Chapter 1: Covalent bonding (C8165750)

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1 Sigma bonds

Covalent bond is the sharing of electrons between two atoms. They can be subdivided into the:

  • Sigma bond, which is the first covalent bond, where a [single] pair of electrons are shared. Due to the tug of war (see ), this bond is located directly between two atoms. Sigma bonds are present in all covalent bonds (i.e. both single, as well as double and triple bonds)
  • Pi bonds, which are the second or third covalent bonds, where [two and three, respectively] electron pairs are shared. As the sigma bond occupies the space directly between two atoms, pi bonds are located above and/or below the sigma bond. Pi bonds are used exclusively in double and triple bonds (i.e. not in single bonds)

This can be memorized with the mnemonic that “sigma is singular, and pi is plural”.

Frequently asked questions
What is a covalent bond? How does it differ from an ionic bond?
Covalent bond is the sharing of electrons between atoms. Ionic bond is the donation and accepting of an electron between atoms. Both causes a bond.

What is a sigma bond?
It is the first covalent bond. Therefore, it is found in both single and double bonds - as it is the "first" covalent bond made.

What is a pi bond?
It is a subsequent covalent bond. So it's only found in double, triple, and so-forth bonds.

What is the difference in location of the sigma and pi bonds, and why?
Sigma bond is located directly between the two atoms. Thefore, the pi bond occupies where the sigma bond doesn't - that is, above or below sigma bond.

Formative learning activityMaps to RK1.A
What is a Sigma bond? What is a Pi bond? How are these concepts related?

2 Multiple bonds

Multiple bond is where there is more than a single bond, thereby [apart from requiring a sigma bond] also requiring one or more pi bonds. Double bonds are common for period 2 elements [carbon, nitrogen and oxygen], and less common with elements of higher periods. Electrons in the pi bond [indicative of a double bond] have higher energy than a sigma bond, as they are further away from the nucleus [than a sigma bond], which causes double bonds to be more reactive. However, because a double bond contains both a sigma [as well as a pi bond], the overall bond strength is greater, and therefore, there is less bond length (i.e. proximity of nucleus, see ).

Frequently asked questions
What is a multiple bond?
Where there is more than a single bond, so this could be a double, triple, quadruple, or so-forth bond.

Why are the [double] pi bonds, of higher energy than the [single] sigma bonds?
The sigma bond is localized between the atoms, and the pi bonds are located above or below [the sigma bond]. Therefore, pi bonds are further away from the nucleus. This is a higher energy state. Therefore, [double] pi bonds are of higher energy.

And higher energy means more reactive?
Yes. Multiple bonds are more reactive.

So lower energy means more stable? So single bonds, which are closer to the nucleus, are more stable?
You got it !

But a multiple bond is a combination of both sigma and pi bonds?
Yes, which is why their energy, and therefore reactivity, lies between the two extremities.

Formative learning activityMaps to RK1.B
What are examples of multiple bonds? What is unique about them?

3 Stereochemistry of covalent bonds

Orbital hybridization is where orbitals (s, p, d, f, etc.) mix to form hybrids. As these hybrids result from consideration of an entire molecule [rather than a single atom], they are known as molecular orbitals. The hybrid can be determined by the sum of the superscripts on the s and p, being equivalent to the number of sigma bonds [but not pi bonds] and lone pairs. Exponents to 1 are not expressed.

“For example, carbon in methane [latex]CH_{4}[/latex] has 4 sigma bonds, and no lone pairs,” Em said, “Thus, the hybrid orbitals of carbon in methane is [latex]s^{1}p^{3}[/latex], or rewriting, [latex]sp^{3}[/latex].”

This makes sense because carbon makes 4 single bonds, which should be at the same energy level, despite one is coming from the lower energy [and therefore more stable, and thus stronger, see ] s orbital, and 3 are coming from the higher energy p orbital.

“Another example, carbon in ethene [latex]C_{2}H_{4}[/latex] has 3 sigma bonds [one bond is a pi bond, which is not counted], and no lone pairs,” Em said, “Thus, the hybrid orbitals of carbon in ethene is, [latex]sp^2[/latex].”

