Figure 1: sulphur Molecule
The periodic table is composed of 118 discovered elements. Each of them has unique properties differentiating it from the other. However, elements can be classified into different categories based on some specific criteria. One of the most common ways of classifying elements is as metals, nonmetals and metalloids.
Sulphur has a unique position in the periodic table just as the other elements. One of the most intriguing properties of sulphur is that at room temperature and normal pressure conditions (RTP), it exists as an elementary molecule made up of 8 atoms. The question is why, in normal conditions, can it not exist as a molecule consisting of 2,3 or even more than 8 atoms while oxygen, having the same valency as sulphur, exists predominantly as a di-atomic elementary molecule.
It is important to note that sulphur has a variety of other structural forms in terms of the number or arrangement of atoms. These are less common and are found in more severe temperature and pressure conditions. However, the objective of this article is to identify the reason behind the existence of sulphur in the octa-atomic form at RTP.
Polarisability, Catenation, London Dispersion Forces, Bond Energy, Double Bond Rule, VSEPR Theory
Some elements are monatomic while others exist as molecules in their elemental forms such as hydrogen (H2), oxygen (O2, O3), chlorine (Cl2), nitrogen(N2), and sulphur (S8).
The most abundant form of sulphur (α-sulphur, which is thermodynamically stable) is the orthorhombic polymorph of S8, having a \”crown\” structure. Sulphur has over 30 allotropes including disulphur. Sulphur rings of 6, 7, 9–15, 18 and 20 atoms are known but are less stable. What determines the stability of S8?
“Atomic size represents the mean distance from the nucleus to the boundary of the surrounding cloud of electrons.”  It is also referred to as the atomic radius.
The atomic size trends observed in the periodic table have to do with three factors:
- Number of protons(nuclear charge) in the nucleus
- Number of energy levels containing electrons
- Number of valence electrons
Sulphur has 16 protons, 3 energy levels, and 6 electrons in the outer energy level giving it an electron configuration of 1s² 2s², 2p⁶, 3s², 3p⁴. Analysing sulphur’s position and the trends in the periodic table, we can safely predict that sulphur has a small atomic size compared to most elements of the periodic table.
Figure 2: Periodic Table of Elements: Atomic size (source: sciencenotes.org)
It can be observed that the atomic size, in general, decreases across the periods and increases down the groups of the periodic table.
However, in comparison to oxygen, which has the same valency as sulphur, sulphur’s atomic size is relatively large. This results in it behaving differently than oxygen, since the atomic size, as we have learned, directly or indirectly influences various other properties of sulphur and its bond formation. For example, smaller atomic size means greater electronegativity. Therefore, sulphur’s electronegativity is greater than most elements of the periodic table.
Empirical Atomic Radius(in pm)
Calculated Atomic radius
van der Waals radius
Covalent (single bond) radius
Figure 3: Atomic radii of sulphur and oxygen (source: webelements.com)
Electronegativity is a measure of the relative tendency of an atom to attract a shared pair of electrons in a covalent bond. Fluorine (the most electronegative element) is assigned a value of 3.98, and francium(the least electronegative element in theory) has an electronegativity of 0.7 as measured by using the Pauling Scale. The electronegativity of sulphur is 2.58 and that of oxygen is 3.44.  Clearly, oxygen is more electronegative than sulphur. It means that when in a covalent bond with sulphur, oxygen will attract electrons towards itself more than sulphur. It will gain a partial negative charge.
