Nomenclature and oxidation State Questions in English

(C) The ligand $CO$ is a neutral ligand with a charge of $0$.
Let the oxidation state of $Ni$ be $x$.
For the complex $[Ni(CO)_4]$,the sum of oxidation states equals the total charge of the complex,which is $0$.
$x + 4(0) = 0$
$x = 0$
Therefore,the oxidation state of $Ni$ in $[Ni(CO)_4]$ is $0$.

(A) The complex $[Co(NH_3)_6]Cl_3$ dissociates as $[Co(NH_3)_6]Cl_3 \rightarrow [Co(NH_3)_6]^{3+} + 3Cl^-$.
Let the oxidation state of $Co$ be $x$.
The oxidation state of $NH_3$ is $0$.
So,$x + 6(0) = +3$.
Therefore,$x = +3$.

(C) $1$. Identify the ligands: There are $5$ ammine $(NH_3)$ ligands and $1$ chloro $(Cl^-)$ ligand.
$2$. Alphabetical order: 'Ammine' comes before 'Chlorido'.
$3$. Name the coordination sphere: $5$ ammine ligands are named as 'pentaammine' and $1$ chloro ligand is named as 'chlorido'.
$4$. Name the metal: The central metal is Cobalt $(Co)$. Since the complex ion is cationic,it is named as 'cobalt'.
$5$. Oxidation state: Let the oxidation state of $Co$ be $x$. $x + 5(0) + 1(-1) = +2$ (since there are $2$ chloride ions outside the sphere),so $x - 1 = +2$,which gives $x = +3$.
$6$. Combine the parts: The name is 'pentaamminechloridocobalt $(III)$ chloride'.

(A) $1$. Identify the ligands: $NH_3$ (ammine),$NO_2^-$ (nitro),$Cl^-$ (chloro),$CN^-$ (cyano).
$2$. Arrange ligands in alphabetical order: Ammine,Chloro,Cyano,Nitro.
$3$. Since there are three $NH_3$ ligands,the prefix is 'triammine'.
$4$. The central metal is Cobalt $(Co)$. The oxidation state is calculated as: $x + 3(0) + (-1) + (-1) + (-1) = 0$,so $x = +3$.
$5$. Combining these,the name is Triamminochlorocyanonitrocobalt $(III)$.

(B) In the complex $[Cr(CO)_6]$,the ligand $CO$ (carbonyl) is a neutral ligand with an oxidation state of $0$.
Since the overall charge of the complex is $0$,the oxidation state of the metal $Cr$ is calculated as: $x + 6(0) = 0$,which gives $x = 0$.
Therefore,the metal in $[Cr(CO)_6]$ has an oxidation state of $0$.

(D) The chemical formula of sodium nitroprusside is $Na_2[Fe(CN)_5(NO)]$.
In this complex,the ligand $NO^+$ is nitrosyl.
Let the oxidation state of $Fe$ be $x$.
$2(+1) + x + 5(-1) + 1(+1) = 0$
$2 + x - 5 + 1 = 0$
$x - 2 = 0$
$x = +2$.
Thus,the oxidation state of $Fe$ is $II$.
The $IUPAC$ name is Sodium pentacyanonitrosylferrate $(II)$.

(C) $1$. Identify the ligands: There are $2$ ammine $(NH_3)$ ligands and $4$ aqua $(H_2O)$ ligands. According to alphabetical order,'ammine' comes before 'aqua'.
$2$. Name the coordination sphere: The complex ion is $[Co(H_2O)_4(NH_3)_2]^{3+}$. The name is 'diamminetetraaquacobalt'.
$3$. Determine the oxidation state of the central metal atom $(Co)$: Let the oxidation state be $x$. $x + 2(0) + 4(0) = +3$,so $x = +3$.
$4$. Combine the parts: The full name is 'diamminetetraaquacobalt $(III)$ chloride'.

