Chemistry 101: Chemical Bonding

Valence electrons are the electrons in the atom’s highest (outermost) energy subshells. They are chemically relevant because they are the electrons that form chemical bonds.

Valence electron number can quickly be read off of the periodic table as it will be the column number (counting from the left) that the element is in.

Ex: Nitrogen is in the 5th column from the left, so it must have 5 valence shell electrons. Nitrogen is 1s22s22p3, n=2 is the outermost energy level. Add all of those electrons (2 from the s, 3 from the p) to get valence = 5.

Oxygen has 6 electrons in the outermost energy level (2 in the 2s and 4 in the 2p).

Silicon has more electrons total, but it only has 4 valence electrons (2 in the 3s and 2 in the 3p).

The octet rule states that atoms desire eight electrons in their valence shells, as this gives them the electron configuration of a noble gas.

An atom will usually have to bond with other atoms to acquire this electron structure.

Chemical bonds form because they lower the potential energy of the electron clouds. Electrons are shared between atoms across the bond, allowing the final state to be more stable than the two were alone.

In general: bonding proceeds so that as many atoms as possible gain a full octet of valence shell electrons.

1. single bond: one pair of electrons is shared between two atoms
   Ex: O-H bond in H2O, or C-H bond in CH4

2. double bond: two pairs of electrons are shared between atoms
   Ex: O=O bonds in O2, or C=O bonds in CO2

3. triple bond: three pairs of electrons are shared between atoms
   Ex: N≡N bonds in N2, or C≡N bonds in CNOH

1. odd-electron species. Molecules which have an odd total number of valence electrons to distribute (hence some atom will come up lacking)

2. incomplete octets. Atoms where attaining a full octet would require too many bonds. H, He, Li, Be, B are all considered incomplete octet species due to the high number of electrons they would need.

3. expanded octets. Atoms in period 3 or higher that can hold electrons in their d orbitals. The term is a misnomer, as this is no longer an octet, but will instead have 10, 12, or 14 electrons depending on the central atom being bonded.

The most electronegative atom will always gain a full octet first.

Nitric oxide has 11 valence electrons. Oxygen is more electronegative, so will end up with a full octet (two sets of lone e-pairs and a double bond with N). Nitrogen will be left with 3 lone electrons (and two bonds), as it is less electronegative, for a total of 7 electrons.

Lithium has only one valence electron. It would need to acquire 7 additional electrons in order to have a full octet. This is statistically (and structurally) unlikely.

H, He, Li, Be, B are all elements that will from incomplete octets due to the improbability of them acquiring enough electrons.

Phosphorus can expand its five valence electrons into the 3d block, allowing it to bond to five chlorine atoms, completing those chlorine atoms’ octets.

Elements in the third row of the periodic table and beyond (such as P, Cl, S, Xe, and Ar) often exhibit expanded octets of 10, 12, or 14 electrons. This is due to them expanding into the d-block for greater bonding stability.

1. ionic bonds: electrons are transferred from a metal to nonmetal

2. covalent bonds: electrons are shared between nonmetals

3. metallic bonds: electrons ‘“float” between metals in a lattice

An ionic bond is formed when a metal transfers one or more electrons to a nonmetal. Often in chemistry exams this will be metal from column I or II transferring electrons to a halogen.

Ex: The classic example is an “ionic salt” like NaCl. Sodium transfers its electron to chlorine.

Coulomb’s law states that the magnitude of the electrostatic force between two charged particles is directly proportional to the product of the magnitude of each of the charges, and inversely proportional to the square of the distance between the two particles.

This holds for all charged particles, and can be applied to calculate force between the atoms in an ionic bond.

F ∝ q1*q2 / r2

q1 and q2: charge magnitude of the ions
r = distance between the ions

NaCl will have stronger bonds between adjacent atoms than KBr, due to the stronger electrostatic force between ions.

The electrostatic force would be increased by a factor of 4, quadruple the original value.

Forig∝ q1*q2 / r2
since new R = r/2 :
Fnew ∝ q1*q2 / R2
= q1*q2 / (r/2)2
= q1*q2 / (r2/4)
= Forig/(1/4) = Forig*4

The lattice energy of an ionic compound is the energy associated with forming a crystalline lattice of the compound from the gaseous ions. This may also be referred to as “heat of formation”.

