(A) Let the oxidation number of \(\mathrm{Mn}\) be \(\mathrm{x}\).
We know that:
Oxidation number of \( \mathrm{O} =-2\)
\(\mathrm{x}+4(-2)=-1\)
or, \(\mathrm{x}-8=-1\)
or, \(\mathrm{x}=-1+8\)
or, \(\mathrm{x} =+7\)
The oxidation number of \(\mathrm{Mn}\) in \(\left[\mathrm{MnO}_{4}\right]^{-}\)ion is \(+7\).
(B) Let the oxidation number of \(\mathrm{Cr}\) be \(\mathrm{x}\).
In \([\mathrm{Cr}(\mathrm{CN})_{6}]^{3-}\), the charge is \(-3\).
We know that:
Oxidation number of \(\mathrm{CN}=-1\)
Therefore,
\(\mathrm{x}+6\left(\mathrm{C} \mathrm{N} \right)=-3\)
\(\mathrm{x}+6(-1)=-3\)
\(\mathrm{x}=+3\)
Therefore, oxidation state of \(\mathrm{Cr}\) is \(+3\).
(C) Let the oxidation number of \(\mathrm{Ni}\) be \(\mathrm{x}\).
We know that :
Oxidation number of \(\mathrm{F}=-1\)
Then,
\(\mathrm{x+6(-1)=-2}\)
\(\mathrm{x-6=-2}\)
\(\mathrm{x=-2+6}\)
\(\mathrm{x=+4}\)
Therefore, oxidation state of \(\mathrm{Ni}\) is \(+4\).
(D) Let the oxidation state of central metal atom \(C r\) be \(\mathrm{x}\).
We know that:
Oxidation number of \(\mathrm{O}=-2, \mathrm{Cl}=-1\)
Then,
\(\mathrm{x}+2(-2)+2(-1)=0\)
\(\mathrm{x}=4+2\)
\(\mathrm{x}=+6\)
\({CrO}_{2} {Cl}_{2}\) is the species in which the central metal atom is in \(+6\) oxidation state.