In the complex K[Cr(H2O)2(C2O4)2], Central metal ion is and .
Step 1: Identify the Oxidation State of Chromium
- The given complex is K[Cr(H2O)2(C2O4)2].
- Potassium (K+) has a charge of +1.
- The ligands are:
H2O (Water): Neutral ligand (charge = 0).
C2O42- (Oxalate): Bidentate ligand (charge = -2 each).
Step 2: Oxidation State Calculation
\[ +1 + x + 2(0) + 2(-2) = 0 \] \[ x - 4 + 1 = 0 \] \[ x = +3 \] So, the oxidation state of Chromium (Cr) is +3.
Step 3: Coordination Number of Chromium
- H2O (Water) is a monodentate ligand (2 × 1 = 2).
- C2O42- (Oxalate) is a bidentate ligand (2 × 2 = 4).
- Total coordination number: \[ 2 + 4 = 6 \] So, the coordination number of Chromium is 6.
Step 4: Conclusion
- The central metal ion is Cr3+.
- The coordination number is 6.
If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]