each of these orbitals, electrons can have positive or negative spin. Thus, there are 5 × 2 = 10 possible combinations of quantum numbers for this electron.
π bonds do not permit free rotation, unlike σ bonds; this makes triple bonds more rigid than single bonds. Triple bonds are stronger and shorter bonds than single bonds, eliminating choices (A) and (B). Single bonds do not contain π bonds, while triple bonds have two π bonds in their makeup, eliminating choice (C).