In the early parts of a chemistry class we think of a chemical reaction as a one-time event: either compounds react, or they don’t react. Nothing.

But quite often the reality is dynamic: Chemical A and B combine to make AB…. but AB breaks apart back into A and B. Then those individual A and B can eventually recombine again into AB. 

So on a microscopic level, individual reactions never cease.

Yet at the macroscopic level, the reaction seems to have come to a stop.

What does happen, is that at any given pressure and temperature, we’ll end up with an equilibrium: there will be a constant, certain amount of separate pieces, and a constant, certain amount of combined pieces.

We can make a ratio of [separate pieces] compared to [combined pieces.]

This ratio is called an equilibrium constant.

Here is a visual of a situation, not about chemical reactions, but about locations. We create a ratio of how much is one one side compared to how much is on another side. 

 

Online lessons

CK-12 Chemistry LeChatelier’s Principle

CK-12 LeChatelier’s Principle and the Equilibrium Constant

Dynamic Equilibrium and Le Chatelier’s Principle

Opentextbc.ca Shifting Equilibria: Le Chatelier’s Principle

Libretexts Chemistry – Le Chatelier’s Principle

Here is a fantastic infographic by Compound Interest

 

Apps & interactives

PhET apps – Reactions & Rates, and Reversible Reactions

interactives CK-12 Scroll down to “Flat vs Fizyy Soda”

elearning at Cal Poly Pomona – Kinetics, Equilibrium, and then Le Chatelier.

PLIX Le Châtelier’s Principle and the Equilibrium Constant

The Law of Mass Action, Wolfram

Le Chatelier’s Principle in Chemical Equilibrium, Wolfram

 

Constructing an equilibrium expression

See the lesson here Dynamicscience.com equilibrium4

 

Learning Standards

NGSS

HS-PS1-6. Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium. Clarification Statement: Emphasis is on the application of Le Chatelier’s Principle and on refining designs of chemical reaction systems, including descriptions of the connection between changes made at the macroscopic level and what happens at the molecular level.

Massachusetts

HS-PS1-6. Design ways to control the extent of a reaction at equilibrium (relative amount of products to reactants) by altering various conditions using Le Chatelier’s principle. Make arguments based on kinetic molecular theory to account for how altering conditions would affect the forward and reverse rates of the reaction until a new equilibrium is established.*

Massachusetts State Assessment Boundaries:
• Calculations of equilibrium constants or concentrations are not expected in state assessment.
• State assessment will be limited to simple reactions in which there are only two reactants and to specifying the change in only one variable at a time.

 

Content objective (What are we learning & why?)

Lewis theory and the octet rule are not enough to describe the shapes of molecules and many of their properties.
To go beyond such limitations we learn molecular orbital theory.

Prerequisites (What do we need to know before starting this unit?)

Lewis structures; the octet rule; covalent & ionic bonds

sub-atomic particles;  s, p, d, and f orbitals

the wave nature of matter; Schrödinger model of the atom

Shorthand notation reminder

e- = electron

Introduction

By this time it may be no surprise to you that the name of this theory – molecular orbitals – is a misnomer. There are no orbitals involved.

We should really call this

“Three dimensional electron-clouds, overlapping with other three dimensional electron-clouds, to make even more complicated and pretty electron-clouds theory”

But that’s way too many words. So “molecular orbitals” it is 😉

Remember, electrons are not solid objects like billiard balls.

And e- don’t really orbit an atom’s nucleus.

Electrons are better described as a rippling waves.

How does the Schrödinger equation create orbitals?

When we interact with e- in certain ways, sure they have particle-like properties.

But most of the time they have wave-like properties.

If you feel like it, you can learn a bit about quantum mechanics here.

What does this mean? When atoms get close to each other, the 3D wave function of one e- overlaps with the 3D wave function of another e-.

This creates constructive interference and destructive interference:

high parts of one wave combine with high parts of another wave to make even higher waves

A high part of a wave can be canceled out by hitting a low point of another wave.

Electrons work like this – except they have three dimensional waves (the GIF above is only 2D.)

In this unit we’re going to see what happens to the shape of orbitals when atoms come close enough to bond with each other.

