Why, though, do atoms bond together, and how can chemical bonds be described electronically? The why question is relatively easy to answer: atoms bond together because the compound that results is more stable and lower in energy than the separate atoms. Energy-usually as heat-is always released and flows out of the chemical system when a bond forms. Conversely, energy is added to the chemical system when a bond breaks. Making bonds always releases energy, and breaking bonds always absorbs energy. The how question is more difficult. To answer it, we need to know more about the electronic properties of atoms.


RULE 1 - 1.4 Development of Chemical Bonding Theory

We know through observation that eight electrons (an electron octet) in an atom's outermost shell, or valence shell, impart special stability to the noble-gas elements in group 8A of the periodic table: $\mathrm{Ne}(2+8)$; $\mathrm{Ar}(2+8+$ 8 ); $\mathrm{Kr}(2+8+18+8)$. We also know that the chemistry of the main-group elements on the left and right sides of the periodic table is governed by their tendency to take on the electron configuration of the nearest noble gas. The alkali metals such as sodium in group 1A, for example, achieve a noble-gas configuration by losing the single $s$ electron from their valence shell to form a cation, while the halogens such as chlorine in group 7A achieve a noble-gas configuration by gaining a $p$ electron to fill their valence shell and form an anion. The resultant ions are held together in compounds like $\mathrm{Na}^{+} \mathrm{Cl}^{-}$by the electrical attraction of unlike charges that we call an ionic bond.


But how do elements closer to the middle of the periodic table form bonds? Look at methane, $\mathrm{CH}_{4}$, the main constituent of natural gas, for example. The bonding in methane is not ionic because it would take too much energy for carbon ( $1 s^{2} 2 s^{2} 2 p^{2}$ ) either to gain or lose four electrons to achieve a noble-gas configuration. Instead, carbon bonds to other atoms, not by gaining or losing electrons, but by sharing them. Such a sharedelectron bond, first proposed in 1916 by the American chemist G. N. Lewis, is called a covalent bond. The neutral collection of atoms held together by covalent bonds is called a molecule. Ionic compounds such as sodium chloride, however, are not called molecules.


A simple way of indicating the covalent bonds in molecules is to use what are called Lewis structures, or electron-dot structures, in which the valence-shell electrons of an atom are represented as dots. Thus, hydrogen has one dot representing its $1 s$ electron, carbon has four dots ( $2 s^{2} 2 p^{2}$ ), oxygen has six dots ( $2 s^{2} 2 p^{4}$ ), and so on. A stable molecule results whenever a noble-gas configuration of eight dots (an octet) is achieved for all main-group atoms or two dots for hydrogen. Even simpler than Lewis structures is the use of Kekulé structures, or line-bond structures, in which the two-electron covalent bonds are indicated as lines drawn between atoms.


| Electron-dot structures (Lewis structures) | <smiles></smiles> | $\begin{gathered} H: \ddot{\mathrm{N}}: \mathrm{H} \\ \ddot{\mathrm{H}} \end{gathered}$ | $H: \ddot{O}: H$ | <smiles></smiles> |
| :---: | :---: | :---: | :---: | :---: |
| Line-bond structures (Kekulé structures) | <smiles>C</smiles> | <smiles>[NH]</smiles> | $\mathrm{H}-\ddot{\mathrm{O}}-\mathrm{H}$ | <smiles>CO</smiles> |
|  | Methane $\left(\mathrm{CH}_{4}\right)$ | Ammonia $\left(\mathrm{NH}_{3}\right)$ | Water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ | Methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ |


The number of covalent bonds an atom forms depends on how many additional valence electrons it needs to reach a noble-gas configuration. Hydrogen has one valence electron (1s) and needs only one more to reach the helium configuration ( $1 s^{2}$ ), so it forms one bond. Carbon has four valence electrons ( $2 s^{2} 2 p^{2}$ ) and needs four more to reach the neon configuration $\left(2 s^{2} 2 p^{6}\right)$, so it forms four bonds. Nitrogen has five valence electrons ( $2 s^{2}$ $2 p^{3}$ ), needs three more, and forms three bonds; oxygen has six valence electrons ( $2 s^{2} 2 p^{4}$ ), needs two more, and forms two bonds; and the halogens have seven valence electrons, need one more, and form one bond.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0008.jpg?height=229&width=979&top_left_y=891&top_left_x=573)


Valence electrons that are not used for bonding remain as dots in structures and are called lone-pair electrons, or nonbonding electrons. The nitrogen atom in ammonia, $\mathrm{NH}_{3}$, for instance, shares six valence electrons in three covalent bonds and has its remaining two valence electrons as two dots in a nonbonding lone pair. As a time-saving shorthand, nonbonding electrons are often omitted when drawing line-bond structures, but you still have to keep them in mind since they're often crucial in chemical reactions.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0008.jpg?height=225&width=917&top_left_y=1362&top_left_x=601)


Ammonia


WORKED EXAMPLE 1.1 -


Predicting the Number of Bonds Formed by Atoms in Molecules -

How many hydrogen atoms does phosphorus bond to in forming phosphine, $\mathrm{PH}_{\text {? }}$ ?


Strategy -

Identify the periodic group of phosphorus, and find from that how many electrons (bonds) are needed to make an octet.


Solution -

Phosphorus is in group 5A of the periodic table and has five valence electrons. It thus needs to share three more electrons to make an octet and therefore bonds to three hydrogen atoms, giving $\mathrm{PH}_{3}$.


WORKED EXAMPLE 1.2 -


Drawing Electron-Dot and Line-Bond Structures -

Draw both electron-dot and line-bond structures for chloromethane, $\mathrm{CH}_{3} \mathrm{Cl}$.


Strategy -

Remember that a covalent bond-that is, a pair of shared electrons-is represented as a line between atoms.


Solution -

Hydrogen has one valence electron, carbon has four valence electrons, and chlorine has seven valence electrons. Thus, chloromethane is represented as


Solution -

Chloromethane


Solution -

PROBLEM Draw a molecule of chloroform, $\mathrm{CHCl}_{3}$, using solid, wedged, and dashed lines to show its tetrahedral 1-3 geometry.