When the atomic number increases, the number of electrons also increases to maintain the neutrality of the atom. But whether the number of energy levels will increase depends on ‘how much’ the number of electrons increased. For instance, if the K-shell holds 2 electrons, addition of 1 electron will result in addition of another energy level i.e. L-shell. If the atomic number, Z=3, then the addition of an electron would not result in the addition of an energy level. This would happen only when at least 8 more electrons are added. In general,
number of electrons to be added to add another shell= (maximum number of electrons the current valence shell can hold) – (the number of electrons that the valence shell is currently holding) + 1
Here’s an illustration of how atomic number and shielding determine the effective nuclear charge:
Figure 4: Effective nuclear charge across some elements in Period 3 of the Periodic Table
Clearly, the effective nuclear charge increases across a period, in this case period 3. Due to this, the atomic size decreases. But down a group in a periodic table, the effective nuclear charge nearly remains the same. However, addition of a shell every time, results in an increase in the atomic radius.
Hence, in general, as elements get bigger, the effective nuclear charge on the valence electrons decreases due to the shielding provided by the inner shell electrons. So the valence electrons can move around more freely. Sulphur’s convenient atomic size and presence of more(i.e 6) valence electrons allow the single-bonded sulphur atoms to catenate and polarise more easily as compared to many other elements. This statement is further explained in the discussions on polarisability and catenation in the article.
Since oxygen has a smaller atomic size, in the case of the formation of single-bonded oxygen molecules, there are more interelectronic repulsions because there are more lone pairs of electrons. Hence, di-atomic oxygen in which atoms of oxygen share two pairs of electrons(i.e. a double-bonded molecule) is more common. But in the case of single sulphur bonds, the repulsions between the lone pairs of electrons are not very high as the size has increased.
Bond Energy is a measure of the strength of a chemical bond which is determined by measuring the heat (or enthalpy) required to break a mole of molecules into their constituent individual atoms.
The S-S bond energy is about 215kJ/mol while O-O bond energy is about 140kJ/mol.  Therefore, the single-bonded sulphur atoms are more strongly bonded as compared to single-bonded oxygen atoms. But a single bond between the two sulphur atoms does not satisfy valency of both the atoms. Hence, a longer chain of sulphur atoms is formed and sulphur has much more tendency to catenate compared to oxygen.
Carbon has an electronegativity of 2.55 on the Pauling Scale while that of sulphur is 2.58. Thus, their electronegativities are very close. But their atomic size and valency differ. Carbon is much smaller and has only 4 valence electrons. Both these factors of size and tetravalency enable carbon to exhibit the highest degree of catenation. Also, the C-C bond energy is of about 345kJ/mol(greater than sulphur, making C-C bonds stronger). This makes long chains of carbon very stable. Hence, sulphur chains are much smaller as compared to carbon, to maintain stability.
Considering normal temperature and pressure conditions, sulphur seems to be most stable in the form of ‘rhombic’ octasulphur, although other allotropes also exist in a relatively much smaller quantity. For example, at 95.3°C(368.45K), α-sulphur(rhombic octasulphur) converts to β-sulphur(monoclinic). 
At very high temperatures, the sulphur chains break to form smaller molecules like S2 which happens to be the predominant in that condition. So we can see that the environmental conditions highly influence the bond formation of elements.
Figure 5: Transition of sulphur from the rhombic form to the monocyclic form(source:thechemistrysite)
Covalent bonds are formed between atoms of elements having very small or no difference in their electronegativities, whereas ionic bonds are formed between atoms of elements with greater difference in their electronegativities. Atoms of the same elements have the same electronegativities, therefore sulphur atoms are covalently, and not ionically, bonded (electrons are shared) to form sulphur molecules.
Figure 6: Electronegativity difference between bonding atoms(source:chem.libretexts.org)
The intermolecular forces are relatively less between molecules that have covalently bonded atoms/elements especially when the molecules are made up of the same elements. The reason is that, in such a case, the molecule is not polarised and has an overall uniform distribution of electrons between the constituent atoms. However, at times, instantaneous or momentary dipoles are formed. This happens due to the formation of an electron-dense region in one molecule which induces dipoles in other molecules. These dipoles attract each other and the force between them is known as the London Dispersion Force. London Dispersion Forces are stronger in those molecules that are not compact, but longer chains of elements. This is an added factor in case of molecules like S8 which results in stronger bonds between them.