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This next section has been adapted from Prentice Hall Chemistry by Wilbraham, Staley, Matta and Waterman.

Sigma Bonds

Atomic orbitals can combine to form a molecular orbital that is symmetrical around the axis connecting atomic nuclei. This is called a sigma bond.

We use the Greek letter sigma (σ).

Covalent bonding results from an imbalance between the attractions and repulsions of the nuclei and e- involved.

This next image is from Valence Bond Theory, LibreTexts

Because their charges have opposite signs, the nuclei and e- attract each other.

Because their charges have the same sign, nuclei repel other nuclei, and e- repel other e-.

In a hydrogen molecule (H2), the nuclei repel each other, as do the e-.

In a bonding molecular orbital of hydrogen, however, the attractions between the H nuclei and the e- are stronger than the repulsions.

The balance of all the interactions between the H atoms is thus tipped in favor of holding the atoms together.

The result is a stable, diatomic molecule of H2.

Atomic p orbitals can also overlap to form molecular orbitals.

A fluorine atom, for example, has a half-filled 2p orbital.

When two fluorine atoms combine then the p orbitals overlap to produce a bonding molecular orbital.

There is a high probability of finding a pair of e- between the positively charged nuclei of the two fluorines.

The fluorine nuclei are attracted to this region of high e- density.

This attraction holds the atoms together in the fluorine molecule (F2).

The overlap of the 2p orbitals produces a bonding molecular orbital that is symmetrical when viewed around the F⎯F bond axis connecting the nuclei.

Therefore, the F⎯F bond is a sigma bond.

Pi bonds, π bonds

“Pi” is symbolized by the Greek letter π.

In the sigma bond of the F2 molecule, the p atomic orbitals overlap end-to-end.

In some molecules, however, orbitals can overlap side-by-side.

The side-by-side overlap of atomic p orbitals produces pi molecular orbitals.

When a pi molecular orbital is filled with two electrons, a pi bond results.

In a pi bond, the bonding e- are most likely to be found in sausage-shaped regions above and below the bond axis of the bonded atoms.

It is not symmetrical around the F⎯F bond axis.

Atomic orbitals in pi bonding overlap less than in sigma bonding.

Therefore, pi bonds tend to be weaker than sigma bonds.

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Bonding and antibonding

When orbitals interact, the result can be bonding or antibonding.

Bonding molecular orbitals

Occurs when the interactions between the orbitals are constructive.

They are lower in energy than the orbitals that combine to produce them.

Antibonding molecular orbitals

Occurs when the interactions between the orbitals are are destructive (out-of-phase.)

The destructive interference creates a long, thin, region where the probability of finding an e- is effectively zero. We call this region a nodal plane.

They are basically an orbital containing an e- outside the region between the two nuclei.

They are higher in energy than the orbitals that combine to produce them.

Do both bonding and antibonding orbitals exist in the same molecule at the same time?

Yes. They both can develop as atoms come together to form a molecule. Both exist at the same time.

The resultant behavior of the molecule depends on how all the orbitals – bonding and antibonding – add together.

Let’s watch Pi orbitals develop

Here we see the Pi bonding orbital forming as P orbitals, from two atoms moving closer, slowly come together.

Here we see two P orbitals come together to form what is known as the antibonding Pi orbital. Notice that we see a nodal plane develop!

These two animations were created by Mohammad Alhudaithi using Wolfram Alpha. See Visualizing Molecular Orbitals for One Electron Diatomic Molecules.

Example: two O atoms bonding

Here we see 2 O atoms bonding together to create an O2 molecule.

Each atom has its own three-dimensional e- orbitals.

As the atoms get closer the wave functions overlap. The subsequent constructive and destructive interference creates a new three dimensional shape, one for the molecule as a whole.

The original 2s and 2p atomic orbitals merge to create Sigma and Pi orbitals. These bind the atoms together.

The 1s orbitals do not combine and still show the individual atoms.

This GIF is from O2 Molecular Orbitals Animation at Wikimedia by Kilohn Limahn.

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Deep thoughts

Because arguments based on atomic orbitals focus on the bonds formed between valence electrons on an atom, they are often said to involve a valence-bond theory.