(A) $1$. The complex is $[Pt(NH_3)_4Cl_2] [PtCl_4]$.
$2$. The cation is $[Pt(NH_3)_4Cl_2]^{2+}$ and the anion is $[PtCl_4]^{2-}$.
$3$. In the cation $[Pt(NH_3)_4Cl_2]^{2+}$,let the oxidation state of $Pt$ be $x$. $x + 4(0) + 2(-1) = +2$,so $x = +4$.
$4$. The name of the cation is tetraamminedichloridoplatinum $(IV)$.
$5$. In the anion $[PtCl_4]^{2-}$,let the oxidation state of $Pt$ be $y$. $y + 4(-1) = -2$,so $y = +2$.
$6$. The name of the anion is tetrachloridoplatinate $(II)$.
$7$. Combining these,the correct name is tetraamminedichloridoplatinum $(IV)$ tetrachloridoplatinate $(II)$.

(D) Let the oxidation state of $Cr$ be $x$.
In the complex $[Cr(NH_3)_6]Cl_3$,the oxidation state of $NH_3$ is $0$ and $Cl$ is $-1$.
Applying the rule: $x + 6 \times (0) + 3 \times (-1) = 0$.
$x - 3 = 0$.
$x = +3$.
Therefore,the oxidation state of $Cr$ is $+3$.

(A) $1$. Identify the ligands: There are $5$ ammonia $(NH_3)$ ligands,named as 'pentaammine',and $1$ $NCS^-$ ligand,named as 'thiocyanato-$N$' because it is bonded through the nitrogen atom.
$2$. Determine the oxidation state of the central metal atom $(Co)$: Let the oxidation state be $x$. The charge on $NH_3$ is $0$,$NCS^-$ is $-1$,and $Cl^-$ is $-1$. The total charge of the complex is $0$. So,$x + 5(0) + (-1) + 2(-1) = 0$,which gives $x - 3 = 0$,so $x = +3$.
$3$. Assemble the name: The name is written as 'pentaammine(thiocyanato-$N$)cobalt$(III)$ chloride'.

(A) $1$. Identify the ligands: There are $4$ ammonia $(NH_3)$ ligands named as 'tetraammine' and $2$ chloride $(Cl^-)$ ligands named as 'dichlorido'.
$2$. Determine the oxidation state of the central metal atom $(Co)$: Let the oxidation state be $x$. The charge on $NH_3$ is $0$,and the charge on $Cl$ is $-1$. The total charge of the complex is $0$. So,$x + 4(0) + 2(-1) + (-1) = 0$,which gives $x - 3 = 0$,so $x = +3$.
$3$. Name the complex: Since the complex is a cation,the metal name remains 'cobalt'. The ligands are named alphabetically: 'ammine' before 'chlorido'.
$4$. Combining these,the name is 'Tetraamminedichloridocobalt$(III)$ chloride'.

(A) The complex $[Ni(NH_3)_4][NiCl_4]$ is a coordination compound consisting of a cationic part $[Ni(NH_3)_4]^{2+}$ and an anionic part $[NiCl_4]^{2-}$.
In the cationic part,$Ni$ has an oxidation state of $+2$ because $NH_3$ is a neutral ligand.
In the anionic part,$Ni$ has an oxidation state of $+2$ because $4 \times (-1) + x = -2$,which gives $x = +2$.
According to $IUPAC$ rules,the cation is named first followed by the anion.
The cation $[Ni(NH_3)_4]^{2+}$ is named tetraamminenickel $(II)$.
The anion $[NiCl_4]^{2-}$ is named tetrachloridonickelate $(II)$ because it is a negatively charged complex.
Therefore,the correct name is tetraamminenickel $(II)$ tetrachloridonickelate $(II)$.

(B) $1$. Identify the ligands: $NH_3$ (ammine),$Br^-$ (bromo),$NO_2^-$ (nitro),$Cl^-$ (chloro).
$2$. Arrange ligands in alphabetical order: ammine,bromo,chloro,nitro.
$3$. Determine the oxidation state of $Pt$: Let $x$ be the oxidation state of $Pt$. $x + 3(0) + (-1) + (-1) + (-1) = 0$,so $x - 3 = 0$,$x = +3$.
$4$. Note: The complex is neutral,so the name is written as a single word.
$5$. The correct name is triamminebromochloronitroplatinum $(III)$.

