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Dot diagrams


2016 Massachusetts Science and Technology/Engineering Standards
HS-PS1-2. Use the periodic table model to predict and design simple reactions that result in two main classes of binary compounds, ionic and molecular. …Predictions of reactants and products can be represented using Lewis dot structures, chemical formulas, or physical models.

Objective: Students will be able to interpret and draw Lewis dot diagrams for individual atoms and both covalent and ionic compounds.

Evaluation: Use the activity sheets from Dot diagrams in-class to gives students practice interpreting Lewis dot diagrams. Use same types of problems following week as a basis for the formative assessment.

Rationale: We know that atoms may come together to form molecules. But why do they do under some circumstances, but not others? How come atoms join in certain ratios, not others? Lewis dot structures let us understand why atoms come together in the way that they do.


Atoms bond by sharing electrons  ( e- )

General rule: If the # of e- around each atom adds up to 8, and if they share a pair of e-, then they bond.

They may share 1, 2 or 3 pairs of e-

a set of 8 e- around an atom is called an octet

shared e- are a pair that count for 2 different atoms

Example: Carbon has 4 valence e-. Oxygen has 6 valence e-.

Neither has a full outer energy level (stable octet)

C and O atoms Lewis

Enter a caption

But if we put many of these atoms together then they exchange e-

Each atom feels itself surrounded by 8 e-, by sharing some of them


How many e- does an atom have available for sharing?

Consider the element Lithium. 3 p, 3 e-
How are the e- arranged?
1st energy level : 2 e-
2nd energy level: 1 e-
So only 1 e- is in the outer energy level -> 1 e- is available for sharing


Consider the element Sodium. 11 p, 11 e-
How are the e- arranged?
1st energy level : 2 e-
2nd energy level: 8 e-
3rd energy level: 1 e-
So only 1 e- is in the outer energy level -> 1 e- is available for sharing

Sodium energy levels

This will be a pattern
All elements in a vertical column (group, family) have the same # of e- available to share.

(This is only a general pattern, not a law of physics)

The same info can be represented in different ways

(For now we’re skipping transition elements. Their pattern is more complicated)

What is a dot diagram?

Why do we draw dot diagrams?

How do we draw dot diagrams?

We draw e- as dots  •

There are many names for this

dot diagrams / dot structures

Lewis diagrams / Lewis structures

Named after Gilbert Lewis, who introduced it in his 1916 article The Atom and the Molecule

Gilbert Lewis Dot structure

While most electrons are tightly bound to their parent atom,
the electrons in the outermost energy level are more loosely bound,
and can be ripped off and shared.  These are valence electrons.

_ _ _ ____

Electron-dot symbols are derived by placing
valence e- (represented by dots) to the right, left, top,
and bottom of the element’s symbol.

Starting on any side, we place one dot at a time until there are
up to four unpaired e- around the symbol.

If there are more than four valence e- for an atom,
the remaining e- are added – one by one –
to the unpaired e- to form up to four pairs.

Lewis dot example placement

There is no set convention for the placement.
For example, chlorine atoms could be

Lewis Cl dot example placement

Noble gases have an octet (except helium, which has only 2 e- total),
and they are so stable that they rarely form chemical bonds
with other atoms.

Lewis Noble gas dot example placement

When atoms (other than the noble gas) form bonds,
they often have eight electrons around them in total.

Example: the unpaired e- of a chlorine atom often pairs
with an unpaired e- of another atom to form one covalent bond.

This gives Cl an octet. 2 e- from the two‑electron covalent bond,
and 6 from its three lone pairs.
This is why Cl gas exists as Cl2 molecules.

Lewis Cl2 gas dot example placement

Note that each chlorine atom in Cl2 has an octet of electrons.
Apparently, the formation of an octet of electrons leads to stability.

Lewis Cl2 gas second

This way of depicting a molecule—using the elements’
symbols to represent atoms and using dots to represent
valence electrons—is called a Lewis structure.
Covalent bonds are usually represented by lines in
Lewis structures, so the Lewis structure of a Cl2 molecule
can have either of two forms:

Lewis Cl2 gas third

Some atoms do not form octets.

Hydrogen atoms form one bond, achieving 2 e- around them.

H2 atoms

Enter a caption

Atoms of helium – a noble gas – have 2 e-.

When H atoms form one covalent bond, they get 2 e- around them, like He atoms.

Knowing that hydrogen atoms form one covalent bond and that chlorine atoms form one bond and have three lone pairs helps us to build the Lewis structure for a hydrogen chloride molecule, HCl:

HCl Lewis

Like chlorine, the other elements in group 7A also have seven valence electrons, so their electron-dot symbols are similar to that of chlorine. The unpaired dot can be placed on any of the four sides of each symbol.

F Br I dot structures

In order to obtain octets, atoms tend to form compounds in which they have one bond and three lone pairs.