Figure 7: Electrostatic Attraction (Source: chem.ucla.edu)
The Polarisability of a molecule can be defined as a measure of its ability to acquire an electrical dipole moment in response to an electrical field. 
The greater the distance of the electrons from the nucleus, the lesser the control of the nuclear charge on the electron distribution. This means that the electrons are freer to move. This allows for more distortions in the electron distribution or say, greater variability in electron density, and the polarisability of the atom increases. This in turn affects the polarisability of the molecule/compound of which the atom is a part. Note that since the constituent atoms are bigger, the molecule will also be bigger.
Sulphur at room temperature, ‘catenates’ to form an octa-atomic molecule. But why?
Catenation is the self-linking ability of elements. More catenation means the formation of larger molecules which results in greater polarisability which in turn increases the probability of the formation of instantaneous dipoles. This increases the strength of the intermolecular forces, here the London Dispersion Forces between sulphur molecules. The stronger the exhibition of dispersion forces, the shorter the distance between two corresponding molecules. This means that the molecules are more strongly bonded to each other because more energy would be required to break the chemical bond between them. A good analogy to explain why this happens would be the gravitational force between two point masses. The force increases as the distance between the two objects decreases and vice versa. The objects now experience more attraction towards each other.
The decrease in the bond length between two atoms (here, the constituent atoms of a molecule) also acts as a secondary factor contributing to the reduction in the intermolecular space between molecules. Change in the kinetic energies of particles (atoms, ions, molecules) proportionally causes change in the amount of collisions between the particles and as a result, the amount of space between them changes. In essence, the distance between two molecules, their bond dissociation energy and their kinetic energies determine the state of the substance composed of such molecules.
Now as the intermolecular space reduces, the aggregation of molecules(i.e the substance) has increased chances of being solid at room temperature and normal pressure conditions. On the other hand if the intermolecular space increases, the substance is more likely to be in the liquid or gaseous states. The exact state depends on the substance taken into consideration and its properties.
As observed, in the environment, sulphur, because of its properties which were discussed, is predominantly found in the solid state, when most nonmetals and molecules bonded by London Dispersion Forces are in the gaseous state.
As stated in \”New Element‐Carbon (p‐p)π Bonds\” by Peter Jutzi,
“The double bond rule states that chemical elements with a principal quantum number greater than 2 (e.g. Period 3 elements and lower) do not form multiple bonds (e.g. double bonds and triple bonds) with themselves or with other elements. The double bonds if they exist are weak due to weak pi bonds as a result of poor orbital overlap… An example is the rapid polymerization that occurs upon condensation of disulphur, the heavy analogue of O2.” 
Sulphur, as we know, is a Period 3 element. This rule, therefore, explains the stable nature of octasulphur instead of disulphur.
A covalent bond between two atoms is formed when there is an overlap between their orbitals and electron pairs are formed between them. The degree of overlap of involved orbitals is an important factor determining the strength of a covalent bond. Orbitals that overlap more, structure bonds that are stronger than those that have less orbital overlap.
We have already discussed that the atomic size of sulphur is greater than oxygen and carbon atoms. Since the atomic radius is longer, the distance between two sulphur atoms is also more, which results in a very poor overlap of pi-orbitals.
The basic assumption of the VSEPR theory is that each atom in a molecule tends to achieve a geometry that minimizes the repulsion between the valence electrons of that atom. Sulphur atoms, as seen in Figure 7, contain two lone pairs. The arrangement of the eight atoms of sulphur in a crown structure minimises the interelectronic repulsions between the lone pairs, thus increasing the stability of the molecule.
Figure 8: Octasulphur Crown Structure- Each sulphur atom has 2 lone pairs of electrons.
Throughout the discussion, sulphur was described in comparison to two elements- oxygen and carbon. Since sulphur has the same valency as oxygen, it is assumed to have similar properties of bond formation. But this idea is far from reality. A lot of factors, many of which are yet unknown, play a significant role in the formation of molecules.