(A) $1$. Identify the ligands: $Cl^-$ is chloro,$NO_2^-$ is nitro,and $en$ is ethylenediamine. Since there are two $en$ ligands,we use the prefix 'bis'.
$2$. Determine the oxidation state of the central metal atom $(Co)$: Let the oxidation state be $x$. The charge on $Cl$ is $-1$,$NO_2$ is $-1$,$en$ is $0$,and the outer $Cl$ is $-1$. Thus,$x + (-1) + (-1) + 2(0) + (-1) = 0$,which gives $x = +3$.
$3$. Arrange ligands alphabetically: 'chloro' comes before 'nitro'.
$4$. Combine: The name is chloronitro bis(ethylenediamine)cobalt$(III)$ chloride.

(C) $1$. Identify the coordination entity: $[Cu(NH_3)_4]^{2+}$.
$2$. The ligand is $NH_3$ (ammine),and there are $4$ of them,so it is 'tetraammine'.
$3$. The central metal ion is $Cu$. Let its oxidation state be $x$. $x + 4(0) = +2$,so $x = +2$.
$4$. The metal is named 'copper $(II)$'.
$5$. The counter ion is $NO_3^-$ (nitrate). Since there are two,it is simply 'nitrate' in the name (the prefix 'di' is not used for the anion in the coordination compound name).
$6$. Combining these,the name is 'tetraamminecopper $(II)$ nitrate'.

(B) Let the oxidation state of $Ni$ be $x$.
For the complex $K_4[Ni(CN)_4]$,the sum of oxidation states of all atoms is equal to $0$.
$4(+1) + x + 4(-1) = 0$
$4 + x - 4 = 0$
$x = 0$.
Therefore,the oxidation state of nickel is $0$.

(C) Let the oxidation state of $Cr$ be $x$.
In the complex $[(H_2O)_4Cr(OH)_2Cr(H_2O)_4]^{4+}$,the ligands are $H_2O$ (neutral,charge $= 0$) and $OH^-$ (charge $= -1$).
The total charge of the complex is $+4$.
Applying the oxidation state rule:
$2x + 8(0) + 2(-1) = +4$
$2x - 2 = +4$
$2x = 6$
$x = +3$
Therefore,the oxidation state of chromium is $+3$.

(B) $1$. Identify the ligands: There are $4$ water molecules (aqua) and $2$ chloride ions (chlorido). Alphabetically,'aqua' comes before 'chlorido'.
$2$. Name the coordination sphere: The ligands are named as tetraaqua and dichlorido. The metal is chromium.
$3$. Determine the oxidation state of $Cr$: Let $x$ be the oxidation state of $Cr$. The charge on $H_2O$ is $0$,$Cl$ is $-1$,and $NO_3$ is $-1$. So,$x + 2(-1) + 4(0) = +1$ (since $NO_3$ is $-1$,the complex ion is $+1$). Thus,$x - 2 = +1$,which gives $x = +3$.
$4$. Combine: The name is tetraaquadichloridochromium $(III)$ nitrate.

(B) In the complex ion $[Cu(NH_3)_4]^{2+}$,let the oxidation state of $Cu$ be $x$.
Since $NH_3$ is a neutral ligand,its oxidation state is $0$.
The total charge on the complex ion is $+2$.
Therefore,$x + 4(0) = +2$.
$x = +2$.
Thus,the oxidation state of copper is $+2$.

(C) $1$. Identify the ligands: There are $5$ ammonia $(NH_3)$ ligands,named as 'pentaammine',and $1$ nitro $(NO_2^-)$ ligand,named as 'nitrito-$N$' because it is bonded through nitrogen.
$2$. Determine the oxidation state of the central metal atom $(Co)$: Let the oxidation state be $x$. The charge on $NH_3$ is $0$,the charge on $NO_2^-$ is $-1$,and the charge on $Cl^-$ is $-1$. The total charge of the complex is $0$. Thus,$x + 5(0) + 1(-1) + 2(-1) = 0$,which gives $x - 3 = 0$,so $x = +3$.
$3$. Assemble the name: The ligands are named in alphabetical order (ammine before nitrito). The metal is 'cobalt' followed by its oxidation state in Roman numerals in parentheses,and finally the counter-ion 'chloride'.
$4$. The correct $IUPAC$ name is 'Pentaamminenitrito-$N$-cobalt$(III)$ chloride'.

