Periodic Table: What is it Showing?
Periodic Tables on Walls and In Books: What are they showing? Why is there a problem?
Periodic tables use the design as an organising schema to list the chemical elements and to present physical data & material properties of the elements.
In their simplest form, the periodic tables show elements with only the atomic number Z and the element symbol. Strictly, this is showing the elements as the basic [transcendental, abstract] substance.
However, they may go on to state:
In this author's opinion, there has been a logical sleight-of-hand.
The metaphysical periodic table of abstract, basic substances is being passed off as a periodic table of the material properties of simple substances, which is not the same thing at all.
This causes confusion as to what exactly it is that a particular periodic table is showing.
At least three periodic tables can be identified:
When moving across these three periodic tables, the system complexity and the number of properties dramatically increases.
And there are yet more periodic tables:
Periodic tables may show the phase (solid, liquid or gas) state of the elemental materials at the standard temperature of 25°C and at other temperatures, for example 2025°C (from pTable):
All of these many & various periodic tables morph into each other to give the compound object that is commonly known as [and presented as] The Periodic Table.
The long form periodic table of basic, abstract, transcendental substances showing the only property, atomic number Z:
Periodic Table of Basic Substances (Atomic Number Z)
Element symbols and names are assigned to the atomic number Z:
Periodic Table of Basic Substances (Atomic Symbol)
In the basic substance formulation, oxygen atomic number 8 is "O" and not the common molecule "O2". Likewise, sulfur (Z = 16) is S and not the yellow solid S8.
The usual periodic table schema simply shows the element symbols in their respective periods, groups & blocks.
This, or an equivalent formulation, and there are many see the next page of this web book is the periodic table as Mendeleev would have intended it: a schema showing the elements as basic substances with their positions in the schema emphasising the periodic law:
"The periodic law is the principle that certain properties of elements occur periodically when arranged by atomic number. These similarities can be reflected best by a table, so that commonalties between elements appear both in rows and in columns of the table." Wikipedia
Author's Analysis & Comment
Arranging the chemical elements by atomic number, Z, gives simple list:
By placing the chemical elements into a table formulation explicitly assigns group & period co-ordinates to the entities that make up the [periodic] table.
For this to make any sense, some other property is being implicitly implied.
It follows, IMHO, that properties that pertain to the periodic table schema group, period & block are [must be] implicit properties of the basic element.
Thus – in this author's opinion – the quantum numbers [see the previous page of this web book] must be a basic elemental property. However, it should be said not everybody agrees with this analysis!
MRL's Basic Element Properties:
Z = 8 ∴ symbol = O ∴ electronic configuration = 1s2, 2s2, 2p4
The chemical elements as real, simple substances can be physically normalised by studying ground-state, monoatomic gas phase atoms of the material substance.
The periodic table of ground state gas phase atoms is known, and it represents the periodic table of the very simplest simple substances:
Periodic Table of Gas Phase Atoms
Apart from the title, the graphic is exactly the same as the periodic table of basic substances, but this periodic table represents real chemical entities with actual, measurable, physical properties, including:
Many modern technologies utilise gas phase atoms, including:
Crucially, when we consider the electronic structure of an atom [or the orbital structure of a molecule, for that matter], we are considering the atom to be an isolated entity, exactly as it would be in the gas phase.
Under standard conditions, 298K and 100kPa (25°C & 1.0 atm), the chemical elements as simple substances – chemical reagents, real chemicals in bottles – present as:
Several Group 4, 5 & 6 (14, 15 & 16) elements have multiple allotropes (structural forms).
Carbon can exist as graphite, diamond, C60, single walled nanotubes, etc.
The P4 form of phosphorus is defined as the standard state of the element.
The structure of astatine is actually unknown, but it may be isostructural with iodine
or it may be a metalloid.
The chemical elements as material substances have many properties, including [from WebElements: Cu]:
elements (Earth's crust)
Hardness - Vickers
NMR relative sensitivity
In the first half of twentieth century, much effort was expended trying to make the periodic table of the elements axiomatic ("self-evident" or "unquestionable"), ie. trying to fully understand the Mendeleev system in terms of quantum mechanics.
"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble."
P.A.M. Dirac, Proc.R.Soc.Lond.Ser.A 123 (1929) 714
We certainly teach school and university students that "the periodic table is fully understood in terms of electronic theory", and this line of reasoning is advanced elsewhere in this web book, here and the HyperPhysics site, here.
The argument is put forward that:
Yes, there is an empirical (experimental) correspondence between gas phase atoms and their spectra, But is there a 1-to-1-to-1 correspondence between QM, spectra and the periodic table?
Eric Scerri disputes the full and complete axiomatic mapping between theory and the periodic table:
"Electronic configurations are not [fully] reduced to quantum mechanics nor can they be derived from any other theoretical approach. They are obtained by a mixture of spectroscopic observations and semi-empirical methods like Bohr's aufbau scheme".