Solution -

PROBLEM Convert the following representation of ethane, $\mathrm{C}_{2} \mathrm{H}_{6}$, into a conventional drawing that uses solid, 1-4 wedged, and dashed lines to indicate tetrahedral geometry around each carbon (black = C, gray = H).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0009.jpg?height=282&width=335&top_left_y=992&top_left_x=445)


Ethane -

PROBLEM What are likely formulas for the following substances?
1-5 (a) $\mathrm{CCl}_{\text {? }}$
(b) AlH ?
(c) $\mathrm{CH}_{?} \mathrm{Cl}_{2}$
(d) SiF
(e) $\mathrm{CH}_{3} \mathrm{NH}_{?}$


Ethane -

PROBLEM Write line-bond structures for the following substances, showing all nonbonding electrons:
1-6 (a) $\mathrm{CHCl}_{3}$, chloroform (b) $\mathrm{H}_{2} \mathrm{~S}$, hydrogen sulfide (c) $\mathrm{CH}_{3} \mathrm{NH}_{2}$, methylamine
(d) $\mathrm{CH}_{3} \mathrm{Li}$, methyllithium


Ethane -

PROBLEM Why can't an organic molecule have the formula $\mathrm{C}_{2} \mathrm{H}_{7}$ ?


1-7 -


1-7 - 1.5 Describing Chemical Bonds: Valence Bond Theory

How does electron sharing lead to bonding between atoms? Two models have been developed to describe covalent bonding: valence bond theory and molecular orbital theory. Each model has its strengths and weaknesses, and chemists tend to use them interchangeably depending on the circumstances. Valence bond theory is the more easily visualized of the two, so most of the descriptions we'll use in this book derive from that approach.


According to valence bond (VB) theory, a covalent bond forms when two atoms approach each other closely and a singly occupied orbital on one atom overlaps a singly occupied orbital on the other atom. The electrons are now paired in the overlapping orbitals and are attracted to the nuclei of both atoms, thus bonding the atoms together. In the $\mathrm{H}_{2}$ molecule, for instance, the $\mathrm{H}-\mathrm{H}$ bond results from the overlap of two singly occupied hydrogen $1 s$ orbitals.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0009.jpg?height=198&width=657&top_left_y=2335&top_left_x=731)


The overlapping orbitals in the $\mathrm{H}_{2}$ molecule have the elongated egg shape we might get by pressing two spheres together. If a plane were to pass through the middle of the bond, the intersection of the plane and the overlapping orbitals would be a circle. In other words, the $\mathrm{H}-\mathrm{H}$ bond is cylindrically symmetrical, as shown in FIGURE 1.8. Such bonds, which are formed by the head-on overlap of two atomic orbitals along a line drawn between the nuclei, are called sigma ( $\boldsymbol{\sigma}$ ) bonds.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0010.jpg?height=445&width=402&top_left_y=458&top_left_x=875)

FIGURE 1.8 The cylindrical symmetry of the $\mathbf{H - H} \boldsymbol{\sigma}$ bond in an $\mathbf{H}_{\mathbf{2}}$ molecule. The intersection of a plane cutting through the $\boldsymbol{\sigma}$ bond is a circle.


During the bond-forming reaction $2 \mathrm{H} \cdot \longrightarrow \mathrm{H} 2,436 \mathrm{~kJ} / \mathrm{mol}(104 \mathrm{kcal} / \mathrm{mol})$ of energy is released. Because the product $\mathrm{H}_{2}$ molecule has $436 \mathrm{~kJ} / \mathrm{mol}$ less energy than the starting $2 \mathrm{H} \cdot$ atoms, the product is more stable than the reactant and we say that the $\mathrm{H}-\mathrm{H}$ bond has a bond strength of $436 \mathrm{~kJ} / \mathrm{mol}$. In other words, we would have to put $436 \mathrm{~kJ} / \mathrm{mol}$ of energy into the $\mathrm{H}-\mathrm{H}$ bond to break the $\mathrm{H}_{2}$ molecule apart into two H atoms (FIGURE 1.9). For convenience, we'll generally give energies in both kilocalories (kcal) and the SI unit kilojoules (kJ): $1 \mathrm{~kJ}=0.2390$ kcal; $1 \mathrm{kcal}=4.184 \mathrm{~kJ}$.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0010.jpg?height=429&width=1139&top_left_y=1268&top_left_x=496)

FIGURE 1.9 Relative energy levels of two $\mathbf{H}$ atoms and the $\mathbf{H}_{\mathbf{2}}$ molecule. The $\mathrm{H}_{2}$ molecule has $436 \mathrm{~kJ} / \mathrm{mol}(104 \mathrm{kcal} / \mathrm{mol})$ less energy than the two separate H atoms, so $436 \mathrm{~kJ} / \mathrm{mol}$ of energy is released when the $\mathrm{H}-\mathrm{H}$ bond forms. Conversely, $436 \mathrm{~kJ} / \mathrm{mol}$ is absorbed when the $\mathrm{H}-\mathrm{H}$ bond breaks.


How close are the two nuclei in the $\mathrm{H}_{2}$ molecule? If they are too close, they will repel each other because both are positively charged. Yet if they're too far apart, they won't be able to share the bonding electrons. Thus, there is an optimum distance between nuclei that leads to maximum stability (FIGURE 1.10). Called the bond length, this distance is 74 pm in the $\mathrm{H}-\mathrm{H}$ molecule. Every covalent bond has both a characteristic bond strength and bond length.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0011.jpg?height=635&width=847&top_left_y=195&top_left_x=636)


FIGURE 1.10 A plot of energy versus internuclear distance for two hydrogen atoms. The distance between nuclei at the minimum energy point is the bond length.


$1.6 s p^{3}$ Hybrid Orbitals and the Structure of Methane -

The bonding in the hydrogen molecule is fairly straightforward, but the situation is more complicated in organic molecules with tetravalent carbon atoms. Take methane, $\mathrm{CH}_{4}$, for instance. As we've seen, carbon has four valence electrons $\left(2 s^{2} 2 p^{2}\right)$ and forms four bonds. Because carbon uses two kinds of orbitals for bonding, $2 s$ and $2 p$, we might expect methane to have two kinds of $\mathrm{C}-\mathrm{H}$ bonds. In fact, though, all four $\mathrm{C}-\mathrm{H}$ bonds in methane are identical and are spatially oriented toward the corners of a regular tetrahedron, as shown previously in FIGURE 1.7. How can we explain this?