(D) $1$. The central metal ion is Cobalt $(Co)$ with an oxidation state of $+III$.
$2$. The ligands are: triammine $(3 \ NH_3)$,diaqua $(2 \ H_2O)$,and chlorido $(1 \ Cl^-)$.
$3$. The coordination sphere is $[Co(NH_3)_3(H_2O)_2Cl]$.
$4$. To balance the charge: $x + 3(0) + 2(0) + (-1) = +3$,so $x = +4$. Wait,the oxidation state is $+3$. Let the charge on the complex be $y$. $Co$ is $+3$,$Cl$ is $-1$,so $y = +3 - 1 = +2$.
$5$. The formula is $[Co(NH_3)_3(H_2O)_2Cl]Cl_2$.

(C) In $Fe(NO_3)_2$,the nitrate ion is $NO_3^-$,so the oxidation state of $Fe$ is $+2$.
In $FeC_2O_4$,the oxalate ion is $C_2O_4^{2-}$,so the oxidation state of $Fe$ is $+2$.
In $[Fe(H_2O)_6]Cl_3$,let the oxidation state of $Fe$ be $x$. Since $H_2O$ is neutral and $Cl^-$ has a charge of $-1$,we have $x + 6(0) + 3(-1) = 0$,which gives $x = +3$.
In $(NH_4)_2SO_4 \cdot FeSO_4 \cdot 6H_2O$ (Mohr's salt),the iron is in the $+2$ oxidation state.

(D) The given coordination compound is $Na_4[Fe(CN)_5NOS]$.
To determine the $IUPAC$ name:
$1$. The cation is Sodium $(Na^+)$.
$2$. The coordination entity is $[Fe(CN)_5(NOS)]^{4-}$.
$3$. The ligands are five cyanide $(CN^-)$ groups and one $NOS$ group (thionitrosyl or sulfido-nitrosyl).
$4$. The oxidation state of Iron $(Fe)$ is calculated as: $x + 5(-1) + (-1) = -4$,so $x - 6 = -4$,which gives $x = +2$.
$5$. Thus,the name is Sodium pentacyanonitrosylsulfidoferrate $(II)$.

(A) $1$. Identify the ligands: There are $8$ ammine ligands $(NH_3)$,one bridging chloro ligand $(\mu-Cl)$,and one bridging nitro ligand $(\mu-NO_2)$.
$2$. The metal center is cobalt $(Co)$. Since there are two cobalt atoms,we use the prefix 'di' for cobalt.
$3$. Determine the oxidation state of $Co$: Let the oxidation state of $Co$ be $x$. The total charge of the complex is $+4$ (since $2 \times SO_4^{2-} = -4$).
$2x + 8(0) + (-1) + (-1) = +4$
$2x - 2 = +4$
$2x = +6$
$x = +3$.
$4$. Arrange the name alphabetically: Ammine comes before chloro,which comes before nitro.
$5$. The correct $IUPAC$ name is Octaammine-$\mu$-chloro-$\mu$-nitrodicobalt $(III)$ sulfate.

(C) Let the oxidation state of $Co$ be $x$.
The charge on the cyanide ligand $(CN^-)$ is $-1$.
The overall charge on the complex $[Co(CN)_6]^{3-}$ is $-3$.
Therefore,the equation is: $x + 6(-1) = -3$.
$x - 6 = -3$.
$x = +3$.
Thus,the oxidation state of $Co$ is $+3$.

(D) The complex is $[Fe(CO)_5]$.
$CO$ (carbonyl) is a neutral ligand with an oxidation state of $0$.
Let the oxidation state of $Fe$ be $x$.
Applying the rule: $x + 5 \times (0) = 0$.
Therefore,$x = 0$.
The oxidation state of $Fe$ in $[Fe(CO)_5]$ is $0$.