Note how the structures of HF, HBr and HI resemble the structure of hydrogen chloride.

Hydrogen flouride Lewis

Lewis dot larger capture

from https://kaiserscience.files.wordpress.com/2014/09/bishop_book_3_ebook.pdf

PCl3 is used to make pesticides and gasoline additives.

Carbon, in group 4A, has four unpaired electrons in its electron-dot symbol

Carbon Lewis

from “An Introduction to Chemistry”, Chapter 3,  by Mark Bishop. http://preparatorychemistry.com/

Limits of dot structures

When drawing Lewis structures, sometimes you will find that there are many ways to place double bonds and lone pairs about a given framework of atoms. How does we decide whether one or another placement is correct? Neither and both.

The actual arrangement  is a weighted average of all the valid Lewis structure… The “real” molecule is said to be a resonance hybrid of all its contributing Lewis structures. .

The classical example of resonance is benzene, C6H6 .
2 good Lewis structures for benzene exist, that differ only in their placement of double bonds.
If either structure were correct, then benzene would consist of alternating long single bonds and short double bonds.
However, it has been determined experimentally that all 6 bonds are identical.
One interpretation is that the 3 double bonds are distributed evenly around the ring, so that each bond has a bond order of one and a half.
A double headed arrow is placed between resonance structures to denote them as such.




What does it really mean?

The beneze molecule doesn’t switch back-and-forth from one form to another.

Rather, Lewis diagrams simply fail for e- placement in many molecules.

If we insist on using them, then we need to draw the molecule with 2 or 3 different e- arrangements, and use arrows to imply that shift from one to the other.

But really the molecule exists in one form -an intermediate of the drawn structures.

What do the e- “really” look like?


More resources

Represent Bonding with Lewis Dot Diagrams, American Chemical Society


Overview: Dot structure and the periodic table (Click for the PDF file)

Dot structures “An Introduction to Chemistry” Mark Bishop.

11th grade: Molecular structure, Covalent bonds, Lewis structures, Resonance, Molecular Geometry


What is Lewis Theory?

from Mark R. Leach, http://www.meta-synthesis.com/webbook/30_timeline/lewis_theory.php

the study of the patterns that atoms display when they bond and react with each other.

look at many chemical systems, study patterns, count the electrons in the various patterns, and devise simple rules…Lewis theory makes no attempt to explain how or why these empirically derived numbers of electrons – these magic numbers – arise. Although, it is striking that the magic numbers are generally (but not exclusively) positive integers of even parity: 0, 2, 4, 6, 8…

For example:

  • Atoms and atomic ions show particular stability when they have a full outer or valence shell of electrons and are isoelectronic with He, Ne, Ar, Kr & Xe: Magic numbers 2, 10, 18, 36, 54.

  • Atoms have a shell electronic structure: Magic numbers 2, 8, 8, 18, 18.

  • Sodium metal reacts to give the sodium ion, Na+, a species that has a full octet of electrons in its valence shell. Magic number 8.

  • A covalent bond consist of a shared pair electrons: Magic number 2.

  • Atoms have valency, the number of chemical bonds formed by an element, which is the number of electrons in the valence shell divided by 2: Magic numbers 0 to 8.

  • Ammonia, H3N:, has a lone pair of electrons in its valence shell: Magic number 2.

  • Ethene, H2C=CH2, has a double covalent bond: Magic numbers (2 + 2)/2 = 2.

  • Nitrogen, N2, N≡N, has a triple covalent bond: Magic numbers (2 + 2 + 2)/2 = 3.

  • The methyl radical, H3C•, has a single unpaired electron in its valence shell: Magic number 1.

  • Lewis bases (proton abstractors & nucleophiles) react via an electron pair: Magic number 2.

  • Electrophiles, Lewis acids, accept a a pair of electron in order to fill their octet: Magic numbers 2 + 6 = 8.

  • Oxidation involves loss of electrons, reduction involves gain of electrons. Every redox reaction involves concurrent oxidation and reduction: Magic number 0 (overall).

  • Curly arrows represent the movement of an electron pair: Magic number 2.

  • Ammonia, NH3, and phosphine, PH3, are isoelectronic in that they have the same Lewis structure. Both have three covalent bonds and a lone pair of electrons: Magic numbers 2 & 8.

  • Aromaticity in benzene is associated with the species having 4n+2 π-electrons. Magic number 6.Naphthalene is also aromatic: Magic number 10.

  • Etc.

Lewis theory is numerology , or accountancy

 Ernest Rutherford famously said
“Physics is the only real science. The rest are just stamp collecting”

Imagine an alien culture trying to understand planet Earth using only a large collection of postage stamps. The aliens would see all sorts of patterns and would be able to deduce the existence of: countries, national currencies, pricing strategies, differential exchange rates, inflation, the existence of heads of state, what stamps are used for, etc., and – importantly – they would be able to make predictions about missing stamps.