An answer was provided in 1931 by Linus Pauling, who showed mathematically how an $s$ orbital and three $p$ orbitals on an atom can combine, or hybridize, to form four equivalent atomic orbitals with tetrahedral orientation. Shown in FIGURE 1.11, these tetrahedrally oriented orbitals are called $\boldsymbol{s p}^{\mathbf{3}}$ hybrid orbitals. Note that the superscript 3 in the name $s p^{3}$ tells how many of each type of atomic orbital combine to form the hybrid, not how many electrons occupy it.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0011.jpg?height=706&width=1484&top_left_y=1512&top_left_x=304)

FIGURE 1.11 Four $s p^{3}$ hybrid orbitals, oriented toward the corners of a regular tetrahedron, are formed by the combination of an $s$ orbital and three $\boldsymbol{p}$ orbitals (red/blue). The $s p^{3}$ hybrids have two lobes and are unsymmetrical about the nucleus, giving them a directionality and allowing them to form strong bonds to other atoms.

The concept of hybridization explains how carbon forms four equivalent tetrahedral bonds but not why it does so. The shape of the hybrid orbital suggests the answer to why. When an $s$ orbital hybridizes with three $p$ orbitals, the resultant $s p^{3}$ hybrid orbitals are unsymmetrical about the nucleus. One of the two lobes is larger than the other and can therefore overlap more effectively with an orbital from another atom to form a bond. As a result,
$s p^{3}$ hybrid orbitals form stronger bonds than do unhybridized $s$ or $p$ orbitals.
The asymmetry of $s p^{3}$ orbitals arises because, as noted previously, the two lobes of a $p$ orbital have different algebraic signs, + and - in the wave function. Thus, when a $p$ orbital hybridizes with an $s$ orbital, the positive $p$ lobe adds to the $s$ orbital but the negative $p$ lobe subtracts from the $s$ orbital. The resultant hybrid orbital is therefore unsymmetrical about the nucleus and is strongly oriented in one direction.


When each of the four identical $s p^{3}$ hybrid orbitals of a carbon atom overlaps with the $1 s$ orbital of a hydrogen atom, four identical $\mathrm{C}-\mathrm{H}$ bonds are formed and methane results. Each $\mathrm{C}-\mathrm{H}$ bond in methane has a strength of $439 \mathrm{~kJ} / \mathrm{mol}(105 \mathrm{kcal} / \mathrm{mol})$ and a length of 109 pm . Because the four bonds have a specific geometry, we also can define a property called the bond angle. The angle formed by each $\mathrm{H}-\mathrm{C}-\mathrm{H}$ is $109.5^{\circ}$, the so-called tetrahedral angle. Methane thus has the structure shown in FIGURE 1.12.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0012.jpg?height=275&width=995&top_left_y=692&top_left_x=565)


FIGURE 1.12 The structure of methane, showing its $109 . \mathbf{5}^{\circ}$ bond angles.


$1.7 s p^{3}$ Hybrid Orbitals and the Structure of Ethane -

The same kind of orbital hybridization that accounts for the methane structure also accounts for the bonding together of carbon atoms into chains and rings to make possible many millions of organic compounds. Ethane, $\mathrm{C}_{2} \mathrm{H}_{6}$, is the simplest molecule containing a carbon-carbon bond.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0012.jpg?height=247&width=567&top_left_y=1248&top_left_x=779)


We can picture the ethane molecule by imagining that the two carbon atoms bond to each other by head-on sigma ( $\sigma$ ) overlap of an $s p^{3}$ hybrid orbital from each (FIGURE 1.13). The remaining three $s p^{3}$ hybrid orbitals on each carbon overlap with the 1 s orbitals of three hydrogens to form the six $\mathrm{C}-\mathrm{H}$ bonds. The $\mathrm{C}-\mathrm{H}$ bonds in ethane are similar to those in methane, although a bit weaker: $421 \mathrm{~kJ} / \mathrm{mol}$ ( $101 \mathrm{kcal} / \mathrm{mol}$ ) for ethane versus $439 \mathrm{~kJ} / \mathrm{mol}$ for methane. The C-C bond is 153 pm in length and has a strength of $377 \mathrm{~kJ} / \mathrm{mol}(90 \mathrm{kcal} / \mathrm{mol})$. All the bond angles of ethane are near, although not exactly at, the tetrahedral value of $109.5^{\circ}$.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0012.jpg?height=711&width=1221&top_left_y=1794&top_left_x=455)


FIGURE 1.13 The structure of ethane. The carbon-carbon bond is formed by $\sigma$ overlap of two $s p^{3}$ hybrid orbitals. For clarity, the smaller
lobes of the $s p^{3}$ hybrid orbitals are not shown.
PROBLEM Draw a line-bond structure for propane, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$. Predict the value of each bond angle, and 1-8 indicate the overall shape of the molecule.


PROBLEM Convert the following molecular model of hexane, a component of gasoline, into a line-bond 1-9 structure (black $=\mathrm{C}$, gray $=\mathrm{H}$ ).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0013.jpg?height=181&width=501&top_left_y=476&top_left_x=430)


Hexane


$1.8 s p^{2}$ Hybrid Orbitals and the Structure of Ethylene -

The bonds we've seen in methane and ethane are called single bonds because they result from the sharing of one electron pair between bonded atoms. It was recognized nearly 150 years ago, however, that carbon atoms can also form double bonds by sharing two electron pairs between atoms or triple bonds by sharing three electron pairs. Ethylene, for instance, has the structure $\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}$ and contains a carbon-carbon double bond, while acetylene has the structure $\mathrm{HC} \equiv \mathrm{CH}$ and contains a carbon-carbon triple bond.


How are multiple bonds described by valence bond theory? When we discussed $s p^{3}$ hybrid orbitals in Section 1.6, we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent $s p^{3}$ hybrids. Imagine instead that the $2 s$ orbital combines with only $t w o$ of the three available $2 p$ orbitals. Three $\boldsymbol{s p}^{\mathbf{2}}$ hybrid orbitals result, and one $2 p$ orbital remains unchanged. Like $s p^{3}$ hybrids, $s p^{2}$ hybrid orbitals are unsymmetrical about the nucleus and are strongly oriented in a specific direction so they can form strong bonds. The three $s p^{2}$ orbitals lie in a plane at angles of $120^{\circ}$ to one another, with the remaining $p$ orbital perpendicular to the $s p^{2}$ plane, as shown in FIGURE 1.14.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0013.jpg?height=489&width=481&top_left_y=1382&top_left_x=535)


Side view
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0013.jpg?height=457&width=457&top_left_y=1406&top_left_x=1124)


Top view


FIGURE $1.14 \boldsymbol{s p} \boldsymbol{p}^{2}$ Hybridization. The three equivalent $\boldsymbol{s p ^ { 2 }}$ hybrid orbitals lie in a plane at angles of $120^{\circ}$ to one another, and a single unhybridized $\boldsymbol{p}$ orbital (red/blue) is perpendicular to the $s p^{2}$ plane.


