In the thiosulphate ion $\mathrm{S}_2\mathrm{O}_3^{2-}$, what is the AVERAGE oxidation number of sulphur?

1. The species $\mathrm{S}_2\mathrm{O}_3^{2-}$ carries an overall charge of $-2$. 2. Therefore the algebraic sum of oxidation numbers of all atoms equals $-2$. 3. Let the average oxidation number of S be $x$. With 2 S atoms and 3 O atoms ($-2$ each): $2x + 3(-2) = -2 \Rightarrow 2x - 6 = -2 \Rightarrow 2x = +4 \Rightarrow x = +2$. 4. This is an AVERAGE — the two S atoms in thiosulphate are actually inequivalent: one is central and S(VI)-like ($+5$), the other terminal and S(-II)-like ($-1$). The average happens to be $+2$. 5. Your syllabus ("Paradox of Fractional Oxidation Number", §7.3) explicitly notes that average values like this are useful for stoichiometry even when individual atoms are in different states. _Source: syllabus Chemistry Part 2, Ch 7, §7.3 + "The Paradox of Fractional Oxidation Number" box, p. 10._