But the aliens would be able to infer little about the biology of life on our planet by only studying stamps, although there would be hints in the data: various creatures & plants, males & females, etc.

So it is with atoms, ions, molecules, molecular ions, materials, etc. As chemists we see many patterns in chemical structure and reactivity, and we try to draw conclusions and make predictions using these patterns:

This is Lewis theory. But this Lewis approach is not complete and it only gives hints about the underlying quantum mechanics, a world observed through spectroscopy and mathematics.


Consider the pattern shown in Diagram-1:

Now expand the view slightly and look at Diagram-2:

You may feel that the right hand side “does not fit the pattern” of Diagram-1 and so is an anomaly.

So, is it an anomaly?

Zoom out a bit and look at the pattern in Diagram-3, the anomaly disappears:

But then look at Diagram-4. The purple patch on the upper right hand side does not seem to fit the pattern and so it may represent anomaly:

But zooming right out to Diagram-5 we see that everything is part of a larger regular pattern:

Digital Flowers at DryIcons

When viewing the larger scale the overall pattern emerges and everything becomes clear. Of course, the Digital Flowers pattern is trivial, whereas the interactions of electrons and positive nuclei are astonishingly subtle.

This situation is exactly like learning about chemical structure and reactivity using Lewis theory. First we learn about the ‘Lewis octet’, and we come to believe that the pattern of chemistry can be explained in terms of the very useful Lewis octet model.

Then we encounter phosphorous pentachloride, PCl5, and discover that it has 10 electrons in its valence shell. Is PCl5 an anomaly? No! The fact is that the pattern generated through the Lewis octet model is just too simple.

As we zoom out and look at more chemical structure and reactivity examples we see that the pattern is more complicated that indicated by the Lewis octet magic number 8.

Our problem is that although the patterns of electrons in chemical systems are in principle predictable, new patterns always come as a surprise when they are first discovered:

  • The periodicity of the chemical elements

  • The 4n + 2 rule of aromaticity

  • The observation that sulfur exists in S8 rings

  • The discovery of neodymium magnets in the 1990s

  • The serendipitous discovery of how to make the fullerene C60 in large amounts

While these observations can be explained after the fact, they were not predicted beforehand. We do not have the mathematical tools to do predict the nature of the quantum patterns with absolute precision.

The chemist’s approach to understanding structure and reactivity is to count the electrons and take note of the patterns. This is Lewis theory.

As chemists we attempt to ‘explain’ many of these patterns in terms of electron accountancy and magic numbers.

Caught In The Act: Theoretical Theft & Magic Number Creation

The crucial time for our understand chemical structure & bonding occurred in the busy chemistry laboratories at UC Berkeley under the leadership of G. N. Lewis in the early years of the 20th century.

Lewis and colleagues were actively debating the new ideas about atomic structure, particularly the Rutherford & Bohr atoms and postulated how they might give rise to models of chemical structure, bonding & reactivity.

Indeed, the Lewis model uses ideas directly from the Bohr atom. The Rutherford atom shows electrons whizzing about the nucleus, but to the trained eye, there is no structure to the whizzing. Introduced by Niels Bohr in 1913, the Bohr model is a quantum physics modification of the Rutherford model and is sometimes referred to the Rutherford–Bohr model. (Bohr was Rutherford’s student at the time.) The model’s key success lay in explaining (correlating with) the Rydberg formula for the spectral emission lines of atomic hydrogen.

[Greatly simplifying both the history & the science:]
In 1916 atomic theory forked or bifurcated into physics and chemistry streams:

  • The physics fork was initiated and developed by Bohr, Pauli, Sommerfield and others. Research involved studying atomic spectroscopy and this lead to the discovery of the four quantum numbers – principal, azimuthal, magnetic & spin – and their selection rules. More advanced models of chemical structure, bonding & reactivity are based upon the Schrödinger equation in which the electron is treated as a resonant standing wave. This has developed into molecular orbital theory and the discipline ofcomputational chemistry

  • Note: quantum numbers and their selection rules are not ‘magic’ numbers. The quantum numbers represent deep symmetries that are entirely self consistent across all quantum mechanics.

  • The chemistry fork started when Lewis published his first ideas about the patterns he saw in chemical bonding and reactivity in 1916, and later in a more advanced form in 1923. Lewis realised that electrons could be counted and that there were patterns associated with structure, bonding and reactivity behaviour.These early ideas have been extensively developed and are now taught to chemistry students the world over. This is Lewis theory.


Lewis Theory and Quantum Mechanics

Quantum mechanics and Lewis theory are both concerned with patterns. However, quantum mechanics actively causes the patterns whereas Lewis theory is passive and it only reports on patterns that are observed through experiment.



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