The valence-bond model can’t adequately explain the fact that some molecules contains two equivalent bonds with a bond order between that of a single bond and a double bond.

The best it can do is suggest that these molecules are mixtures, or hybrids, of the two Lewis structures that can be written for these molecules.

This problem, and many others, can be overcome by using a more sophisticated model of bonding based on molecular orbitals.

Molecular orbital theory is more powerful than valence-bond theory because the orbitals reflect the geometry of the molecule to which they are applied. But this power carries a significant cost in terms of the ease with which the model can be visualized.

Molecular Orbital Theory, Purdue, Chemical Education Division Groups, Bodner Research Web, General Chemistry Help, The Covalent bond

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Deep thoughts

Molecular Orbital theory (MO) is the most important quantum mechanical theory for describing bonding in molecules. It is an approximate theory (as any theory that utilizes “orbitals”), but it is a very good approximation of the bonding.

The MO perspective on electrons in molecules is very different from that of a localized bonding picture such as valence bond (VB) theory.

In VB we describe particular bonds as coming from the overlap of orbitals on atomic centers.

In MO this idea is not completely gone, but now rather than just looking at individual bonds, MO describes the whole molecule as one big system.

The orbitals from MO theory are spread out over the entire molecule rather than being associated with a bond between only two atoms.

Each MO can have a particular shape such that some orbitals have greater electron density in one place or another, but in the end the orbitals now “belong” to the molecule rather than any particular bond.

For diatomic molecules (which we look at a lot), the VB picture and the MO picture are very similar. This is because the whole molecule is simply two atoms bonded together. The difference become more apparent when we look at MO in larger molecules.

Molecular orbitals, Chemistry 301 , Univ of Texas

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Teaching molecular orbitals with the relationships analogy:

This is a great lesson which starts of simple and then brings you into a series of analogy that eventually lets you understand the topic:

From the introduction – “A lot of people say they’re happy being single, and I believe that many likely are. But in the back of their mind of many single people is the thought that if they just found the right person, they might be even happier – or less unhappy, which is a crappy way to look at it psychologically but necessary if you wish to draw a diagram where a “happy couple” is occupying a “potential energy well”, below.”

and then analogies and diagrams grow from here…

Bonding And Antibonding Pi Orbitals, by James Ashenhurst, Master organic chemistry

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Relating molecular orbital theory to quantum mechanics and standing waves

The Lewis Structure approach provides an extremely simple method for determining the electronic structure of many molecules. It is a bit simplistic, however, and does have trouble predicting structures for a few molecules.

Nevertheless, it gives a reasonable structure for many molecules and its simplicity to use makes it a very useful tool for chemists.

A more general, but slightly more complicated approach is the Molecular Orbital Theory. This theory builds on the electron wave functions of Quantum Mechanics to describe chemical bonding.

To understand MO Theory let’s first review constructive and destructive interference of standing waves starting with the full constructive and destructive interference that occurs when standing waves overlap completely.

Molecular Orbital Theory by Philip J. Grandinetti

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Very advanced questions

Valence electrons are associated with molecular orbitals and hybridizations. Do core electrons have molecular/hybridized orbitals, or the original atomic orbitals?

Do core electrons have molecular orbitals?

Apps and interactives

Real-Time Visualization of the Quantum Mechanical Atomic Orbitals, Dauger Research, Atom In A Box, app for Macintosh and iPad

When we draw electron structures or orbital box diagrams, we are following a pattern, the octet “rule.” But there are many exceptions to this pattern, especially with heavier atoms and transition metals.

See page 190, Prentice Hall Chemistry, Wilbraham et al. Section 7.1 ions.

Article

This section excerpted from 9.6: Exceptions to the Octet Rule, from Chemistry: Principles, Patterns, and Applications by Bruce A. Averill and Patricia Eldredge.

General exceptions to the octet rule include molecules that have an odd number of electrons and molecules in which one or more atoms possess more or fewer than eight electrons.

Molecules with an odd number of electrons are relatively rare in the s and p blocks but rather common among the d– and f-block elements.

Compounds with more than an octet of electrons around an atom are called expanded-valence molecules.

