Periodic Table: What is it Showing?
Periodic Tables & The Philosophy of Science
Table of the Chemical Elements is a cultural icon and an extraordinary object in science space. This
page explores what the periodic table is in terms of basic & simple elemental
substance, quantum theory and the philosophy of science.
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.
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
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.
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.
the basic element survives in a compound. Sodium's metallic
properties and chlorine, the green gas, do not exist in the ionic salt,
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:
- ordered domain
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.
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.
The boiling point of oxygen is -182.9 °C, but this is the bp of the molecular substance dioxygen, O2.
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:
- 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
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 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.
- Atomic number,
Z, plus name & symbol (assigned to Z)
- Quantum Numbers
Block of periodic
table: s, p, d, f
Periodic Table of Gas Phase
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
- Atomic radius
- Accurate mass & abundance of the isotopes
- Effective nuclear
- Electron affinity
- Electron binding
- 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
- Metals, metalloids
- Metallic, network
or molecular materials
The chemical elements as material
substances have many properties, including [from WebElements:
- Properties at standard
conditions 25°C and 1.0 atm: crystal structure, molar volume, hardness,
- Phase changes under
non-standard conditions: boiling point, etc.
elements (Earth's crust)
Abundance of elements (oceans)
Abundance of elements (meteorites)
Abundance of elements (stream)
Abundance of elements (sun)
Abundance of elements (Universe)
Abundances in humans
Bond enthalpy (diatomics)
Element bond length
Enthalpy of atomization
Enthalpy of fusion
Enthalpy of vaporization
Examples of compounds
Hardness - Brinell
Hardness - Vickers
History of the element
Ionic radii (Shannon)
Ionic radius (Pauling)
Ionic radius (Pauling) of monocation
Isotope nominal mass
Isotope nuclear magnetic moment
Linear expansion coefficient
Meaning of name
Names and symbols
NMR magnetogyric ratio
NMR quadrupole moment
NMR relative sensitivity
Properties of some compounds
Reactions of elements
Standard atomic weights
Van der Waals radius
Velocity of sound
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
claimed this situation had been fully and completely achieved in
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
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?
Philosopher, Theorist, Chemist, Author
Scerri disputes the
full and complete axiomatic mapping between theory and the periodic table:
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
- 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.
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.
There is no axiomatic mapping between quantum mechanical theory and material properties:
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.
The quantum chemistry methodologies are numerical models, and as a result the periodic table of even the simplest of simple substances ground state gas phase atoms is not fully axiomatized.
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.
The question becomes: Does quantum theory predict/explain the patterns of the periodic table and the periodic law, even if the quantum chemistry mathematical techniques do not exist that enable us to crunch the numbers with absolute precision? Is the periodic table of basic substances axiomatic?
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.
Quantum theory, sometimes called the old quantum theory, produced the four quantum numbers (principal, subsidiary, magnetic & spin), and four rules that are used to construct the periodic table: the Pauli exclusion principle, the aufbau principle, the Pauli exclusion principle, Hund's rule and Madelung's rule.
The pattern of the periodic table schema can be shown to directly arise from these rules followed by a couple of trivial mappings – as discussed on the previous page of this chemogenesis webbook here – and thus, the periodic table of the basic meta-physical elements is axiomatic with respect to the Old Quantum Theory.
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...
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
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.
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
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.
Numbers to Periodic Tables
© Mark R. Leach 1999-
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