Very few elements(C, S, B, P, Si) are capable of showing catenation. Carbon’s tendency to catenate far outweighs any element in the periodic table. The bond energy of S-S is lower than that of C-C and hence the catenation tendency is also lower. Other factors include sulphur’s larger size and longer bond length. S-S bond energy is greater than O-O bond energy, allowing it to catenate more than oxygen. Oxygen is far more stable when it forms a double bond than a single bond. The O-O bond energy is about 140kJ/mol and the O=O bond energy is about 498kJ/mol. But the S-S bond energy is about 215kJ/mol while the S=S bond energy is about 425kJ/mol. But disulphur(S=S) rarely occurs at room temperature. It readily undergoes photodissociation within about 7.5 minutes in sunlight. Disulphur’s instability is generally described in connection with the double bond rule.
The S-S bond energy in S8 is about 226kJ/mol. It is mainly found in solid-state. The octasulfur size and crown structure ensures more polarisability and greater strength of dispersion forces. Hence, the molecule is more stable.
Atomic number and other factors determine the atomic size. These determine the electronegativity of an element which determines the type of intramolecular forces which exist between atoms, in turn affecting the nature of intermolecular forces between molecules. These properties, and many more, determine the physical and chemical properties of molecules. All these properties are interconnected and one property depends on the other.
The conditions and properties discussed are the equilibrium factors for stable sulphur(as a substance) to be in a solid-state consisting of mainly S8 molecules at room temperature and normal pressure conditions.
- David Wiley and Kim Thanos. “Atomic Size”. Lumen Learning. Accessed April, 2021. https://courses.lumenlearning.com/introchem/chapter/atomic-size/
- Neeru Khosla and Murugan Pal. “Periodic Trends in Atomic Size.” CK-12. Last Modified August 2, 2014. Accessed April, 2021. https://www.ck12.org/book/ck-12-chemistry-second-edition/r18/section/9.2
- “Electronegativity.” Truro School in Cornwall. Last Modified August 16, 2020. Accessed April 2021.
- “sulphur: electronegativity”. WebElements. Accessed April, 2021. https://www.webelements.com/sulphur/electronegativity.html
- “Oxygen: electronegativity”. WebElements. Accessed April, 2021. https://www.webelements.com/oxygen/eectronegativity.html
- David Wiley and Kim Thanos. “Bond Energy”. Lumen Learning. Accessed April, 2021. https://courses.lumenlearning.com/introchem/chapter/bond-energy/
- “Bond Strength and Energy.” chem libretexts (2019). Last Modified June 6, 2019. Accessed March, 2021.
- Greenwood and Norman N, Earnshaw, Alan. “Chemistry of the Elements (2nd ed.)”. Butterworth-Heinemann (1997). ISBN 0080379419. Accessed April, 2021.
- K. Cho. “Encyclopedia of Condensed Matter Physics”. Elsevier Academic Press (2005). Accessed April, 2021.
- “Polarizability.” (2020). Last Modified August 16, 2020. Accessed March, 2021. https://chem.libretexts.org/@go/page/1663.
- BBC Bitesize. n.d. “Chemical formulae- valency.” bbc.co.uk. Accessed April 2021. https://www.bbc.co.uk/bitesize/guides/zqrxsbk/revision/2.
- Jutzi and Peter. \”New Element‐Carbon (p‐p)π Bonds\”. Angewandte Chemie International Edition in English (1975). 14 (4): 232–245. doi:10.1002/anie.197502321. Accessed April, 2021.
- OpenStax. n.d. Chemistry. Accessed June 26, 2021.
- Purdue University. n.d. “Valence-Shell Electron-Pair Repulsion Theory (VSEPR).” chemed.chem.purdue.edu. Accessed June 14, 2021. https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch8/vsepr.html.
