Introduction

A classic periodic table can be viewed at WebElements:

WebElements employs the most common of many possible formulations, and these can be explored using the INTERNET Database of Periodic Tables and Periodic Table Formulations, on the next page of this webbook, here.

The vast majority of Periodic Tables – and the excellent WebElements is a perfect example – are used to arrange physical, chemical, technological & historical data/information about the chemical elements in a systematic way.

Check out the various way that physical, chemical, technological & historical data/information are mapped to the Periodic Table, here.

The chemogenesis web book explores how chemical reactivity emerges from the periodic table of the elements using a root-trunk-branch chemistry-tree metaphor, with the periodic table at the base of the trunk:

The periodic schema is used in many ways and so it is interesting to ask what the periodic table actually is, and what it is showing?

It transpires that matters are a little more involved than they may at first appear...

Philosophy, Chemistry & The Periodic Table

Philosophers of chemistry consider the chemical elements in two distinct ways:

Firstly, there is the chemical element as the basic element, that is the abstract or transcendental element, the essence of the element, a bearer of properties but not having any actual properties, except for [historically, atomic mass, but now] atomic number Z. Chemical symbols, such as H and Cu, are assigned to the basic element.

Secondly, there is the element as simple substance, for example, a real piece of copper metal placed on a table has numerous, measurable, intrinsic properties such as: purity, density, conductivity, colour, melting point, molar volume, etc.

Crucially, only the basic element survives in a compound. Sodium's metallic properties and chlorine, the green gas, do not exist in the ionic salt, sodium chloride.

These matters are discussed in a paper by Eric Scerri, Some Aspects of the Metaphysics of Chemistry and the Nature of The Elements, available here. Briefly summarising these arguments:

• There is a metaphysical view about the nature of the elements as basic substances and bearers of properties that goes back to the ancient Greeks, long before the discovery of atoms.
  
  
• Mendeleev insisted that his periodic classification system concerned the elements as basic substances possessing only one attribute, atomic weight.
  
  
• Paneth, one of the founders of modern radiochemistry took Mendeleev's view about the nature of basic and simple substance, but changed the basic/transcendental/abstract property of an element from atomic weight/mass to atomic number, Z.
  
  
• Elements as basic substance represent natural kinds, a well understood philosophical position concerning the nature of classification. Elements as simple substances fail the natural kind test, due to the existence of isotopes and allotropes, etc.

Eric Scerri points out that the periodic table has, at times, been characterised as a:

• representation
• ordered domain
• classification
• system
• model
• law
• theory

This author agrees with Scerri that the periodic table is an ordered domain. But it is also a schema, a 'map', that that can be used to organise information, data & knowledge concerning the chemical elements.  

Morphing Multi-PTs

At least three periodic tables can be identified:

• The periodic table of basic elements with atomic number Z.
  
  
• The periodic table of gas phase atoms with their associated spectra.
  
  
• Then there is the periodic table of chemicals in bottles, the actual materials under standard conditions, 25°C and 1.0 atm.

There are other periodic tables:

• Phase changes (melting points, boiling points, etc., that show the real materials at 1.0 atm but not at a standard temperature)
• Dates of discovery
• NMR properties
• etc...

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 Table of Basic Elements

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:

• Atomic number, Z, plus name & symbol (assigned to Z)
• Quantum Numbers
  
  Block of periodic table: s, p, d, f
  Group number: 1-18
  Period: 1-7
  Periodicity
  Electronic configuration

Periodic Table of Gas Phase Atoms

The chemical elements as real, simple substances can be physically normalised by studying ground-state, monoatomic gas phase atoms of the material substance.

• For some elements this is trivial: the group 18 rare gases are already monoatomic, gas phase entities at 25°C and 1.0 atm. In other words, they are naturally in the desired state.
• Oxygen is a molecular gas at room temperature, but it must be converted into an atomic gas.
• Carbon boils at 4027°C and it difficult to obtain a vapour of ground-state carbon atoms, carbon gas, but it is possible.

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.

Periodic Table Chemical of Substances Under Standard Conditions

Under standard conditions, 25°C & 1.0 atm, the chemical elements as simple substances – real chemicals in bottles – present as:

• Gases, liquids or solids
• Metals, metalloids or non-metals
• Metallic, network or molecular materials

The chemical elements as material substances have many properties, including [from WebElements: Copper]:

• Properties at standard conditions 25°C and 1.0 atm: crystal structure, molar volume, hardness, etc.
• Phase changes under non-standard conditions: boiling point, etc.
• History
• Biology
• etc.

Quantum Mechanics, Atomic Emission Spectra & The Periodic Table

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.

Paul Dirac famously claimed this situation had been fully and completely achieved in principle:

"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.

• We teach that there is a full, complete and beautiful correspondence. We say that the relationship between electronic theory and atomic spectra is linear in the sense that there is a one-to-one mapping between theory and experiment, like the one-to-one mapping between behaviour of a real gas in a piston and the ideal gas equation, PV = nRT.

But is there a 1-to-1-to-1 correspondence between QM, spectra and the periodic table?

Eric Scerri: Philosopher, Theorist, Chemist, Author

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

The reason for the discrepancy concerns multi-electron atoms, ions and molecules.

• The Schrödinger wave equation can only be solved analytically for one electron systems like the hydrogen-atom, H^•, and other one electron systems: He⁺, Li²⁺, Be³⁺, etc., Wikipedia. For multielectron systems, approximations in the math have to be made to deal with electron-electron interactions and correlations. Multi-electron atoms are complex objects, in the systems sense. The mathematical techniques employed to describe chemical systems are usually pragmatic rather than rigorous, and they are often semiempirical: ie partially based on experimental data.
  
  
  From the Wikipedia: "For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation. Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen, and in the simplest models, they are taken to have the same form. For more rigorous and precise analysis, numerical approximations must be used. Atomic orbitals are often expanded in a basis set of Slater-type orbitals which are orbitals of hydrogen-like atoms with arbitrary nuclear charge Z."
  
  
• The effect is to produce nice fast computer code that efficiently predicts atomic & molecular energies, geometries and spectra, etc., but at the expense of the theory being fully axiomatic: formally the logic of the underlying theory becomes blurred. As a result, we get a useful model but not a mathematical proof.

On this page we identify three different periodic tables:

• Periodic table of basic substances
• Periodic table of gas phase atomic simple substances
• Periodic table of standard state material simple substances

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.

The Periodic Law, The Nature of Periodicity & Electronegativity

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):

H   2.20
Li  1.00
F   3.98
O   3.44
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.

Basic & Simple Substance, Theoretical & Practical Chemistry: Does Any of This stuff Matter?

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.

© Mark R. Leach 1999-

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