(a) Complete the following chemical equations :
(i) `MnO_(4)^(-)(aq)+S_(2)O_(3)^(2-)(aq)+H_(2)O(l)to`
(ii) `Cr_(2)O_(7)^(2-)(aq)+Fe^(2+)(aq)+H^(+)(aq)to`
(b) Explain the following observations:
(i) `La^(3+)` (Z = 57) and `Lu^(3+)` (Z = 71) do not show any colour in solutions.
(ii) Among the divalent cations in the first series of transition elements, manganese exhibits the maximum paramagnetism.
(iii) `Cu^(+)` ion is not known in aqueous solutions.

Explanation

(a) (i) `8MnO_(4)^(-)(aq)+3S_(2)O_(3)^(2-)(aq)+H_(2)O(l)to 8MnO_(2) (s)+6SO_(4)^(2-)(aq)+2OH^(-)(aq)`
(ii) `Cr_(2)O_(7)^(2-)(aq)+6Fe^(2+)(aq)+14H^(+)(aq)to2Cr^(3+)(aq)+6Fe^(3+)(aq)+7H_(2)O(l)`
(b) (i) `La^(3+)` (Z = 57) and `Lu^(3+)`. (Z = 71) do not show any colour in solutions. There is no f-electrons in `La^(3+)` and `Lu^(3+)`. Hence, there is no possibility of f-f transition. Therefore, they show no colour in solution.
(ii) `Mn^(2+)` has the `3d^(5)` configuration. Thus, it has maximum (5) unpaired electrons. Therefore, it exhibits maximum paramagnetism.
(iii) `Cu^(+)` ion undergoes disproportionation in aqueous solution as under:
`2Cu^(+)toCu^(2+)+Cu`