(D) The coordination number is determined by the total number of donor atoms directly bonded to the central metal atom $X$. Here,$SO_4^{2-}$ acts as a bidentate ligand (or monodentate depending on context,but usually considered as occupying one coordination site in this specific complex geometry) and $5$ $NH_3$ molecules are monodentate. However,in $[X(SO_4)(NH_3)_5]Cl$,$SO_4$ is a bidentate ligand ($2$ sites) and $5$ $NH_3$ are monodentate ($5$ sites),but typically in this specific coordination sphere,$SO_4$ acts as a monodentate ligand. Thus,$1 + 5 = 6$.
To find the oxidation state of $X$:
Let the oxidation state of $X$ be $x$.
The charge of $SO_4$ is $-2$,$NH_3$ is $0$,and the outer $Cl$ is $-1$.
The complex is neutral,so: $x + (-2) + 5(0) + (-1) = 0$.
$x - 3 = 0$,which gives $x = +3$.
Therefore,the coordination number is $6$ and the oxidation number is $3$.

(B) The complex is $K[Co(CO)_4]$.
Let the oxidation number of $Co$ be $x$.
The oxidation number of $K$ is $+1$ and the ligand $CO$ (carbonyl) is neutral,so its oxidation number is $0$.
Setting the sum of oxidation states to $0$ for the neutral complex:
$1 \times (+1) + x + 4 \times (0) = 0$
$1 + x = 0$
$x = -1$
Therefore,the oxidation number of $Co$ is $-1$.

(A) Let the oxidation state of $Fe$ be $x$.
In $K_4[Fe(CN)_6]$,the oxidation state of $K$ is $+1$ and the oxidation state of $CN^-$ is $-1$.
Setting the sum of oxidation states to zero:
$4 \times (+1) + x + 6 \times (-1) = 0$
$4 + x - 6 = 0$
$x - 2 = 0$
$x = +2$
Therefore,the oxidation state of $Fe$ is $+2$.

(C) In $IUPAC$ nomenclature for coordination compounds,when the complex ion is an anion,the name of the central metal atom ends with the suffix $-ate$.
For the complex ion $[Fe(CN)_6]^{3-}$:
$1$. The ligand is $CN^-$,which is named as $cyanido$ (according to current $IUPAC$ recommendations).
$2$. There are $6$ such ligands,so the prefix is $hexa-$.
$3$. The central metal is $Fe$,which is named as $ferrate$ because the complex is an anion.
$4$. The oxidation state of $Fe$ is calculated as: $x + 6(-1) = -3$,which gives $x = +3$.
Thus,the name is $hexacyanidoferrate(III)$ ion.

(B) $1$. Identify the ligands: The complex contains two fluoride ions $(F^-)$ and two ethylenediamine $(en)$ molecules. The ligand $F^-$ is named 'fluorido' and $en$ is named 'ethane$-1,2-$diamine'.
$2$. Determine the order: Ligands are named in alphabetical order. 'Ethane$-1,2-$diamine' starts with 'e' and 'fluorido' starts with 'f'. Since there are two of each,we use the prefix 'bis' for the bidentate ligand $en$ and 'di' for $F^-$.
$3$. Oxidation state of central metal: Let the oxidation state of $Cr$ be $x$. The charge on $F$ is $-1$ and $en$ is $0$. The total charge of the complex $[CrF_2(en)_2]^+$ is $+1$ (since $Cl$ is $-1$). So,$x + 2(-1) + 2(0) = +1$,which gives $x = +3$.
$4$. Assemble the name: The name is 'difluoridobis(ethane$-1,2-$diamine)chromium$(III)$ chloride'. Among the given options,'difluoridobis(ethylene diamine) chromium$(III)$ chloride' is the standard nomenclature representation.

(B) The $IUPAC$ name is constructed by naming the cation first,followed by the anion.
For the complex $[Cr(en)_2Br_2]Br$:
$1$. The ligands are two bromide ions $(dibromido)$ and two ethylenediamine molecules $(bis(ethylenediamine))$.
$2$. The central metal ion is chromium,and its oxidation state is calculated as: $x + 2(0) + 2(-1) = +1$,so $x = +3$,which is written as $chromium(III)$.
$3$. The counter ion is bromide $(Br^-)$.
Combining these,the name is $dibromidobis(ethylenediamine)chromium(III)$ bromide.