Note: The value of lattice energy is negative, showing that the formation of an ionic compound is exothermic.

E ∝ q1*q2 / r

This holds for all charged particles, hence can be applied to calculate energy between the atoms in an ionic bond.

q1 and q2: charge magnitude of the atom
r = distance

Note: the value of E will always be negative, due to the charges always being opposite in an ionic compound.

The energy will be decreased by a factor of 2, or half the initial value.

Eorig ∝ q1*q2 / r

since new R = 2r :

Enew ∝ q1*q2 / R

= q1*q2 / 2r = Eorig/2

These are all ionic compounds, commonly referred to as salts. Ionic bonds will generally form between metals and nonmetals.

Ex: Classic examples of ionic compounds will usually include a cation from column I or II bonded to an anion from the halogen family.

A covalent bond forms when a nonmetal bonds with another nonmetal by sharing electrons between them, resulting in an overlap of their electron orbitals.

The image below of methane shows the polar covalent C-H bonds.

1. polar covalent (electrons are held more closely by the higher electronegative species)

2. non-polar covalent bond (electrons are perfectly shared between atoms of the same element)

3. coordinate covalent bond (molecules share electrons for greater net stability)

Ionic bonds create stronger intermolecular forces than pure covalent bonds. Since ionic bonds are extremely polar (more so than ANY covalent bond, by definition), there is a strong electrostatic interaction between the ions.

The melting point and boiling point will both be higher for ionic compounds, as more energy is required to pull the molecules apart.

In a nonpolar covalent bond, both atoms are the same element hence the electron pair is shared equally. On many exams like the AP Chem exam, pure covalent can only be the following diatomics: Br2, I2, N2, Cl2, H2, O2, F2.
(BrINClHOF)

Note: though some chemistry texts will also include bonds like the C-H bond (since it only measures .4 on the Pauling scale), this is clearly still polar since electrons favor carbon over hydrogen.

In a polar covalent bond, the electron pair is pulled closer to the more electronegative atom. The result of this is a bond dipole (one end positive, one end negative), hence the term “polar”. The atom that is more electronegative will carry a partial negative charge and the atom that is less electronegative will carry a partial positive charge.

Examples of polar covalent bonds include O-H bonds, N-H bonds, and C-N bonds.

In a coordinate covalent bond between molecules, one atom from one molecule will contribute both electrons to the bond pair. This creates better stability between both molecules.

Ex: Lewis Acid/Base pairs: NH3 (N donates the electron pair) and H+ (H+ accepts the electron pair). Nitrogen had a full octet to start with, but was very polar until donating the electrons to the bond with hydrogen; H+ didn't have any electrons, but now will have a full 1s subshell; both are now more stable.
The first equation below is showing all of the actual valence electrons, the second equation below is the Lewis diagram representation.

By definition, a coordinate-covalent bond is sharing electrons from one molecule to another. Lewis acid/base pairs combine in exactly that fashion.

A Lewis acid is a species that will accept an electron pair (ex: Boron in BF3).
A Lewis base is a species that will donate an electron pair (ex: Nitrogen in NH3).

Nonmetallic elements form covalent bonds.

Nonmetals tend to have similar values of electronegativity, and thus share electron density fairly evenly when bound together.

Metals-nonmetal bonds will be ionic.

The electronegative nonmetal withdraws one or more electrons from the electropositive metal, leaving each species ionically charged.

A lattice of positively charged nuclei in a background "sea" of free-flowing negatively charged electrons.

The valence electrons of metals are loosely bound to the atomic cores, and can be considered to be effectively unattached.

The "sea" of electrons are able to drift through the electron structure, moving from ion to ion gives these molecules the ability to conduct electricity.

In metallic bonding each metal atom in the crystal structure contributes valence electrons to form a "sea" of delocalized electrons.

A molecule is polar when the polar covalent bonds in the molecule add via the molecular geometry to give the entire molecule a positive vs negative end.

Ex: H2O has polar bonds between O-H, with Oxygen more electronegative = – (red in the picture) and Hydrogen = + (blue in the picture). There is a negative region (top) and a positive region (bottom). H20 is therefore a polar molecule.

When a molecule has a balanced charge distribution, such that there is not any one general positive or negative region, it is nonpolar.