Has The Periodic Table Been Fully Axiomatized? Erkenntnis, 47, 229-243, 1997
Eric Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Read an interview with the author, here, and a review of the book here.
The reason for the discrepancy concerns multi-electron atoms, ions and molecules.
On this page we identify three different periodic tables:
Are any of these periodic tables axiomatized with respect to theory?
Note that a distinction has been introduced between "quantum chemistry", the techniques, methodologies and computer software used by physical chemists and chemical physicists, and the underlying quantum mechanics in the form of quantum electrodynamics (QED), the most accurate and precise theory known to humankind. However, chemical problems are simply too involved [currently] to be studied by QED, although in principle they can be.
Q: Has The Periodic Table of Chemical Substances Under Standard Conditions Been Axiomatized?
The elements-as-chemicals periodic table – real simple material substances under standard conditions of temp & pressure – is certainly not axiomatized. Quantum chemistry calculations cannot predict the equation of state of an element.
The Schrödinger wave equation without mathematical approximation cannot be used to predict that sulfur exists in S8 rings, that copper is a reddish coloured metal or that mercury is a liquid at room temperature.
Q: Has The Periodic Table of Gas Phase Atoms Been Axiomatized?
Multi-electron atoms, even as isolated gaseous atoms, are too complex to be understood fully and exactly... although modern quantum chemistry mathematical modelling techniques do give very good and useful answers.
There is no formal proof of one-to-one-to-one correspondence between quantum chemistry methodology, atomic spectra and the periodic table of gas phase atomic simple substances, although the predictions are useful:
Q: Has The Periodic Table of Metaphysical Basic Elements Been Axiomatized?
The essential, metaphysical basic elements do not have properties other than atomic number, group and period... so we can can ignore spectra and simply concentrate on the pattern of the periodic table schema.
It is proposed here that yes, the periodic table of metaphysical basic substances is axiomatic with respect to theory, in that the pattern of the periodic table can be deduced from the quantum theory directly.
The techniques of quantum chemistry cannot/do not completely axiomatically describe gas phase atoms (except H, He+, Li2+, etc.), because multi-electron systems are too complex to be described analytically.
However, the various quantum chemistry techniques/models are good enough for the periodicity of the metaphysical basic substances to be mapped to the periodic tables of gas phase and material simple substances.
The periodic table of metaphysical, essential, basic elemental substances can be reduced to quantum numbers and simple rules (the old quantum theory)... but Richard Feynman told us (here): "I think I can safely say that nobody understands quantum mechanics."
In other words, we cannot unpick quantum mechanics and ask "where it all comes from": it is simply how our world works.
The relationship between the old quantum theory and the Schrödinger wave equation is mysterious...
The periodic law is a property of the periodic table. As a consequence, periodicity and periodic trends get mapped to the element-the-basic-substance along with block, period & group.
Average atomic mass maps closely but not exactly to atomic number, and there are anomalies. However, most commentators would agree with the statement that "generally atomic mass increases with atomic number, Z" and this is a classic manifestation of the periodic law.
Electronegativity is a parameter of huge importance to understanding and predicting chemical structure and reactivity.
There is a clear electronegativity trend across the periodic table in its long form from the (Group 17) top-right where the most electronegative elements are found to the bottom-left where there are electropositive elements. This trend is a manifestation of the periodic law.
This author holds that while the actual elemental electronegativity data, for example (revised Pauling):
Cl 3.16, etc.
is a property of the simple elemental substance, the periodic trend is a manifestation of the periodic law that is inherent to the periodic table.
Like atomic number, Z, electronegativity is an atomic property that is conserved in molecules and ionic substances.
It follows that relative electronegativity is a basic property and not a simple property.
From the underlying quantum patterns element Z = 9 [Period 2, Group 17, fluorine, F] is electronegative, and indeed *must* be the most electronegative element. It is just how quantum mechanics works (and we do not understand QM in terms of a deeper theory).
Thus, the relative electronegativity of element Z = 9, for example, is a basic (essential) elemental property that comes from periodicity and the periodic law, even though the absolute electronegativity of the simple (real) elemental substance is 3.98.
The reader may consider that the concept of element-as-basic-substance and element-as-simple-substance to be an arcane distraction limited to the study of the periodic table. However, the idea is actually rather general and has implications for how we understand and teach the subject of chemistry.
Beginning students of chemistry always have access to periodic tables, but unfortunately not the PT they actually need.
Students are expected to know that in all equations hydrogen is molecular should [nearly always] be written as H2. Likewise, nitrogen is N2, oxygen O2, fluorine F2, chlorine Cl2, bromine Br2 and iodine I2, and should always be written as the dimeric species. But somehow students are expected to know that molecular sulfur, S8, and phosphorus, P4, should be written as S and P.
These matters are explored further elsewhere in the Chemogenesis web book.
|Quantum Numbers to Periodic Tables||
Periodic Table Formulations
© Mark R. Leach 1999-
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