One model to explain their existence uses one or more d orbitals in bonding in addition to the valence ns and np orbitals.

Such species are known for only atoms in period 3 or below, which contain nd subshells in their valence shell.

Learning Objective: assign a Lewis dot symbol to elements not having an octet of electrons in their compounds.

Lewis dot structures provide a simple model for rationalizing the bonding in most known compounds. However, there are three general exceptions to the octet rule:

1. Molecules, such as NO, with an odd number of electrons;

2. Molecules in which one or more atoms possess more than eight electrons, such as SF₆; and

3. Molecules such as BCl₃, in which one or more atoms possess less than eight electrons.

Example 1: The NO Molecule. Draw the Lewis structure for the molecule nitrous oxide (NO).

5. There are currently 5 valence electrons around the nitrogen.

A double bond would place 7 electrons around the nitrogen, and a triple bond would place 9 around the nitrogen. We appear unable to get an octet around each atom.

 

More Than an Octet of Electrons

The most common exception to the octet rule is a molecule or an ion with at least one atom that possesses more than an octet of electrons. Such compounds are found for elements of period 3 and beyond.

Examples from the p-block elements include SF₆, a substance used by the electric power industry to insulate high-voltage lines, and the SO₄²⁻ and PO₄³⁻ ions.

Let’s look at sulfur hexafluoride (SF₆), whose Lewis structure must accommodate a total of 48 valence electrons [6 + (6 × 7) = 48].

If we arrange the atoms and electrons symmetrically, we obtain a structure with six bonds to sulfur; that is, it is six-coordinate.

Each fluorine atom has an octet, but the sulfur atom has 12 electrons surrounding it rather than 8.

The third step in our procedure for writing Lewis electron structures, in which we place an electron pair between each pair of bonded atoms, requires that an atom have more than 8 electrons whenever it is bonded to more than 4 other atoms.

Basis of the octet rule

The octet rule is based on the fact that each valence orbital (typically, one ns and three np orbitals) can accommodate only two electrons.

To accommodate more than eight electrons, sulfur must be using not only the ns and np valence orbitals but additional orbitals as well.

Sulfur has an [Ne]3s²3p⁴3d⁰ electron configuration, so in principle it could accommodate more than eight valence electrons by using one or more d orbitals.

Thus, species such as SF₆ are often called expanded-valence molecules.

Whether or not such compounds really do use d orbitals in bonding is controversial, but this model explains why compounds exist with more than an octet of electrons around an atom.

There is no correlation between the stability of a molecule or an ion and whether or not it has an expanded valence shell.

Some species with expanded valences, such as PF₅, are highly reactive, whereas others, such as SF₆, are very unreactive.

In fact, SF₆ is so inert that it has many commercial applications. In addition to its use as an electrical insulator, it is used as the coolant in some nuclear power plants, and it is the pressurizing gas in “unpressurized” tennis balls.

An expanded valence shell is often written for oxoanions of the heavier p-block elements, such as sulfate (SO₄²⁻) and phosphate (PO₄³⁻).

Sulfate, for example, has a total of 32 valence electrons [6 + (4 × 6) + 2]. If we use a single pair of electrons to connect the sulfur and each oxygen, we obtain the four-coordinate Lewis structure

(a). We know that sulfur can accommodate more than eight electrons by using its empty valence d orbitals, just as in SF₆.

An alternative structure (b) can be written with S=O double bonds, making the sulfur again six-coordinate.

We can draw five other resonance structures equivalent to (b) that vary only in the arrangement of the single and double bonds.

In fact, experimental data show that the S-to-O bonds in the SO₄²⁻ ion are intermediate in length between single and double bonds, as expected for a system whose resonance structures all contain two S–O single bonds and two S=O double bonds.

When calculating the formal charges on structures (a) and (b), we see that the S atom in (a) has a formal charge of +2, whereas the S atom in (b) has a formal charge of 0.

Thus by using an expanded octet, a +2 formal charge on S can be eliminated.

Less Than an Octet of Electrons

Molecules with atoms that possess less than an octet of electrons generally contain the lighter s- and p-block elements.

Especially so for beryllium, typically with just four electrons around the central atom, and with boron, typically with six.

