Write IUPAC names of the following coordination entities:
(a) \( [Fe(en)_2Cl_2]^+ \)
(b) \( [Co(NH_3)_4(H_2O)Br]SO_4 \)
(c) \( [Ni(CN)_4]^{2-} \)
To solve the problem, we need to write the IUPAC names of the given coordination entities: (a) \( [Fe(en)_2Cl_2]^+ \), (b) \( [Co(NH_3)_4(H_2O)Br]SO_4 \), and (c) \( [Ni(CN)_4]^{2-} \).
1. Name \( [Fe(en)_2Cl_2]^+ \):
- Central metal: Fe, oxidation state: +3 (since 2 Cl⁻ give -2, total charge +1, so Fe is +3).
- Ligands: en (ethylenediamine, neutral) × 2, Cl⁻ × 2.
- Name ligands alphabetically: ‘en’ (di- for 2) as ethylenediamine, Cl as chloro.
- Complex is cationic, so metal name is iron(III).
IUPAC name: \( \text{Dichloridobis(ethylenediamine)iron(III)} \).
2. Name \( [Co(NH_3)_4(H_2O)Br]SO_4 \):
- Central metal: Co, oxidation state: +3 (Br⁻ gives -1, \( SO_4^{2-} \) gives -2, total charge 0, so Co is +3).
- Ligands in complex: \( NH_3 \) (neutral) × 4, \( H_2O \) (neutral) × 1, Br⁻ × 1.
- Name ligands alphabetically: ammine (\( NH_3 \), tetra- for 4), aqua (\( H_2O \)), bromido (Br⁻).
- Complex is cationic, counter ion is sulfate, metal name is cobalt(III).
IUPAC name: \( \text{Tetraammineaquabromidocobalt(III) sulfate} \).
3. Name \( [Ni(CN)_4]^{2-} \):
- Central metal: Ni, oxidation state: +2 (4 CN⁻ give -4, total charge -2, so Ni is +2).
- Ligands: CN⁻ × 4, named as cyano (but in IUPAC, ‘cyano’ is used, tetra- for 4).
- Complex is anionic, so metal name is nickelate(II).
IUPAC name: \( \text{Tetracyanonickelate(II)} \).
Final Answer:
(a) \( \text{Dichloridobis(ethylenediamine)iron(III)} \), (b) \( \text{Tetraammineaquabromidocobalt(III) sulfate} \), (c) \( \text{Tetracyanonickelate(II)} \).
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).