(B) Let us analyze each option:
$A$: The complex $[Co(NH_3)_5NO_2]_3 [Co(NO_2)_6]_2$ is named correctly as pentaamminenitrito-$N$-cobalt$(III)$ hexanitrito-$N$-cobaltate$(III)$.
$B$: For $H_2[OsCl_5N]$,the oxidation state of $Os$ is $x + 5(-1) + (-3) = 0$,so $x = +8$. The name should be hydrogen pentachloridonitridoosmate$(VIII)$,not $(VI)$. Thus,this is incorrect.
$C$: For $K_2[OsCl_5N]$,the oxidation state of $Os$ is $2(+1) + x + 5(-1) + (-3) = 0$,so $x = +6$. The name is correct.
$D$: $[Cr(H_2O)_6]^{3+}$ is correctly named as hexaaquachromium$(III)$ ion.

(B) The ligand $C_2O_4^{2-}$ is named as oxalato.
Since there are three oxalato ligands,the prefix 'tri' is used.
The complex anion is $[Al(C_2O_4)_3]^{3-}$.
Let the oxidation state of $Al$ be $x$.
$x + 3(-2) = -3 \implies x - 6 = -3 \implies x = +3$.
The name of the central metal atom in the anionic complex ends with '-ate',so it becomes aluminate.
Thus,the $IUPAC$ name is Potassium trioxalatoaluminate $(III)$.

(B) To determine the oxidation state of $Ni$ in each complex:
$1$. In $Ni(CO)_4$: $x + 4(0) = 0 \implies x = 0$.
$2$. In $K_2NiF_6$: $2(+1) + x + 6(-1) = 0 \implies 2 + x - 6 = 0 \implies x = +4$.
$3$. In $[Ni(NH_3)_6](BF_4)_2$: $x + 6(0) + 2(-1) = 0 \implies x = +2$.
$4$. In $K_4[Ni(CN)_6]$: $4(+1) + x + 6(-1) = 0 \implies 4 + x - 6 = 0 \implies x = +2$.
Therefore,the highest oxidation state of nickel is $+4$ in $K_2NiF_6$.

(B) The given complex is $[Co(dmgH)_2Cl_2]$.
Here,$dmgH$ represents the dimethylglyoximate ligand,which is a neutral or monoanionic ligand depending on the context,but in this specific coordination structure,it acts as a neutral ligand (dimethylglyoxime).
There are two $Cl^-$ ligands (chloro) and one dimethylglyoxime ligand (which is bidentate,but here it is shown as a single unit chelating the metal).
However,looking at the structure,the complex is $[Co(dmgH)_2Cl_2]$.
The correct $IUPAC$ name for this coordination compound is Dichlorobis(dimethylglyoxime)cobalt $(II)$.

(B) Let the oxidation number of molybdenum $(Mo)$ be $x$.
Oxidation number of $H_2O = 0$,$C_2H_4 = 0$,$O = -2$.
For the complex $[Mo_2O_4(H_2O)_2(C_2H_4)_2]^{2-}$:
$2x + 4(-2) + 2(0) + 2(0) = -2$
$2x - 8 = -2$
$2x = 6$
$x = +3$
The oxidation state of molybdenum in the given complex is $+3$.

(C) To determine the oxidation state of the central metal atom,we use the rule that the sum of oxidation states of all atoms in a neutral complex is $0$.
In $[Ni(CO)_4]$,$CO$ is a neutral ligand with an oxidation state of $0$.
Let the oxidation state of $Ni$ be $x$.
$x + 4(0) = 0 \implies x = 0$.
Thus,in $[Ni(CO)_4]$,the transition metal $Ni$ is in the $0$ oxidation state.

