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 question regarding the oxidation number, coordination number, and magnetic moment of the complex compound \([Cr(C_2O_4)_2(NH_3)_2]^-\), we will follow these steps:

### Step 1: Determine the Oxidation Number of Chromium
1. Identify the charges of the ligands:
- The oxalate ion \((C_2O_4)^{2-}\) has a charge of \(-2\).
- There are 2 oxalate ions, contributing a total charge of \(-4\).
- The ammonia \((NH_3)\) is a neutral ligand, contributing \(0\) charge.

2. Set up the equation for the overall charge of the complex:
\[ \text{Total charge} = \text{Oxidation state of Cr} + \text{Charge from ligands} \]
\[ -1 = x + (-4) \]
where \(x\) is the oxidation state of chromium.

3. Solve for \(x\):
\[ x - 4 = -1 \implies x = +3 \]

### Step 2: Determine the Coordination Number
1. Identify the number of ligands attached to the central metal ion (Cr):
- Each oxalate ion is a bidentate ligand, meaning it can attach through two donor atoms (O atoms).
- Therefore, 2 oxalate ions contribute \(2 \times 2 = 4\) coordination sites.
- The 2 ammonia ligands each contribute 1 coordination site, adding 2 more.

2. Calculate the total coordination number:
\[ \text{Coordination number} = 4 (\text{from oxalate}) + 2 (\text{from ammonia}) = 6 \]

### Step 3: Determine the Magnetic Moment
1. Determine the electronic configuration of chromium in the +3 oxidation state:
- The electronic configuration of neutral chromium (Cr) is \([Ar] 3d^5 4s^1\).
- In the +3 oxidation state, it loses 3 electrons, resulting in \([Ar] 3d^3\).

2. Count the number of unpaired electrons in \(3d^3\):
- There are 3 unpaired electrons in the \(3d\) subshell.

3. Calculate the magnetic moment using the formula:
\[ \mu = \sqrt{n(n+2)} \]
where \(n\) is the number of unpaired electrons:
\[ \mu = \sqrt{3(3+2)} = \sqrt{15} \]

### Final Answers
- **Oxidation Number of Chromium**: +3
- **Coordination Number**: 6
- **Magnetic Moment**: \(\sqrt{15}\)