Periodic Table: What is it Showing?
Periodic Tables on Walls and In Books: What are they showing?
Most periodic tables in books, most periodic tables on classroom walls and most periodic tables on web sites use the periodic table as an organising schema to present physical data & material properties of the elements.
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:
There are other periodic tables:
The various periodic tables morph into each other to give the compound object commonly presented as The Periodic Table.
When moving across these various PTs the system complexity increase.
There is also the important notion of the elements in a compound; ie the nature of the element sodium and the nature of the element chlorine in the ionic substance sodium chloride.
Periodic tables generally show the chemical elements as the basic substance:
For example, oxygen is show as O and not as the common molecular form O2. Likewise, sulfur is shown as S and not 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
It is commonly held [Scerri] that there is only one basic elemental property: atomic number, Z, where the element's name and symbol are assigned to Z.
But arranging the chemical elements by mass or atomic number, Z, will only give a simple list.
Placing the chemical elements into a table that explicitly displays periodicity assigns x, y (group, period) co-ordinates to the entities that make up the periodic table: the chemical elements. It follows that properties that pertain to the periodic table schema itself block, group, period & periodicity map to, and are properties of, the basic element. Quantum numbers, here, can be used (mapped) to the various periodic table formulations. Therefore – in this author's opinion – quantum numbers must be a basic elemental property.
Basic Element Properties:
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 is the periodic table of the very simplest of simple substances:
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:
- Average atomic mass
- Atomic radius
- Accurate mass & abundance of the isotopes
- Effective nuclear charge
- Electron affinity
- Electron binding energies
- Ionisation energies
- Emission spectra. The University of Oregon Department of Physics has a dynamic periodic table, here, that shows the atomic spectra of all the elements:
Many modern technologies utilise gas phase atoms, including: the sodium vapour lamps used for street lighting and atomic clocks. Many man-made trans-uranium elements are only known as isolated gas phase atoms.
It may be thought that the common form of the periodic table on walls and in books is showing ground state gas phase atoms, but this seems unlikely as a substance like atomic carbon gas, C(g), is very uncommon.
Under standard conditions, 25°C & 1.0 atm, the chemical elements as simple substances – real chemicals in bottles – present as:
The chemical elements as material substances have many properties, including [from WebElements: Copper]:
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, in other words, trying to fully understand the Mendeleev system in terms of a deeper theory, that deeper theory being 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 our school and university students that "the periodic table is fully explained 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:
The pattern of spectral lines experientially obtained from a sample gas phase atoms can be "explained by" (mapped to) quantum mechanics in the form of the Schrödinger wave equation, and the spectral lines and quantum patterns obtained by experiment and theory can be mapped to the Mendeleev Periodic Table of the Elements.
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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