- T.L. Cottrell, \”The Strengths of Chemical Bonds,\” 2nd ed. Butterworths, London. 1958; B. deB. Darwent, \”National Standard Reference Data Series,\” National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965). Accessed June, 2021.
- Ahearn, M. F.; Schleicher, D. G.; Feldman, P. D. 1983. \”The discovery of S2 in comet IRAS-Araki-Alcock 1983d\”. The Astrophysical Journal. 274: L99. Accessed June, 2021.
Tables and Image Credits:
Figure 1: Octasulphur
The illustration is self-created by the writer.
Figure 2: Periodic Table of Elements: Atomic size
Todd Helmenstine, 2014
Figure 3: Atomic radii of sulphur and oxygen:
Data is as quoted at http://www.webelements.com/ from these sources:
Atomic radius (empirical):
J.C. Slater.1964. \”Atomic Radii in Crystals\”. J. Chem. Phys. 41: 3199. Bibcode:1964JChPh..41.3199S. doi:10.1063/1.1725697.
Atomic radius (calculated):
E. Clementi; D.L.Raimondi; W.P. Reinhardt. 1967. \”Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons\”. J. Chem. Phys. 47: 1300. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.
Van der Waals radius:
A. Bondi. 1964. \”van der Waals Volumes and Radii\”. J. Phys. Chem. 68: 441. doi:10.1021/j100785a001.
M. Mantina; A.C. Chamberlin; R. Valero; C.J. Cramer; D.G. Truhlar (2009). \”Consistent van der Waals Radii for the Whole Main Group\”. J. Phys. Chem. A. 113 (19): 5806–12. Bibcode:2009JPCA..113.5806M. doi:10.1021/jp8111556. PMC 3658832. PMID 19382751.
Covalent radii (single bond):
R.T. Sanderson. 1962. “Chemical Periodicity”. New York, USA: Reinhold.
L.E. Sutton. ed.1965. \”Supplement 1956–1959, Special publication No. 18\”. Table of interatomic distances and configuration in molecules and ions. London, UK: Chemical Society.
J.E. Huheey; E.A. Keiter & R.L. Keiter. 1993. “Inorganic Chemistry: Principles of Structure and Reactivity “(4th ed.). New York, USA: HarperCollins. ISBN 0-06-042995-X.
W.W. Porterfield. 1984. “Inorganic chemistry, a unified approach”. Reading Massachusetts, USA: Addison Wesley Publishing Co. ISBN 0-201-05660-7.
A.M. James & M.P. Lord. 1992. Macmillan\’s Chemical and Physical Data. MacMillan. ISBN 0-333-51167-0.
Figure 4: Effective nuclear charge
The illustration is self-created by the writer.
Figure 5: Transition of sulphur from the rhombic form to the monocyclic form
Figure 6: Electronegativity difference between bonding atoms
Figure 7: Electrostatic Attraction
Figure 8: Octasulphur Crown Structure
Valency is the combining capacity of an element. It depends on the number of valence(i.e outer shell) electrons.  ↑
Pauling Scale is the most commonly used method of measuring electronegativity. ↑
Catenation is the self-linking ability of elements to form longer chains. ↑
Bond is merely a term used to refer to a link or interaction between two particles. ↑
Bond length is defined as the distance between the centres of two atoms which are covalently bonded. As the bond becomes stronger, the bond energy increases and the bond length reduces. ↑
The number which Neils Bohr introduced to define the different energy levels of discrete orbits in his atomic model. ↑
Valence shell electron pair repulsion theory is used to predict the shape of a molecule based on the electron pairs that surround the atoms of a molecule. ↑
About the Author
Amna Javed is a 10th Grade student studying in India. She has great interest in Science, Mathematics and Arts and wants to gain knowledge accompanied with wisdom, as much as possible, in her life. She enjoys writing poetry and painting on nature. She also spends her time doing research trying to understand whatever triggers her curiosity in the best possible way. She loves learning!