When two carbons with $s p^{2}$ hybridization approach each other, they form a strong $\sigma$ bond by $s p^{2}-s p^{2}$ head-on overlap. At the same time, the unhybridized $p$ orbitals interact by sideways overlap to form what is called a pi ( $\boldsymbol{\pi}$ ) bond. The combination of an $s p^{2}-s p^{2} \sigma$ bond and a $2 p-2 p \pi$ bond results in the sharing of four electrons and the formation of a carbon-carbon double bond (FIGURE 1.15). Note that the electrons in the $\sigma$ bond occupy the region centered between nuclei, while the electrons in the $\pi$ bond occupy regions above and below a line drawn between nuclei.


To complete the structure of ethylene, four hydrogen atoms form $\sigma$ bonds with the remaining four $s p^{2}$ orbitals. Ethylene thus has a planar structure, with $\mathrm{H}-\mathrm{C}-\mathrm{H}$ and $\mathrm{H}-\mathrm{C}-\mathrm{C}$ bond angles of approximately $120^{\circ}$. (The actual values are $117.4^{\circ}$ for the $\mathrm{H}-\mathrm{C}-\mathrm{H}$ bond angle and $121.3^{\circ}$ for the $\mathrm{H}-\mathrm{C}-\mathrm{C}$ bond angle.) Each $\mathrm{C}-\mathrm{H}$ bond has a length of 108.7 pm and a strength of $464 \mathrm{~kJ} / \mathrm{mol}(111 \mathrm{kcal} / \mathrm{mol})$.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0014.jpg?height=735&width=1289&top_left_y=191&top_left_x=407)


FIGURE 1.15 The structure of ethylene. One part of the double bond in ethylene results from $\sigma$ (head-on) overlap of $s p^{2}$ hybrid orbitals, and the other part results from $\pi$ (sideways) overlap of unhybridized $\boldsymbol{p}$ orbitals (red/blue). The $\pi$ bond has regions of electron density above and below a line drawn between nuclei.


As you might expect, the carbon-carbon double bond in ethylene is both shorter and stronger than the single bond in ethane because it has four electrons bonding the nuclei together rather than two. Ethylene has a $\mathrm{C}=\mathrm{C}$ bond length of 134 pm and a strength of $728 \mathrm{~kJ} / \mathrm{mol}$ ( $174 \mathrm{kcal} / \mathrm{mol}$ ) versus a C-C length of 153 pm and a strength of $377 \mathrm{~kJ} / \mathrm{mol}$ for ethane. The carbon-carbon double bond is less than twice as strong as a single bond because the sideways overlap in the $\pi$ part of the double bond is not as great as the head-on overlap in the $\sigma$ part.


WORKED EXAMPLE 1.3 -


Commonly used in biology as a tissue preservative, formaldehyde, $\mathrm{CH}_{2} \mathrm{O}$, contains a carbon-oxygen double bond. Draw electron-dot and line-bond structures of formaldehyde, and indicate the hybridization of the carbon orbitals.


Strategy -

We know that hydrogen forms one covalent bond, carbon forms four, and oxygen forms two. Trial and error, combined with intuition, is needed to fit the atoms together.


Solution -

There is only one way that two hydrogens, one carbon, and one oxygen can combine:
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0014.jpg?height=237&width=385&top_left_y=1887&top_left_x=870)


Solution -

Like the carbon atoms in ethylene, the carbon atom in formaldehyde is in a double bond and its orbitals are therefore $s p^{2}$-hybridized.


Solution -

PROBLEM Draw a line-bond structure for propene, $\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2}$. Indicate the hybridization of the orbitals on 1-10 each carbon, and predict the value of each bond angle.

PROBLEM Draw a line-bond structure for 1,3-butadiene, $\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2}$. Indicate the hybridization of the 1-11 orbitals on each carbon, and predict the value of each bond angle.


Solution -

PROBLEM A molecular model of aspirin (acetylsalicylic acid) is shown. Identify the hybridization of the
1-12 orbitals on each carbon atom in aspirin, and tell which atoms have lone pairs of electrons (black = C, red $=0$, gray $=H$ ).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0015.jpg?height=435&width=735&top_left_y=346&top_left_x=424)


1.9 sp Hybrid Orbitals and the Structure of Acetylene -

In addition to forming single and double bonds by sharing two and four electrons, respectively, carbon can also form a triple bond by sharing six electrons. To account for the triple bond in a molecule such as acetylene, $\mathrm{H}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}$, we need a third kind of hybrid orbital, an $\boldsymbol{s p}$ hybrid. Imagine that, instead of combining with two or three $p$ orbitals, a carbon $2 s$ orbital hybridizes with only a single $p$ orbital. Two sphybrid orbitals result, and two $p$ orbitals remain unchanged. The two $s p$ orbitals are oriented $180^{\circ}$ apart on the right-left ( $x$ ) axis, while the p orbitals are perpendicular on the up-down $(y)$ axis and the in-out $(z)$ axis, as shown in FIGURE 1.16.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0015.jpg?height=310&width=375&top_left_y=1198&top_left_x=669)


One $s p$ hybrid Another $s p$ hybrid
FIGURE 1.16 sp Hybridization. The two $s p$ hybrid orbitals are oriented $180^{\circ}$ away from each other, perpendicular to the two remaining $\boldsymbol{p}$ orbitals (red/blue).


