Complex compounds are molecular compounds which retain their identities even when dissolved in water. They do not give all the simple ions in solution but instead furnish complex ions. The complex compounds are often called coordination compounds because certain groups called ligands are attached to the central metal ion by coordinate or dative bonds. coordination compounds exhibit isomerism, both structural and stereoisomerism. the structure, magnetic property, colour and electrical properties of complexes are explained by various theories:
Q. The oxidation number, coordination number and magnetic moment in the following complex is:
`[Cr(C_(2)O_(4))_(2)(NH_(3))_(2)^(-)]`

Options

A. O.N.=+3,C.N.=6, M.M.=`sqrt(15)BM`
B. O.N.=-1, C.N.=6, M.M.=`sqrt(15)BM`
C. O.N.=+3, C.N.=6, M.M=`sqrt(3)BM`
D. O.N.+3,C.N.=6, M.M.=`sqrt(12)BM`

Answer

To solve the problem regarding the complex compound \([Cr(C_2O_4)_2(NH_3)_2]^-\), we will determine the oxidation number, coordination number, and magnetic moment step by step.

### Step 1: Determine the Oxidation Number
1. Let the oxidation state of chromium (Cr) be \(X\).
2. The oxalate ion \((C_2O_4)^{2-}\) is a bidentate ligand and has an oxidation number of \(-2\). Since there are two oxalate ligands, their total contribution is:
\[ 2 \times (-2) = -4 \]
3. Ammonia \((NH_3)\) is a neutral ligand, so it contributes \(0\) to the oxidation state.
4. The overall charge of the complex is \(-1\).
5. Setting up the equation:
\[ X + (-4) + 0 = -1 \]
\[ X - 4 = -1 \]
\[ X = +3 \]
6. Therefore, the oxidation number of chromium is \(+3\).

### Step 2: Determine the Coordination Number
1. The coordination number is defined as the total number of ligand donor atoms that are bonded to the central metal ion.
2. The oxalate ion \((C_2O_4)^{2-}\) is bidentate, meaning it can attach to the metal at two points. Since there are two oxalate ligands:
\[ 2 \text{ (oxalate ligands)} \times 2 \text{ (bidentate)} = 4 \]
3. Ammonia \((NH_3)\) is a monodentate ligand, which means each ammonia molecule contributes one coordination site. Since there are two ammonia ligands:
\[ 2 \text{ (ammonia ligands)} \times 1 \text{ (monodentate)} = 2 \]
4. Adding these together gives the total coordination number:
\[ 4 + 2 = 6 \]

### Step 3: Determine the Magnetic Moment
1. In the \(+3\) oxidation state, the electronic configuration of chromium is:
\[ [Ar] 3d^3 4s^0 \]
2. In this state, there are 3 electrons in the \(3d\) subshell, which means there are 3 unpaired electrons.
3. The formula for calculating the magnetic moment (\(\mu\)) in Bohr Magnetons is:
\[ \mu = \sqrt{n(n + 2)} \]
where \(n\) is the number of unpaired electrons.
4. Substituting \(n = 3\):
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{3 \times 5} = \sqrt{15} \]

### Final Results
- **Oxidation Number**: \(+3\)
- **Coordination Number**: \(6\)
- **Magnetic Moment**: \(\sqrt{15}\) Bohr Magnetons

### Summary
- The oxidation number of chromium in the complex \([Cr(C_2O_4)_2(NH_3)_2]^-\) is \(+3\).
- The coordination number is \(6\).
- The magnetic moment is \(\sqrt{15}\) Bohr Magnetons.