One example, boron trichloride (BCl3) is used to produce fibers for reinforcing high-tech tennis rackets and golf clubs.

The compound has 24 valence electrons and the following Lewis structure:

The boron atom has only six valence electrons, while each chlorine atom has eight.

A reasonable solution might be to use a lone pair from one of the chlorine atoms to form a B-to-Cl double bond:

This resonance structure, however, results in a formal charge of +1 on the doubly bonded Cl atom and −1 on the B atom.

The high electronegativity of Cl makes this separation of charge unlikely and suggests that this is not the most important resonance structure for BCl3.

This conclusion is shown to be valid based on the three equivalent B–Cl bond lengths of 173 pm that have no double bond character.

Electron-deficient compounds such as BCl3 have a strong tendency to gain an additional pair of electrons by reacting with species with a lone pair of electrons.

Example 8

Draw Lewis dot structures for each compound.

(a) BeCl2 gas, a compound used to produce beryllium, which in turn is used to produce structural materials for missiles and communication satellites.

(b) SF4, a compound that reacts violently with water

Include resonance structures where appropriate.

Given: two compounds

Asked for: Lewis electron structures

Strategy:

(A) Use the procedure given earlier to write a Lewis electron structure for each compound. If necessary, place any remaining valence electrons on the element most likely to be able to accommodate more than an octet.

(B) After all the valence electrons have been placed, decide whether you have drawn an acceptable Lewis structure.

Solution:

(A) Because it is the least electronegative element, Be is the central atom. The molecule has 16 valence electrons (2 from Be and 7 from each Cl). Drawing two Be–Cl bonds and placing three lone pairs on each Cl gives the following structure:

(B) Although this arrangement gives beryllium only 4 electrons, it is an acceptable Lewis structure for BeCl2. Beryllium is known to form compounds in which it is surrounded by less than an octet of electrons.

Now let’s draw a structure for SF4:

Sulfur is the central atom because it is less electronegative than fluorine.

The molecule has 34 valence electrons (6 from S and 7 from each F).

The S–F bonds use 8 electrons, and another 24 are placed around the F atoms:

The only place to put the remaining 2 electrons is on the sulfur, giving sulfur 10 valence electrons:

Sulfur can accommodate more than an octet, so this is an acceptable Lewis structure.

Example: Draw Lewis dot structures for XeF4 .

Notes

• In oxoanions of the heavier p-block elements, the central atom often has an expanded valence shell.

• Molecules with atoms that have fewer than an octet of electrons generally contain the lighter s- and p-block elements.

• Electron-deficient compounds have a strong tendency to gain electrons in their reactions.

This section of this resource is available as Creative Commons Non Commercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)

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Resources

8.7: Exceptions to the Octet Rule, Chemistry: The Central Science by Brown, LeMay, Busten, Murphy, and Woodward

9.6: Exceptions to the Octet Rule Chemistry: Principles, Patterns, and Applications by Bruce A. Averill and Patricia Eldredge

9.11 Exceptions to the Octet Rule, CK-12 Chemistry for High School FlexBook

Exceptions to the Octet Rule, General Chemistry I, Dr. Michael Blaber

8.8 Exceptions to the Octet Rule Chemistry, Prentice Hall

CoreChem:Exceptions to the Octet Rule

 

Why are there exceptions to the octet rule?

Because the octet “rule” was never a rule in the first place.

https://www.quora.com/What-is-the-octet-rule-in-chemistry-Are-there-any-exceptions-to-it

https://www.quora.com/Why-does-boron-violate-the-octet-rule

Advanced Placement Chemistry discussion

Exceptions to the octet rule and resonances

Trihydridoboron, also known as borane or borine, is an unstable and highly reactive molecule with the chemical formula BH
3. The preparation of borane carbonyl, BH3(CO), played an important role in exploring the chemistry of boranes, as it indicated the likely existence of the borane molecule.[1] However, the molecular species BH3 is a very strong Lewis acid. Consequently it is highly reactive and can only be observed directly as a continuously produced, transitory, product in a flow system or from the reaction of laser ablated atomic boron with hydrogen.

See https://www.quora.com/Why-do-incomplete-octets-occur