(B) The ligand dimethyl glyoxime $(dmgH_2)$ loses a proton to form the dimethyl glyoximato anion $(dmgH^-)$,which acts as a bidentate ligand.
In the complex $[Fe(dmgH)_2]$,the iron is in the $+2$ oxidation state.
Since the complex is neutral,the $IUPAC$ name is constructed by naming the ligands followed by the metal name and its oxidation state.
The ligand $C_4H_7O_2N_2^-$ is named as dimethyl glyoximato.
Therefore,the correct $IUPAC$ name is $bis (dimethyl glyoximato) iron (II)$.

(B) The coordination compound $Ba[BrF_4]_2$ dissociates as: $Ba[BrF_4]_2 \rightarrow Ba^{2+} + 2[BrF_4]^{-}$.
In the complex anion $[BrF_4]^{-}$,let the oxidation state of $Br$ be $x$.
Since the charge on each $F$ atom is $-1$,we have: $x + 4(-1) = -1$.
Solving for $x$: $x - 4 = -1$,which gives $x = +3$.
Therefore,the oxidation state of $Br$ is $+3$.
The name of the complex is barium tetrafluorobromate$(III)$.

(A) In the complex $Na_4[Fe(CN)_5(NOS)]$,the ligand $NOS$ is the nitroprusside-related species,specifically $NO^+$.
Let the oxidation state of $Fe$ be $x$.
The oxidation state of $Na$ is $+1$,$CN$ is $-1$,and $NOS$ is $0$ (as it is a neutral ligand $NO$ attached to $S$ or acting as $NO^+$ depending on the complex structure,but in this specific complex,$NOS$ is treated as a neutral ligand $NO$ or $NOS$ group).
However,for the complex $Na_4[Fe(CN)_5(NOS)]$,the charge balance is: $4(+1) + x + 5(-1) + 0 = 0$.
$4 + x - 5 = 0$.
$x - 1 = 0$.
$x = +1$.
Wait,let us re-evaluate: The complex is $Na_4[Fe(CN)_5(NOS)]$. The $NOS$ ligand is $NO^+$.
$4(+1) + x + 5(-1) + (+1) = 0$.
$4 + x - 5 + 1 = 0$.
$x = 0$.
Therefore,the oxidation state of $Fe$ is $0$.

(B) Let the oxidation state of $Co$ be $x$.
$en$ (ethylenediamine) is a neutral ligand,so its charge is $0$.
$NH_2^-$ (amido) has a charge of $-1$.
$OH^-$ (hydroxo) has a charge of $-1$.
The total charge on the complex ion is $+3$.
Therefore,the equation is: $2x + 4(0) + (-1) + (-1) = +3$.
$2x - 2 = +3$.
$2x = +5$.
$x = +2.5$.
However,in such bridged complexes,the oxidation state is often represented as an average. If we assume the question implies the average oxidation state,the answer is $+2.5$. Given the options provided,there might be a discrepancy. If the complex was $[Co(NH_3)_6]^{3+}$,the oxidation state would be $+3$. Based on the provided image,the calculation leads to $+2.5$. If we must choose the closest standard integer value for such complexes,$+3$ is often cited for $Co$ in similar coordination environments,but mathematically it is $+2.5$.

(C) $1$. The complex is $[Cr(en)_3]Cl_3$.
$2$. The ligand is ethylenediamine,which is a bidentate ligand. Since it contains a numerical prefix in its name,we use the prefix 'tris' for three ligands.
$3$. The central metal atom is chromium. The oxidation state of $Cr$ is calculated as $x + 3(0) = +3$,so $x = +3$.
$4$. The name of the complex is tris(ethylenediamine)chromium $(III)$ chloride.

(D) The given complex is $[Cr(NH_3)_5(CN)]_3[Ir(NO_2)_6]_2$.
In this complex,the cationic part is $[Cr(NH_3)_5(CN)]^{2+}$ and the anionic part is $[Ir(NO_2)_6]^{3-}$.
For the cation $[Cr(NH_3)_5(CN)]^{2+}$,the oxidation state of $Cr$ is $x + 5(0) + (-1) = +2$,so $x = +3$. The name is pentaamminecyanidochromium $(III)$.
For the anion $[Ir(NO_2)_6]^{3-}$,the oxidation state of $Ir$ is $y + 6(-1) = -3$,so $y = +3$. The name is hexanitrito$-N$-iridate $(III)$.
Combining these,the $IUPAC$ name is Pentaamminecyanidochromium $(III)$ hexanitrito$-N$-iridate $(III)$.

