Understanding Sulphur's Variable Valency

The question asks why Sulphur exhibits variable valency. Let's analyze the electronic structure of Sulphur to understand this property.

Sulphur (S) is element number 16, belonging to Group 16 of the periodic table. Its electronic configuration is $1s^2 2s^2 2p^6 3s^2 3p^4$. In its valence shell (the third shell), it has 6 electrons ($3s^2 3p^4$).

According to the octet rule, atoms tend to gain, lose, or share electrons to achieve a stable configuration with 8 valence electrons. Sulphur can gain 2 electrons to achieve an octet, forming compounds where its valency is 2 (e.g., H₂S).

The Role of d Orbitals in Sulphur Valency

However, Sulphur can exhibit valencies other than 2, such as 4 and 6. This is possible because Sulphur is in the third period of the periodic table. Elements in the third period and beyond have access to empty 3d orbitals in addition to the 3s and 3p orbitals in their valence shell.

In its ground state, Sulphur has the valence electron configuration $3s^2 3p^4$.

$\qquad 3s \quad \quad 3p \quad \quad 3d$

$\qquad \boxed{\uparrow\downarrow} \quad \boxed{\uparrow\downarrow|\uparrow |\uparrow} \quad \boxed{\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}}$

To form bonds with valency 2, Sulphur uses the two unpaired electrons in the 3p orbitals.

When Sulphur is bonded to highly electronegative atoms like oxygen or fluorine, it can promote electrons from the 3p or even the 3s orbitals into the empty 3d orbitals. This process is called excitation.

First Excited State: Valency 4

One electron from the 3p orbital can be promoted to the empty 3d orbital:

$\qquad 3s \quad \quad 3p \quad \quad 3d$

$\qquad \boxed{\uparrow\downarrow} \quad \boxed{\uparrow |\uparrow |\uparrow} \quad \boxed{\uparrow|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}}$

Now there are 4 unpaired electrons (one in 3s, three in 3p, one in 3d). These 4 unpaired electrons can form covalent bonds, leading to a valency of 4, as seen in Sulphur dioxide (SO₂).

Second Excited State: Valency 6

Another electron, this time from the 3s orbital, can be promoted to a 3d orbital:

$\qquad 3s \quad \quad 3p \quad \quad 3d$

$\qquad \boxed{\uparrow} \quad \boxed{\uparrow |\uparrow |\uparrow} \quad \boxed{\uparrow|\uparrow|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}|\phantom{\uparrow\downarrow}}$

Now there are 6 unpaired electrons (one in 3s, three in 3p, two in 3d). These 6 unpaired electrons can form covalent bonds, leading to a valency of 6, as seen in Sulphur trioxide (SO₃) or Sulphuric acid (H₂SO₄).

This ability to promote electrons into available d orbitals allows Sulphur to expand its valence shell beyond the octet and exhibit variable valencies (2, 4, and 6).

Analyzing the Options

Let's consider the given options:

1. Bigger size: While size is an atomic property, it doesn't directly explain variable valency based on electron configurations and bonding capacity.
2. High electronegativity: Sulphur is electronegative, but this primarily influences the polarity of bonds it forms or its tendency to gain electrons (like forming S²⁻). It doesn't explain why it can have multiple valency states like 4 or 6.
3. Presence of d orbital in sulphur: As explained above, the availability of empty 3d orbitals allows Sulphur to promote valence electrons and have more unpaired electrons available for bonding, leading to variable valency. This is the correct reason.
4. High ionization energy: Ionization energy is the energy required to remove an electron. High ionization energy means it's difficult to remove electrons. This property doesn't directly explain the ability to form multiple covalent bonds with different valencies.

Therefore, the key factor enabling Sulphur's variable valency is the presence of empty d orbitals in its valence shell.

Revision Table: Sulphur Valency Factors

Additional Information: Octet Expansion

The ability of elements in the third period and beyond to promote electrons into empty d orbitals and have more than 8 valence electrons in their bonded state is known as octet expansion. This is a key reason why elements like Sulphur (S), Phosphorus (P), and Chlorine (Cl) can form compounds with valencies or oxidation states higher than predicted by the simple octet rule based only on s and p orbitals (e.g., PCl₅, SF₆, ClF₃).

Elements in the second period (like Oxygen, Nitrogen, Carbon) do not have access to d orbitals in their valence shell and therefore cannot exhibit octet expansion. This is why oxygen primarily shows valency 2, and its maximum covalency is typically 4 (in species like H₃O⁺), but it doesn't show valency 4 or 6 like Sulphur.