When two $s p$-hybridized carbon atoms approach each other, $s p$ hybrid orbitals on each carbon overlap headon to form a strong $s p-s p \sigma$ bond. At the same time, the $p_{\mathrm{Z}}$ orbitals from each carbon form a $p_{\mathrm{Z}}-p_{\mathrm{Z}} \pi$ bond by sideways overlap, and the $p_{\mathrm{y}}$ orbitals overlap similarly to form a $p_{\mathrm{y}}-p_{\mathrm{y}} \pi$ bond. The net effect is the sharing of six electrons and formation of a carbon-carbon triple bond. Each of the two remaining $s p$ hybrid orbitals forms a $\sigma$ bond with hydrogen to complete the acetylene molecule (FIGURE 1.17).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0016.jpg?height=795&width=1351&top_left_y=193&top_left_x=365)

FIGURE 1.17 The structure of acetylene. The two carbon atoms are joined by one $s p-s p \sigma$ bond and two $p-p \pi$ bonds.
As suggested by $s p$ hybridization, acetylene is a linear molecule with $\mathrm{H}-\mathrm{C}-\mathrm{C}$ bond angles of $180^{\circ}$. The $\mathrm{C}-\mathrm{H}$ bonds have a length of 106 pm and a strength of $558 \mathrm{~kJ} / \mathrm{mol}(133 \mathrm{kcal} / \mathrm{mol})$. The $\mathrm{C}-\mathrm{C}$ bond length in acetylene is 120 pm , and its strength is about $965 \mathrm{~kJ} / \mathrm{mol}(231 \mathrm{kcal} / \mathrm{mol})$, making it the shortest and strongest of any carbon-carbon bond. A comparison of $s p, s p^{2}$, and $s p^{3}$ hybridization is given in TABLE 1.2.


| Molecule | Bond | Bond strength |  | Bond length (pm) |
| :---: | :---: | :---: | :---: | :---: |
|  |  | (kJ/mol) | ( $\mathrm{kcal} / \mathrm{mol}$ ) |  |
| Methane, $\mathrm{CH}_{4}$ | $\left(s p^{3}\right) \mathrm{C}-\mathrm{H}$ | 439 | 105 | 109 |
| Ethane, $\mathrm{CH}_{3} \mathrm{CH}_{3}$ | $\left(s p^{3}\right) \mathrm{C}-\mathrm{C}\left(s p^{3}\right)$ | 377 | 90 | 153 |
|  | $\left(s p^{3}\right) \mathrm{C}-\mathrm{H}$ | 421 | 101 | 109 |
| Ethylene, $\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}$ | $\left(s p^{2}\right) \mathrm{C}=\mathrm{C}\left(s p^{2}\right)$ | 728 | 174 | 134 |
|  | $\left(s p^{2}\right) \mathrm{C}-\mathrm{H}$ | 464 | 111 | 109 |
| Acetylene, $\mathrm{HC} \equiv \mathrm{CH}$ | $(s p) \mathrm{C} \equiv \mathrm{C}(s p)$ | 965 | 231 | 120 |
|  | (sp) $\mathrm{C}-\mathrm{H}$ | 558 | 133 | 106 |


PROBLEM Draw a line-bond structure for propyne, $\mathrm{CH}_{3} \mathrm{C} \equiv \mathrm{CH}$. Indicate the hybridization of the orbitals on
1-13 each carbon, and predict a value for each bond angle.


1.9 sp Hybrid Orbitals and the Structure of Acetylene - 1.10 Hybridization of Nitrogen, Oxygen, Phosphorus, and Sulfur

The valence-bond concept of orbital hybridization described in the previous four sections is not limited to carbon. Covalent bonds formed by other elements can also be described using hybrid orbitals. Look, for instance, at the nitrogen atom in methylamine $\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)$, an organic derivative of ammonia ( $\mathrm{NH}_{3}$ ) and the substance responsible for the odor of rotting fish.


The experimentally measured $\mathrm{H}-\mathrm{N}-\mathrm{H}$ bond angle in methylamine is $107.1^{\circ}$, and the $\mathrm{C}-\mathrm{N}-\mathrm{H}$ bond angle is
$110.3^{\circ}$, both of which are close to the $109.5^{\circ}$ tetrahedral angle found in methane. We therefore assume that nitrogen forms four $s p^{3}$-hybridized orbitals, just as carbon does. One of the four $s p^{3}$ orbitals is occupied by two nonbonding electrons (a lone pair), and the other three hybrid orbitals have one electron each. Overlap of these three half-filled nitrogen orbitals with half-filled orbitals from other atoms ( C or H ) gives methylamine. Note that the unshared lone pair of electrons in the fourth $s p^{3}$ hybrid orbital of nitrogen occupies as much space as an $\mathrm{N}-\mathrm{H}$ bond does and is very important to the chemistry of methylamine and other nitrogen-containing organic molecules.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0017.jpg?height=263&width=635&top_left_y=519&top_left_x=734)

Methylamine
Like the carbon atom in methane and the nitrogen atom in methylamine, the oxygen atom in methanol (methyl alcohol) and many other organic molecules can be described as $s p^{3}$-hybridized. The $\mathrm{C}-\mathrm{O}-\mathrm{H}$ bond angle in methanol is $108.5^{\circ}$, very close to the $109.5^{\circ}$ tetrahedral angle. Two of the four $s p^{3}$ hybrid orbitals on oxygen are occupied by nonbonding electron lone pairs, and two are used to form bonds.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0017.jpg?height=343&width=640&top_left_y=1059&top_left_x=729)


In the periodic table, phosphorus and sulfur are the third-row analogs of nitrogen and oxygen, and the bonding in both can be described using hybrid orbitals. Because of their positions in the third row, however, both phosphorus and sulfur can expand their outer-shell octets and form more than the typical number of covalent bonds. Phosphorus, for instance, often forms five covalent bonds, and sulfur often forms four.


