(a) In $\mathrm{KI}_3$, since the oxidation number of K is +1, therefore, the average oxidation number of iodine = –1/3. In the structure, $\mathrm{K}^{+}[\mathrm{I} - \mathrm{I} \leftarrow \mathrm{I}]^{-}$, a coordinate bond is formed between $\mathrm{I}_2$ molecule and I– ion. The oxidation number of two iodine atoms forming the $\mathrm{I}_2$ molecule is zero while that of iodine ion forming the coordinate bond is –1. Thus, the O.N. of three iodine atoms in $\mathrm{KI}_3$ are 0, 0 and –1 respectively. (b) The structure of $\mathrm{H}_2\mathrm{S}_4\mathrm{O}_6$ is shown below : The O.N. of each of the S atoms linked with each other in the middle is zero while that of each of the remaining two S-atoms is +5. (c) $\overset{x}{\mathrm{Fe}_3}\overset{-2}{\mathrm{O}_4}$ Let O.N. of Fe = x, then 3x + 4 (–2) = 0 or x = + $\frac{8}{3}$ (average) By stoichiometry $\mathrm{Fe}_3\mathrm{O}_4$ is $\overset{2+}{\mathrm{Fe}}\overset{2-}{\mathrm{O}} \cdot \overset{+3}{\mathrm{Fe}} \overset{2-}{\mathrm{O}_3}$. Thus Fe has O.N. of +2 and +3. (d) $\mathrm{H-{}}^{2}\overset{\mathrm{H}}{\underset{\mathrm{H}}{\mathrm{C}}}-{}^{1}\overset{\mathrm{H}}{\underset{\mathrm{H}}{\mathrm{C}}}-\mathrm{OH}$ In this molecule, C-2 is attached to three H-atoms (less electronegative than carbon) and one $\mathrm{CH}_2\mathrm{OH}$ group (more electronegativity than carbon). Therefore O.N. of C-2 = 3 (+1) + x + 1(–1) = 0 or x = –2. C-1 is however, attached to one OH (charge = –1) and one $\mathrm{CH}_3$ (charge = +1), and two H-atoms, O.N. of +1. Therefore, O.N. of C-1 = 1(+1) + 2( +1) + x + 1 (–1) = 0 or x = –2 (e) $\mathrm{H-}\,{}^{2}\overset{\mathrm{H}}{\underset{\mathrm{H}}{\mathrm{C}}}-\overset{\mathrm{O}}{\parallel}-\mathrm{OH}$ In this molecule, C-2 is attached to three H-atoms (less electronegative than carbon) and one –COOH group (more electronegativity than carbon). Therefore, O.N. of C-2 = 3 (+1) + x +1(–1) = 0 or x = –2. C-1 is, however, attached to one oxygen atom by a double bond, one OH (charge = –1) and one $\mathrm{CH}_3$ (charge = +1) group, therefore, O.N. of C-1 = 1 (+1) + x + 1 (–2) + 1 (–1) = 0 or x = +2.