Understanding Oxidation Numbers in Sodium Tetrathionate (Na₂S₄O₆)

Sodium tetrathionate (Na₂S₄O₆) contains four sulphur atoms, but they are not all equivalent. Two are central atoms with a different oxidation state than the two terminal ones. Let's find the oxidation numbers step by step.

Step 1: Know the Rules and Structure

The known oxidation numbers are:

• Sodium (Na) = +1
• Oxygen (O) = -2

The structure of the tetrathionate ion (S₄O₆^2-) is often represented as (O₃S-S-S-SO₃)^2-. The two central sulphur atoms (S-S) are bonded to each other, while the two terminal sulphur atoms are each bonded to three oxygen atoms.

Step 2: Assign Variables for Sulphur Atoms

Let the oxidation number of each terminal S atom (the ones in -SO₃ groups) be $x$.

Let the oxidation number of each central S atom (the ones in the S-S chain) be $y$.

Step 3: Write the Charge Balance Equation

The tetrathionate ion has a charge of -2. The sum of the oxidation numbers of all atoms must equal this charge.

Atoms in S₄O₆^2-: 4 S atoms and 6 O atoms.

Therefore:

$2x+2y+6(-2)=-2$

This simplifies to:

$2x+2y-12=-2$

Which further simplifies to:

$2x+2y=10$

Dividing the entire equation by 2 gives us our first key relationship:

$x+y=5\text{ (Equation 1)}$

Step 4: Analyze a Terminal SO₃ Group

We can find another relationship by looking at one terminal -SO₃ group. This group has an overall charge that we can determine from its bonding.

In the structure, the terminal S atom is bonded to three O atoms (each with an O.N. of -2) and one central S atom. The S-S bond is a non-polar covalent bond between two identical atoms. In a non-polar covalent bond between two identical atoms, the oxidation number for each atom in that bond is zero.

Therefore, for the oxidation number calculation of the terminal S atom, the bond to the other S atom contributes 0.

The sum of oxidation numbers for the atoms in one -SO₃ unit must be the charge on that group. Since it's part of an ion, we consider its oxidation number contribution. The oxidation number of the terminal S atom ($x$) plus its three O atoms ($3\times (-2)=-6$) is often considered to be -2, as it is analogous to a sulphate (SO₄^2-) group.

This gives us our second equation:

$x+(-6)=-2$

Solving for $x$:

$x=-2+6$ $x=+5\text{ (Equation 2)}$

The oxidation number of a terminal S atom is +5.

Step 5: Solve for the Central Sulphur's Oxidation Number

Now, substitute the value of $x=+5$ from Equation 2 into Equation 1.

$x+y=5$ $5+y=5$ $y=5-5$ $y=0$

The oxidation number of a central S atom is 0.

Step 6: Find the Requested Difference

The question asks for the difference in the oxidation numbers of the two types of sulphur atoms.

Oxidation number of terminal S ($x$) = +5

Oxidation number of central S ($y$) = 0

The difference is:

$x-y=5-0=5$

Final Answer

The difference in the oxidation numbers of the two types of sulphur atoms is $5$.

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Related Topics & Formulae

Key Concepts

• Oxidation Number: The hypothetical charge an atom would have if all bonds to atoms of different elements were 100% ionic. It is a bookkeeping tool for redox reactions.
• Rules for Assignment:
  • The oxidation number of an atom in its elemental form is 0.
  • For monatomic ions, it is equal to the ion's charge.
  • Oxygen usually has an oxidation number of -2 (exceptions: peroxides, OF₂).
  • Hydrogen is +1 when bonded to non-metals and -1 when bonded to metals.
  • The sum of oxidation numbers in a neutral compound is zero. In a polyatomic ion, it equals the ion's charge.
• Non-Polar Covalent Bonds: Bonds between two atoms of the same element (e.g., S-S, O-O). For oxidation number calculations, the shared electrons are split equally, so the bond contributes 0 to the oxidation number of each atom.

Important Formulae

The fundamental rule for any molecule or ion:

$$\text{Σ (Oxidation numbers of all atoms)}=\text{Total charge}$$

This is the equation you set up and solve to find unknown oxidation numbers.

Other Thiosalts

This concept applies to other polythionates as well (e.g., dithionate S₂O₆^2-, trithionate S₃O₆^2-). They all contain S atoms in different oxidation states, and the S-S bonds between central atoms are key to understanding their chemistry.