Phosphorus is most commonly encountered in biological molecules in compounds called organophosphates, which contain a phosphorus atom bonded to four oxygens, with one of the oxygens also bonded to carbon. Methyl phosphate, $\mathrm{CH}_{3} \mathrm{OPO}_{3}{ }^{2-}$, is the simplest example. The $\mathrm{O}-\mathrm{P}-\mathrm{O}$ bond angle in such compounds is typically in the range $110^{\circ}$ to $112^{\circ}$, implying $s p^{3}$ hybridization for phosphorus orbitals.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0017.jpg?height=285&width=725&top_left_y=1798&top_left_x=689)


Methyl phosphate (an organophosphate)
Sulfur is most commonly encountered in biological molecules either in compounds called thiols, which have a sulfur atom bonded to one hydrogen and one carbon, $\mathrm{C}-\mathrm{S}-\mathrm{H}$ or in sulfides, which have a sulfur atom bonded to two carbons, $\mathrm{C}-\mathrm{S}-\mathrm{C}$. Produced by some bacteria, methanethiol $\left(\mathrm{CH}_{3} \mathrm{SH}\right)$ is the simplest example of a thiol, and dimethyl sulfide, $\mathrm{H}_{3} \mathrm{C}-\mathrm{S}-\mathrm{CH}_{3}$, is the simplest example of a sulfide. Both can be described by approximate $s p^{3}$ hybridization around sulfur, although both have significant deviation from the $109.5^{\circ}$ tetrahedral angle.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0018.jpg?height=270&width=335&top_left_y=201&top_left_x=315)


Methanethiol
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0018.jpg?height=261&width=706&top_left_y=211&top_left_x=1078)


Dimethyl sulfide


PROBLEM Identify all nonbonding lone pairs of electrons in the following molecules, and tell what geometry
1-14 you expect for each of the indicated atoms.
(a) The oxygen atom in dimethyl ether, $\mathrm{CH}_{3}-\mathrm{O}-\mathrm{CH}_{3}$ (b) The nitrogen atom in trimethylamine,
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(c) The phosphorus atom in phosphine, $\mathrm{PH}_{3}$
(d) The sulfur atom in the amino acid methionine,
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1.9 sp Hybrid Orbitals and the Structure of Acetylene - 1.11 Describing Chemical Bonds: Molecular Orbital Theory

We said in Section 1.5 that chemists use two models for describing covalent bonds: valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let's look briefly at the molecular orbital approach to bonding. We'll return to this topic in Chapters 14, 15, and 30 for a more in-depth discussion.


Molecular orbital (MO) theory describes covalent bond formation as arising from a mathematical combination of atomic orbitals (wave functions) on different atoms to form molecular orbitals, so called because they belong to the entire molecule rather than to an individual atom. Just as an atomic orbital, whether unhybridized or hybridized, describes a region of space around an atom where an electron is likely to be found, so a molecular orbital describes a region of space in a molecule where electrons are most likely to be found.


Like an atomic orbital, a molecular orbital has a specific size, shape, and energy. In the $\mathrm{H}_{2}$ molecule, for example, two singly occupied $1 s$ atomic orbitals combine to form two molecular orbitals. There are two ways for the orbital combination to occur-an additive way and a subtractive way. The additive combination leads to formation of a molecular orbital that is lower in energy and roughly egg-shaped, while the subtractive combination leads to a molecular orbital that is higher in energy and has a node between nuclei (FIGURE 1.18). Note that the additive combination is a single, egg-shaped, molecular orbital; it is not the same as the two overlapping 1 s atomic orbitals of the valence bond description. Similarly, the subtractive combination is a single molecular orbital with the shape of an elongated dumbbell.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0019.jpg?height=548&width=1239&top_left_y=192&top_left_x=454)

FIGURE 1.18 Molecular orbitals of $\mathbf{H}_{\mathbf{2}}$. Combination of two hydrogen $1 s$ atomic orbitals leads to two $\mathrm{H}_{2}$ molecular orbitals. The lowerenergy, bonding MO is filled, and the higher-energy, antibonding MO is unfilled.

The additive combination is lower in energy than the two hydrogen $1 s$ atomic orbitals and is called a bonding MO because electrons in this MO spend most of their time in the region between the two nuclei, thereby bonding the atoms together. The subtractive combination is higher in energy than the two hydrogen $1 s$ orbitals and is called an antibonding MO because any electrons it contains can't occupy the central region between the nuclei, where there is a node, and thus can't contribute to bonding. The two nuclei therefore repel each other.


Just as bonding and antibonding $\sigma$ molecular orbitals result from the head-on combination of two $s$ atomic orbitals in $\mathrm{H}_{2}$, so bonding and antibonding $\pi$ molecular orbitals result from the sideways combination of two $p$ atomic orbitals in ethylene. As shown in FIGURE 1.19, the lower-energy, $\pi$ bonding MO has no node between nuclei and results from the combination of $p$ orbital lobes with the same algebraic sign. The higher-energy, $\pi$ antibonding MO has a node between nuclei and results from the combination of lobes with opposite algebraic signs. Only the bonding MO is occupied; the higher-energy, antibonding MO is vacant. We'll see in Chapters 14, 15 , and 30 that molecular orbital theory is particularly useful for describing $\pi$ bonds in compounds that have more than one double bond.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0019.jpg?height=581&width=1231&top_left_y=1439&top_left_x=458)

FIGURE 1.19 A molecular orbital description of the C-C $\boldsymbol{\pi}$ bond in ethylene. The lower-energy, $\boldsymbol{\pi}$ bonding MO results from an additive combination of $p$ orbital lobes with the same algebraic sign and is filled. The higher-energy, $\boldsymbol{\pi}$ antibonding MO results from a subtractive combination of $p$ orbital lobes with opposite algebraic signs and is unfilled.


1.9 sp Hybrid Orbitals and the Structure of Acetylene - 1.12 Drawing Chemical Structures

Let's cover just one more point before ending this introductory chapter. In the structures we've been drawing until now, a line between atoms has represented the two electrons in a covalent bond. Drawing every bond and every atom is tedious, however, so chemists have devised several shorthand ways for writing structures. In condensed structures, carbon-hydrogen and carbon-carbon single bonds aren't shown; instead, they're understood. If a carbon has three hydrogens bonded to it, we write $\mathrm{CH}_{3}$; if a carbon has two hydrogens bonded to it, we write $\mathrm{CH}_{2}$; and so on. The compound called 2-methylbutane, for example, is written as follows:
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0020.jpg?height=269&width=909&top_left_y=191&top_left_x=603)


2-Methylbutane
Note that the horizontal bonds between carbons aren't shown in condensed structures-the $\mathrm{CH}_{3}, \mathrm{CH}_{2}$, and CH units are simply placed next to each other-but vertical carbon-carbon bonds like that of the first of the condensed structures drawn above is shown for clarity. Notice also in the second of the condensed structures that the two $\mathrm{CH}_{3}$ units attached to the CH carbon are grouped together as $\left(\mathrm{CH}_{3}\right)_{2}$.


Even simpler than condensed structures are skeletal structures such as those shown in TABLE 1.3. The rules for drawing skeletal structures are straightforward.