Yes. Polar covalent bonds can still create a nonpolar molecule if there is symmetry in the geometry, such that the dipoles will cancel and create a balanced molecule.

Ex: in BF3 the B-F bond will pull electrons towards the more electronegative F atoms = – (red in the picture) and away from the B atom = + (blue in the picture). Though these are polar bonds, the trigonal planar symmetry keeps any one side from being net negative vs net positive.

CO2 is a nonpolar molecule. Although the C=O bond is polar, the symmetrical shape of the molecule results in cancelled dipoles and an even distribution of charge.

Ex: in the following diagram oxygen atoms are red, the carbon atom is black.

• bonding pair: a pair of electrons that is shared between two atoms across a bond (represented by a line in the Lewis diagram)

• lone pair: a pair that is associated with only one atom and stays on just that atom (represented by two close dots in the Lewis diagram)

Dipole moment refers to any bond where there is a separation of positive and negative charge across it. By common convention, the partial charges +δ and δ- are used to indicate the positive and negative ends of the bond, respectively.

1. The C=O bonds in CO2 have a higher dipole moment, due to oxygen's high electronegativity, than the less polar C-H bonds in CH4.

2. The ionic NaCl bond has a higher dipole moment than the covalent O-H bond in H2O.

3. The polar covalent N-H bond in NH3 has a higher dipole moment than the pure covalent O=O bond in O2.

A Lewis structure is a representation of a molecule that shows how electrons are being shared between atoms.

Characteristically:

• every line represents a shared electron pair

• every dot represents one electron

Ex: The image below (for H2O) shows the original atoms on the left, then how confusing it would look without a Lewis structure, then on the far right the proper Lewis structure is displayed.

The formal charge of an atom in a Lewis structure is the charge it would have if all bonding electrons were shared equally between the bonded atoms.

Typically, a molecule's ideal Lewis Structures will have zero formal charge each atom.

Formal charge = (# of valence electrons) - (# of lone pair electrons) - (1/2 # of bonding electrons)

FC is essentially a fictitious charge assigned to each atom in a Lewis structure just for the sake of helping distinguish the best Lewis structure for a molecule.

To calculate formal charge for an atom in a given Lewis structure diagram:

FC = # valence electrons - lines - dots.

Ex: in CO2, Carbon has 4 valence, 4 lines and 0 dots, FC = 4-4-0 = 0. Oxygen has 6 valence and 4 dots and 2 lines, FC = 6-4-2 = 0.

A resonance structure is when two or more valid (stable) Lewis structures can be drawn for the same compound.

In resonance structures only the strength of bonds between atoms varies, not the actual placement of the atoms. If multiple resonance structures exist, the actual molecule's structure is an average of all of these.

Ex: the benzene molecule below has two possible structures, so the C-C bonds have an average bond order of 1.5 in any given position, due to resonance.

Average bond strength is simply the average strengths of the bond between the atoms in each resonance structure.

In short: total the bonds between the two atoms in each resonance structure, then divide by the total number of structures.

Ex: To calculate the N-O bond order in nitrate (below), consider the upper oxygen. There are 2 bonds + 1 bond + 1 bond =4 total bonds possible in that position, across the 3 structures. Hence the average bond strength is 4/3.

The valence shell electron pair repulsion (VSEPR) theory states that electron pairs repel each other. Therefore, in order for a molecule to be at its most stable state, electron pairs should be as far from each other as possible in 3-dimensional space.

A chemical bond occurs when one partially-filled orbital of one atom overlaps with a partially-filled orbital of another atom, allowing both to attain a more stable state by sharing electrons. A single bond has one shared pair, a double bond has two pairs (4 total), and a triple bond has three pairs (6 total).

Note: Atoms typically form bonds until they attain a full octet of valence electrons.

When considering electron pair repulsion, remember that it is the negative character of the electrons that forms the basis of the repulsion. A pair of nonbonded electrons has more negative character than a pair of bonding electrons, since the nonbonded electrons are not shared between two positive nuclei.

So, two lone pairs will repel each other the most, while two bonded pair will suffer the least repulsion. The repulsion between a lone pair and a bonded pair is somewhere in between.

A linear molecule:

• has 3 atoms bonded.

• atoms are arranged 180 degrees apart.

• usually contains two double bonds, or one triple and one single bond.

Classic examples include: CO2 (double double) and HCN (single triple)

A bent molecule:

• has 3 atoms bonded.