Frequently asked questions
What is orbital hybridization?
Where the orbitals mix to form hybrids.

What were orbitals again?
They were s, p, d, f, and so forth.

How is a hybrid calculated?
The sum of the superscripts should be equivalent to the number of [single] sigma bonds, but not [multiple] pi bonds - and lone pairs.

Why aren't exponents to 1 expressed.
Because it has no meaning. s1 and s - the exponent to 1 provides no extra information. It's sort of like how exponents to 1 in mathematics aren't expressed - they provide no extra information.

Each hybridization creates unique angles between bonds, including:












Trigonal planar








However, angle changes can be caused by, lone pairs. As lone pairs are un-bonded, [their electrons are not shared, with other atoms] they exhibit negative polar character, and therefore create repulsion between electrons, thereby reducing the bond angle between the bonded pairs. If there are lone pairs, [latex]sp[/latex] can be bent, and [latex]sp^3[/latex] can be pyramidal.

For example, the oxygen in water [latex]\ce{H2O}[/latex] has an [latex]sp^3[/latex] hybrid, but rather than the expected [latex]109.5^{\circ}[/latex], water is bent at a lower angle of [latex]104.5^{\circ}[/latex].


Another example, ammonia has a lone pair, and hence rather than the expected [latex]109.5^{\circ}[/latex], has a lower angle of [latex]107.8^{\circ}[/latex].


Frequently asked questions
From the hybrid, can you predict the angle?
From the valence shell electron pair repulsion (VSEPR) theory, generally, sp will show as linear, sp2 will show as trigonal planar, and sp3 will show as tetrahedral.

Wait, I get why linear is furthest away from another, and trigonal planar too - but why isn't sp3 a square?
Because the world is in 3D, not 2D. Imagine a lift. The flies try to get as far away to each other as possible. Four flies. You'd find the resulting shape is the tetrahedral.

What causes exception to the VESPR theory?
Lone pairs. Lone pairs are un-bonded, meaning their electrons aren't shared - so they are electrically charged. This causes repulsion, increasing bond angle between un-bonded electrons, and therefore decreasing bond angle between bonded pairs.

Delocalized electrons are electrons in a molecule that aren’t associated with a single atom. Rather, delocalized electrons are contained in orbitals that extend over several adjacent atoms, thereby lowering the electrostatic potential energy, thus stabilizing a molecule, by sharing electrons over several adjacent atoms. Delocalized electrons cannot be represented by a single Lewis structure, but rather, require several, known as resonance structures. Remember that resonance means delocalized; do not confuse resonance to meaning that it resonates between different structures. Rather, the molecules are a weighted average between the different resonance structures. The actual structure however, is none of the theoretical resonance structures; the actual structure has an electrostatic potential energy that is even lower than the most stable contributing structure. [Nevertheless, resonance structures must be valid Lewis structures, and obey the octet rules.] However, the more stable contributing structures do make greatest contribution to the actual structure. Resonance structures can be drawn by:

  • Atoms do not change positions between resonance structures
  • All resonance structures have the same number of valence electrons
  • Resonance structures only differ in arrangement of valence electrons

“For example, even though benzene is often drawn theoretically as the first 2, it exists as neither,” Mandy says, “so it is often drawn as the last structure.”


Frequently asked questions
What is delocalized electrons?
Electrons that aren't associated with a single atom, but rather, extend over several adjacent electrons.

How are delocalized electrons represented?
The Lewis structure cannot do this. They are electron dot structures. The electron cannot be... distributed over several atoms. However, the resonance structure can.

The resonance structure is where an atom alternates between two different thingos?
No. They do not alternate. They are a weighted average between these structures.

So the actual structure is one or another of these actual resonant structures?
No. In fact, its none of these theoretical structures. It's actually something that is even more stable than the most stable contributing structure.

How are resonance structures drawn?
Atoms do not change positions. They have the same number of valence electrons. They only differ in the arrangement of valance electrons.