RULE 1 -

Carbon atoms aren't usually shown. Instead, a carbon atom is assumed to be at each intersection of two lines (bonds) and at the end of each line. Occasionally, a carbon atom might be indicated for emphasis or clarity.


RULE 2 -

Hydrogen atoms bonded to carbon aren't shown. Because carbon always has a valence of 4, we mentally supply the correct number of hydrogen atoms for each carbon.


RULE 3 -

Atoms other than carbon and hydrogen are shown.
One further comment: Although such groupings as $-\mathrm{CH}_{3},-\mathrm{OH}$, and $-\mathrm{NH}_{2}$ are usually written with the C , O , or N atom first and the H atom second, the order of writing is sometimes inverted to $\mathrm{H}_{3} \mathrm{C}-, \mathrm{HO}-$, and $\mathrm{H}_{2} \mathrm{~N}$ - if needed to make the bonding connections clearer. Larger units such as $-\mathrm{CH}_{2} \mathrm{CH}_{3}$ are not inverted, though; we don't write $\mathrm{H}_{3} \mathrm{CH}_{2} \mathrm{C}$ - because it would be confusing. There are, however, no well-defined rules that cover all cases; it's largely a matter of preference.


RULE 3 -

| TABLE 1.3 Line-bond and Skeletal Structures for Some Compounds |
| :--- |
| Compound |
| Isoprene, $\mathrm{C}_{5} \mathrm{H}_{8}$ |
| Line-bond structure |
| Shethylcyclohexane, $\mathrm{C}_{7} \mathrm{H}_{14}$ |


WORKED EXAMPLE 1.4 -


Interpreting a Line-Bond Structure -

Carvone, a substance responsible for the odor of spearmint, has the following structure. Tell how many hydrogens are bonded to each carbon, and give the molecular formula of carvone.
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Interpreting a Line-Bond Structure -

Carvone


Strategy -

The end of a line represents a carbon atom with 3 hydrogens, $\mathrm{CH}_{3}$; a two-way intersection is a carbon atom with 2 hydrogens, $\mathrm{CH}_{2}$; a three-way intersection is a carbon atom with 1 hydrogen, CH ; and a four-way intersection is a carbon atom with no attached hydrogens.


Strategy -


Strategy -

Carvone ( $\mathrm{C}_{\mathbf{1 0}} \mathrm{H}_{\mathbf{1 4}} \mathrm{O}$ )


Strategy -

PROBLEM Propose skeletal structures for compounds that satisfy the following molecular formulas: There is
1-16 more than one possibility in each case.
(a) $\mathrm{C}_{5} \mathrm{H}_{12}$
(b) $\mathrm{C}_{2} \mathrm{H}_{7} \mathrm{~N}$
(c) $\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}$
(d) $\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}$


Strategy -

PROBLEM The following molecular model is a representation of para-aminobenzoic acid (PABA), the active
1-17 ingredient in many sunscreens. Indicate the positions of the multiple bonds, and draw a skeletal structure (black $=\mathrm{C}$, red $=\mathrm{O}$, blue $=\mathrm{N}$, gray $=\mathrm{H}$ ).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0021.jpg?height=356&width=502&top_left_y=2039&top_left_x=443)
para-Aminobenzoic acid
(PABA)


Organic Foods: Risk versus Benefit -

Contrary to what you may hear in supermarkets or on television, all foods are organic-that is, complex mixtures of organic molecules. Even so, when applied to food, the word organic has come to mean an absence of synthetic chemicals, typically pesticides, antibiotics, and preservatives. How concerned should we be about traces of pesticides in the food we eat? Or toxins in the water we drink? Or pollutants in the air we breathe?


Organic Foods: Risk versus Benefit -

Life is not risk-free-we all take many risks each day without even thinking about it. We decide to ride a bike rather than drive, even though there is a ten times greater likelihood per mile of dying in a bicycling accident than in a car. We decide to walk down stairs rather than take an elevator, even though 32,000 people die from falls each year in the United States. Some of us decide to smoke cigarettes, even though it increases our chance of getting cancer by $50 \%$. But what about risks from chemicals like pesticides?
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0022.jpg?height=597&width=830&top_left_y=875&top_left_x=645)


Organic Foods: Risk versus Benefit -

FIGURE 1.20 How dangerous is the pesticide being sprayed on this crop? (credit: "NRCSAR83001(265)" by USDA Natural Resources Conservation Service/Wikimedia Commons, Public Domain)


Organic Foods: Risk versus Benefit -

One thing is certain: without pesticides, whether they target weeds (herbicides), insects (insecticides), or molds and fungi (fungicides), crop production would drop significantly, food prices would increase, and famines would occur in less developed parts of the world. Take the herbicide atrazine, for instance. In the United States alone, approximately 100 million pounds of atrazine are used each year to kill weeds in corn, sorghum, and sugarcane fields, greatly improving the yields of these crops. Nevertheless, the use of atrazine continues to be a concern because traces persist in the environment. Indeed, heavy atrazine exposure can pose health risks to humans and some animals. Because of these risks, the United States Environmental Protection Agency (EPA) has decided not to ban its use because doing so would result in lower crop yields and increased food costs, and because there is no suitable alternative herbicide available.
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Organic Foods: Risk versus Benefit -

Atrazine
How can the potential hazards from a chemical like atrazine be determined? Risk evaluation of chemicals is carried out by exposing test animals, usually mice or rats, to the chemical and then monitoring the animals for signs of harm. To limit the expense and time needed, the amounts administered are typically hundreds or thousands of times greater than those a person might normally encounter. The results obtained in animal tests are then distilled into a single number called an $\mathrm{LD}_{50}$, the amount of substance per kilogram of body weight that
is a lethal dose for $50 \%$ of the test animals. For atrazine, the $\mathrm{LD}_{50}$ value is between 1 and $4 \mathrm{~g} / \mathrm{kg}$ depending on the animal species. Aspirin, for comparison, has an $\mathrm{LD}_{50}$ of $1.1 \mathrm{~g} / \mathrm{kg}$, and ethanol (ethyl alcohol) has an $\mathrm{LD}_{50}$ of $10.6 \mathrm{~g} / \mathrm{kg}$.