(D) $1$. Ferrocene is $[Fe(\eta^5-C_5H_5)_2]$. The oxidation state of $Fe$ is $0$.
$2$. Sodium Nitroprusside is $Na_2[Fe(CN)_5NO]$. The oxidation state of $Fe$ is $+2$.
$3$. Brown Ring complex is $[Fe(H_2O)_5NO]SO_4$. The oxidation state of $Fe$ is $+1$.
$4$. Since none of the given oxidation states match the actual oxidation states of the central metal ions,the correct option is $D$.

(D) $1$. Identify the bridging ligands: The two $OH^-$ groups are bridging ligands,denoted by the prefix $\mu$. Since there are two,it is named di-$\mu$-hydroxido.
$2$. Identify the non-bridging ligands: There are eight $NH_3$ (ammine) ligands in total,four on each $Co$ center. This is denoted as octaammine.
$3$. Identify the metal centers: There are two cobalt atoms in the $+3$ oxidation state,denoted as dicobalt $(III)$.
$4$. Combine the parts: The correct $IUPAC$ name is di-$\mu$-hydroxidooctaamminedicobalt $(III)$ ion.
$5$. Therefore,option $(d)$ is the correct nomenclature.

(B) To name the complex $[CrCl_2(H_2O)_4]NO_3$,we follow $IUPAC$ nomenclature rules:
$1$. Ligands are named in alphabetical order: $aqua$ $(H_2O)$ comes before $chloro$ $(Cl^-)$.
$2$. There are $4$ water molecules,so we use the prefix $tetra-$,and $2$ chloride ions,so we use the prefix $di-$.
$3$. The metal is $chromium$. To find its oxidation state $(x)$: $x + 2(-1) + 4(0) = +1$ (since $NO_3$ is $-1$),so $x = +3$.
$4$. The oxidation state is written as $(III)$ in parentheses.
$5$. The anion $NO_3^-$ is named as $nitrate$ at the end.
Thus,the correct name is $tetraaquadichlorochromium(III)$ nitrate.

(A) The oxidation state of $Fe$ is calculated as: $x + (-1) + (-1) + 4(-1) = -4$,which gives $x = +2$.
The ligands present are: $N_3^-$ (azido),$O_2^-$ (superoxido),and $SCN^-$ (thiocyanato-$S$).
Since the complex ion is anionic,the metal name ends in '-ate',hence 'ferrate$(II)$'.
Combining these,the $IUPAC$ name is azidosuperoxidotetrathiocyanato-$S$-ferrate$(II)$.

(C) Let the oxidation state of molybdenum be $x$.
The complex is $[Mo_2O_4(C_2H_4)_2(H_2O_2)]^{2-}$.
Oxidation state of $O$ is $-2$,$C_2H_4$ (ethene) is $0$,and $H_2O_2$ (hydrogen peroxide) is $0$ in this coordination environment.
$2x + 4(-2) + 2(0) + 0 = -2$
$2x - 8 = -2$
$2x = 6$
$x = +3$

(A) $1$. Identify the ligands: There are $5$ ammine $(NH_3)$ ligands and $1$ nitro $(NO_2^-)$ ligand attached to the central metal atom.
$2$. Determine the oxidation state of the central metal $Co$: Let the oxidation state be $x$. The charge on $NH_3$ is $0$,$NO_2$ is $-1$,and $Cl$ is $-1$. The total charge of the complex is $0$. So,$x + 5(0) + 1(-1) + 2(-1) = 0$,which gives $x - 1 - 2 = 0$,so $x = +3$.
$3$. Apply $IUPAC$ naming rules: Name the ligands alphabetically (ammine before nitro),then the metal with its oxidation state in Roman numerals,followed by the counter ion. The name is Pentaamminenitrito-$N$-cobalt$(III)$ chloride.