To solve the problem, we need to determine the type of isomerism shown by the complex \([Co(NH₃)_6][Cr(CN)_6]\).
1. Understanding the Complex:
The given complex is a coordination compound with two parts: \([Co(NH₃)_6]^{3+}\) and \([Cr(CN)_6]^{3-}\). The first part, \([Co(NH₃)_6]^{3+}\), is a complex of cobalt with six ammonia (NH₃) molecules as ligands, while the second part, \([Cr(CN)_6]^{3-}\), is a complex of chromium with six cyanide (CN⁻) ions as ligands.
2. Types of Isomerism:
Coordination compounds can exhibit several types of isomerism, including:
- Ionization isomerism: Occurs when the complex ions in the compound interchange their positions in the formula, leading to different ions in solution.
- Linkage isomerism: Occurs when a ligand can coordinate to the metal through two different atoms, giving rise to different isomers.
- Geometrical isomerism: Occurs when ligands are arranged in different spatial orientations around the metal center.
- Optical isomerism: Occurs when the complex can exist in non-superimposable mirror image forms (chirality).
3. Identifying the Type of Isomerism in \([Co(NH₃)_6][Cr(CN)_6]\):
This complex can exhibit ionization isomerism. Ionization isomerism occurs when two different compounds with the same molecular formula produce different ions in solution due to the exchange of ligands between the metal centers. In this case, if the cyanide ion (CN⁻) were to replace one of the ammonia (NH₃) ligands in the \([Co(NH₃)_6]^{3+}\) complex, and vice versa, two different compounds would result. One complex would have the \([Co(NH₃)_5(CN)]^{3+}\) ion and the \([Cr(CN)_6]^{3-}\) ion, while the other complex would have the \([Co(CN)_6]^{3-}\) ion and the \([Cr(NH₃)_6]^{3+}\) ion. These would give rise to different ions in solution, showing ionization isomerism.
4. Final Answer:
The complex \([Co(NH₃)_6][Cr(CN)_6]\) shows ionization isomerism.
(i) Draw the diagram which indicates the splitting of d-orbitals in tetrahedral field.
(ii) Write any one limitation of valence bond theory.
(i)[Ni(CN)₄]²⁻ and [Ni(CO)(_4)] have different structures, but do not differ in their magnetic behaviour. Explain.
(ii) Write the formula of Tetraamineaquachloridocobalt(III)chloride.
(i) Write two postulates of Werner's coordination theory.
(ii) Draw the geometrical isomers of [(NH_3)_3(NO_2)_3] and give their structures.
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 \(P,O,Q\).