Organic Foods: Risk versus Benefit -

TABLE 1.4 lists the $\mathrm{LD}_{50}$ for some other familiar substances. The lower the value, the more toxic the substance. Note, though, that $\mathrm{LD}_{50}$ values only pertain to the effects of heavy exposure for a relatively short time. They say nothing about the risks of long-term exposure, such as whether the substance can cause cancer or interfere with development in the unborn.

| TABLE 1.4 Some LD 50 |  |  |  |
| :--- | :--- | :--- | :---: |
| Substance | $\mathrm{LD}_{50}(\mathrm{~g} / \mathrm{kg})$ | Substance | $\mathrm{LD}_{50}(\mathrm{~g} / \mathrm{kg})$ |
| Strychnine 0.005 Chloroform 1.2
 Arsenic trioxide 0.015 Iron(II) sulfate 1.5
 DDT 0.115 Ethyl alcohol 10.6
 Aspirin 1.1 Sodium cyclamate 17 |  |  |  |


Organic Foods: Risk versus Benefit -

So, should we still use atrazine? All decisions involve tradeoffs, and the answer is rarely obvious. Does the benefit of increased food production outweigh possible health risks of a pesticide? Do the beneficial effects of a new drug outweigh a potentially dangerous side effect in a small number of users? Different people will have different opinions, but an honest evaluation of facts is surely the best way to start. As of June 2022, atrazine was still approved for continued use in the United States because the EPA believes that the benefits of increased food production outweigh possible health risks. At the same time, atrazine is little used, though not banned, in the European Union.


Key Terms -

- antibonding MO
- atomic number ( $Z$ )
- Aufbau principle
- bond angle
- bond length
- bond strength
- bonding MO
- condensed structure
- covalent bond
- electron shell
- electron-dot structure
- ground-state electron configuration
- Hund's rule
- ionic bond
- isotope
- Kekulé structure
- Lewis structure
- line-bond structure
- lone-pair electrons
- mass number ( $A$ )
- molecular orbital (MO) theory
- molecule
- node
- nonbonding electron
- orbital
- organic chemistry
- Pauli exclusion principle
- pi ( $\pi$ ) bond
- sigma ( $\sigma$ ) bond
- skeletal structure
- sp hybrid orbital
- $s p^{2}$ hybrid orbital
- $s p^{3}$ hybrid orbital
- valence bond (VB) theory
- valence shell


Key Terms -


Summary -

The purpose of this chapter has been to get you up to speed-to review some ideas about atoms, bonds, and molecular geometry. As we've seen, organic chemistry is the study of carbon compounds. Although a division into organic and inorganic chemistry occurred historically, there is no scientific reason for the division.


Summary -

An atom consists of a positively charged nucleus surrounded by one or more negatively charged electrons. The electronic structure of an atom can be described by a quantum mechanical wave equation, in which electrons are considered to occupy orbitals around the nucleus. Different orbitals have different energy levels and different shapes. For example, $s$ orbitals are spherical and $p$ orbitals are dumbbell-shaped. The groundstate electron configuration of an atom can be found by assigning electrons to the proper orbitals, beginning with the lowest-energy ones.


Summary -

A covalent bond is formed when an electron pair is shared between atoms. According to valence bond (VB) theory, electron sharing occurs by the overlap of two atomic orbitals. According to molecular orbital (MO) theory, bonds result from the mathematical combination of atomic orbitals to give molecular orbitals, which belong to the entire molecule. Bonds that have a circular cross-section and are formed by head-on interaction are called sigma ( $\boldsymbol{\sigma}$ ) bonds; bonds formed by sideways interaction of $p$ orbitals are called $\mathbf{p i}$ ( $\boldsymbol{\pi}$ ) bonds.


Summary -

In the valence bond description, carbon uses hybrid orbitals to form bonds in organic molecules. When forming only single bonds with tetrahedral geometry, carbon uses four equivalent $\boldsymbol{s p}^{\mathbf{3}}$ hybrid orbitals. When forming a double bond with planar geometry, carbon uses three equivalent $\boldsymbol{s p}^{\mathbf{2}}$ hybrid orbitals and one unhybridized $p$ orbital. When forming a triple bond with linear geometry, carbon uses two equivalent $\boldsymbol{s p h}$ hybrid orbitals and two unhybridized $p$ orbitals. Other atoms such as nitrogen, phosphorus, oxygen, and sulfur also use hybrid orbitals to form strong, oriented bonds.


Summary -

Organic molecules are usually drawn using either condensed structures or skeletal structures. In condensed structures, carbon-carbon and carbon-hydrogen bonds aren't shown. In skeletal structures, only the bonds and not the atoms are shown. A carbon atom is assumed to be at the ends and at the junctions of lines (bonds), and the correct number of hydrogens is supplied mentally.


WHY YOU SHOULD WORK PROBLEMS -

There's no surer way to learn organic chemistry than by working problems. Although careful reading and rereading of this text are important, reading alone isn't enough. You must also be able to use the information you've read and be able to apply your knowledge in new situations. Working problems gives you practice at doing this.


WHY YOU SHOULD WORK PROBLEMS -

Each chapter in this book provides many problems of different sorts. The in-chapter problems are placed for immediate reinforcement of ideas just learned, while end-of-chapter problems provide additional practice and come in several forms. They often begin with a short section called "Visualizing Chemistry," which helps you see the microscopic world of molecules and provides practice for working in three dimensions. After the visualizations are many further problems, which are organized by topic. Early problems are primarily of the drill type, providing an opportunity for you to practice your command of the fundamentals. Later problems tend to be more thought-provoking, and some are real challenges.


WHY YOU SHOULD WORK PROBLEMS -

As you study organic chemistry, take the time to work the problems. Do the ones you can, and ask for help on the ones you can't. If you're stumped by a particular problem, check the accompanying Study Guide and Student Solutions Manual for an explanation that should help clarify the difficulty. Working problems takes effort, but the payoff in knowledge and understanding is immense.


Additional Problems -


Visualizing Chemistry -

PROBLEM Convert each of the following molecular models into a skeletal structure, and give the formula of
1-18 each. Only the connections between atoms are shown; multiple bonds are not indicated (black = C, red $=0$, blue $=\mathrm{N}$, gray $=\mathrm{H}$ ) .
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0025.jpg?height=272&width=540&top_left_y=203&top_left_x=478)


Visualizing Chemistry -

Coniine (the toxic substance in poison hemlock)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0025.jpg?height=277&width=353&top_left_y=214&top_left_x=1100)


Visualizing Chemistry -

Alanine (an amino acid)