• has a 104.5 degree bond-bond angle.

• contains two single bonds and two lone e- pairs.

Classic examples include: H2O and SCl2

A trigonal planar molecule:

• generally has 4 atoms bonded (one central atom and 3 peripheral).

• has a 120 degrees bond-bond angle.

Classic examples include: SO3 (3 double bonds), BF3 (3 single bonds), H2CO (two single bonds, one double bond)

A trigonal pyramidal molecule:

• generally has 4 atoms bonded (1 central and 3 peripheral).

• has a 107 degree bond-bond angle.

• contains 3 single bonds, and one lone e- pair.

Classic examples include: NH3 and PCl3

A tetrahedral molecule:

• generally has 5 atoms bonded (1 central and 4 peripheral).

• has a 109.5 degrees bond-bond angle.

• contains 4 single bonds.

Classic examples include: CH4 and CCl4

Molecular geometry is the actual placement of atoms in a molecule, ignoring any non-bonded electrons.

Ex: H2O has two hydrogen atoms placed in a "bent" structure, so this is a bent molecular geometry.

Electronic geometry is the position of all bonding electrons and lone e- pairs around one central atom.

Ex: in H2O, oxygen has two hydrogens bonded and two lone e- pairs skew to those bonds, for 4 total electron positions in a tetrahedral shape around the oxygen. H2O has tetrahedral electronic geometry, while its molecular geometry is bent.

1. A hybrid orbital is formed when standard atomic orbitals combine, and are given a name that represents which orbitals have overlapped.

2. The most common hybrid orbitals are sp, sp2, and sp3 orbitals.

sp: an s orbital and a p orbital hybridize
sp2: an s orbital and two p orbitals hybridize
sp3: an s orbital and three p orbitals hybridize

• One s orbital mixes with one p orbital creating two energetically equivalent hybrid sp orbitals.

• The two remaining unhybridized p orbitals lie at right angles to the plane of the hybrid orbitals.

• The molecule will be linear in geometry.

Common examples: C2H2, BeCl2

• One s orbital mixes with two p orbitals.

• The one remaining unhybridized p orbital lies at a right angle to the plane of the three hybrid orbitals.

• The resulting molecule will be trigonal planar in geometry.

Common examples: H2CO, BF3

• One s orbital mixes with three p orbitals.

• The resulting molecule will be tetrahedral in geometry.

• There are 4 single bonds around a central carbon atom.

Common examples: CH4, CCl4

A sigma bond occurs when atomic orbitals overlap end to end and result in an accumulation of electron density directly between the nuclei.

Sigma bonds generally exist as single bonds, but a sigma bond also makes up one bond of a double bond or triple bond.

Pi bonds are parallel regions of electron density that overlap and form orbitals alongside an initial sigma bond. They are generally the result of p orbitals overlapping side by side so the electron density is above and below the internuclear axis.

Pi bonds make up one bond in a double bond, and two bonds in a triple bond.

• The two C-H bonds are single bonds = 2 sigma bonds

• The C≡C form a triple bond = 1 sigma and 2 pi bonds

• Therefore, there are a total of 3 sigma and 2 pi bonds

1. A single bond contains one sigma bond and no pi bonds.

2. A double bond contains one sigma bond and one pi bond.

3. A triple bond contains one sigma bond and two pi bonds.

1. Draw the molecule (or look at the Lewis structure).

2. Count the number of atoms bonded around the carbon.

3. The hybridization of carbon = sp(x-1), where x is the number of atoms bound to the carbon.

Ex: CH4 has 4 atoms bonded around carbon, so its hybridization must be sp(4-1)=sp3

Use the shortcut: if x total atoms are bonded to the carbon, then the carbon's hybridization is sp(x-1).

1. H2CO: sp2 (three atoms bonded)

2. CCl4: sp3 (four atoms bonded)

3. CO2: sp (two atoms bonded)

4. HCN: sp (two atoms bonded)

Note: hybridization does not need to take into account the difference between the double-double bonds in CO2 vs the single-triple bonds in HCN.

A central atom by definition is the atom in a molecule that is bonded to more than one other atom, has the highest number of valence electrons, and the lowest electronegaivity. All of these qualities make it likely to create a hybrid in order have more active valence electrons and hence more bonds.