Huckel’s rule is that planar ring molecules that are aromatic (i.e. resonant), must have [latex]4n+2[/latex] pi electrons, where [latex]n=0, 1, 2, etc[/latex].

“For example, benzene has one pi bond from each of the 6 carbons, adding up to 6 pi bonds,” Mandy said, “thereby satisfying Huckel’s rule with [latex]n=1[/latex].”

Frequently asked questions
What is Huckels rule?
Aromatic molecules have 4n+2 [multiple] pi electrons.

Isomers are compounds with the same molecular formula, but different structural formulas. An exception is conformational isomers, which are simply rotations in the Newman projection (see ); they aren’t even different compounds. Structural isomers are isomers that are bonded differently. Structural isomers have different chemical and physical properties.

For example, a structural isomer of pentan-1-ol is pentan-2-ol.

Frequently asked questions
What is an isomer?
A compound with the same molecular formula, but different structural formula.

Molecular formula? Structural formula?
Molecular formula is the number and type of atoms in it. Structural formula is its arrangement. So isomers have the same constituents, but is arranged differently.

What are conformational isomers?
Rotations in the Newman projection. So that's the representation best for representing the ways molecules can bend. They aren't even different compounds.

Chirality is a property of handedness, such that chiral molecules are like the left and right hands, in that the structures are mirror images of each other. Chiral molecules generally have four different substituents attached. Absolute configuration is the spatial arrangement of a chiral molecule, numbered from highest to lowest property based on descending atomic weight. A circle is then drawn from the highest priority to the lowest priority. A molecule with a clockwise direction is referred to as R, and a molecule with an anticlockwise direction is referred to as S. If there are two atoms with the same priority, the atom attached to these two atoms are respectively compared for higher atomic weight to determine higher priority. Double bonds made to an atom, are to be considered, as being bonded to two of the respective atoms, in the calculation.


Frequently asked questions
What is chirality?
The property of handedness. The left and right hands can be said to be chiral. They are mirror images of another. They are the same; but they are different. You can't place them on top of each other perfectly. They aren't photostats. They are mirrors.

What is absolute configuration?
Describes the spatial arrangement of a chiral molecule. The attachments are numbered from greatest to lowest atomic weight. If they have the same atomic weight, their respective attachments are matched for the greatest atomic weight. Double bonds are to be imagined as being bonded twice. A circle is then drawn from the highest priority to lowest priority.

The circle. What's its significance?
If it is directed clockwise, it is described as R. If it is directed anticlockwise, it is described as S.

Identical relative configuration means the substituents are in the same place, relative to their chiral center. Retention of relative configuration is where a substituent is replaced in the same location about the chiral center, to before. Inversion of relative configuration, is like retention, but after replacement, the entire molecule is mirrored about its chiral center, leading to the substituent now appearing on the opposite side of its original location.

Frequently asked questions
What is relative configuration?
The position of the substituents, relative to their chiral center.

What is the difference between retention and inversion?
Retention is replacement of the stubstituent in the same place. Inversion is like retention, but after replacement, is mirrored about its chiral center.

Plane polarized light is light that is filtered, such that its electric [and therefore magnetic] fields are in one plane only. When photons strike any molecule, it causes change in direction of a wave known as refraction, and therefore rotation in the plane. The degree of rotation of a polarized plane is known as observed rotation, and can be either dextrorotary (d, +) if rotated clockwise, or levorotary (l, -) if rotated anticlockwise. Specific rotation is [latex][\alpha]^T_{\lambda}=\dfrac{\alpha}{l\times c}[/latex], where [latex]\alpha[/latex] is observed rotation, [latex]c[/latex] is concentration, [latex]l[/latex] is length of polarimeter, and [latex]T[/latex] is temperature. In contrast, if a photon strikes a chiral [mirror] molecule, like a mirror, it rotates the plane [back] to its original plane. Since achiral molecules do not have handedness, they are their [own] mirror image, [hence cannot be separated from their mirror image,] and thus cannot rotate light. In contrast, chiral molecules can be separated from their mirror images, and hence like general molecules, chiral compounds can rotate plane polarized light. Note that mirror images rotate light to the same degree, but in different directions.

Frequently asked questions
What is plane polarized light?
Light that is filtered into a single plane.

Why is plane polarized light used?
Because when light strikes a molecule, it rotates the plane of the light. This can only be detected if there is an original plane, and then a final plane. So this requires only a single plane.

So how is rotation described?
Clockwise or anticlockwise. Clockwise is dextrorotary (d, +), and anticlockwise is levorotary (l, -).

What happens if plane polarized light strikes an achiral molecule?
They are their own mirror image, so they cannot rotate light.

Stereoisomers are isomers that are bonded the same, but differ only in 3D orientation in space. They can be divided into:

  • Enantiomer, which are mirror images to another, but not superimposable. You can memorize this with the mnemonic “an ant in a mirror”. Enantiomers have the same chemical and physical properties, except the direction they rotate plane-polarized light, and the way in which they react with other enantiomers. Racemic mixture is a mixture of enantiomers. Racemic mixtures can be separated into its enantiomer components, known as resolution
  • Diastereomer, which are not mirror images to another. For example, cis-trans isomerism is when two atoms are connected by a bond that cannot rotate (such as a double bond, or single bonds in a ring), and the two atoms have an identical substituent. For example, a carbon-carbon double bond, where each carbon has a methyl group attached. If the substituents are on the same side of the molecule, they are known as cis isomers; if the substituents are on the opposite sides of the molecule, they are known as trans isomers. Cis molecules have substituents asymmetrically, and therefore have dipole moments. Trans and cis isomers can also be found across single bonds in ringed structures, as these cannot rotate. Dipole moments increase boiling point (going from liquid to gas, from ) and heat of combustion (discussed ), as dipoles increase intermolecular forces. Trans molecules have substituents symmetrically, and therefore pack into a solid more easily, and therefore have higher melting points (going from solid to liquid, discussed )
    If the carbon-carbon double bonds have different substituents, they can be named according to priority given to elements with higher atomic numbers [and then by competition, their attached groups, as necessary]. If the highest priority atoms for each carbon are on the same side, it is labeled with a prefix [latex](Z)-[/latex], from German zusammen. In contrast, if they are on the opposite side, it is labeled with a prefix [latex](E)-[/latex], from German entgegen. This can be memorized with the mnemonic “Z means it’s on the zame zide”.
    Meso compounds have more than one chiral carbon, and have a plane of symmetry, such that one-half of the compound is a mirror image to the other half. Note therefore, that meso compounds are not chiral, because self-mirrored-ness, means handedness is impossible; and therefore, cannot have enantiomers.
    Diastereomers can be prefixed with “threo-“ or “erythro-“, such that in the Fischer projection, “erythro-” has identical substituents on the same side, and “threo-“ has its [identical] substituents on the opposite side.

Frequently asked questions
What are stereoisomers?
Isomers bonded the same, but differ only in 3D orientation in space. They include the enantiomer and diastereomer.

What is the difference between the enantiomer and diastereomer?
Enantiomer are mirror images. Diastereomer are not mirror images.

What is unique about enantiomers?
Enantiomers have the same chemical and physical properties. However, because enantiomers are chiral molecules, they rotate light in opposite directions.

What is cis-trans isomerism?
Cis is where substituents are on the same side of the molecule, and trans is where substituents are on the opposite side of the molecule.

What is the difference between cis-trans and Z-E? I mean, cis and Z- both mean same side, and trans and E- both mean opposite side.
In cis-trans the substituents must be identical. They aren't in Z-E.

What are meso compounds?
Half the compound is a mirror image of the other half. This means it is not chiral, so handedness is impossible, so cannot have an enantiomer.

What is erthryo- and threo-?
Erthryo- is where identical substituents are on the same side, and threo- is on the opposite side.

Formative learning activityMaps to RK1.C
What is stereochemistry? What is a covalent bond?

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