CBSE · Class 12 · Chemistry · Coordination CompoundsA coordination compound has the formula $CoCl3 \cdot 5NH3$. When an aqueous solution of this compound is treated with excess silver nitrate ($AgNO3$) solution, two moles of silver chloride ($AgCl$) precipitate per mole of the compound. (a) Write the structural formula of the coordination compound. (b) Give the IUPAC name of the compound. (c) What is the secondary valency of the central metal ion in this compound? (d) Calculate the spin-only magnetic moment ($\mu$) of the central metal ion in this complex.

Step-by-Step Solution:

(a) Structural Formula Determination:

• The given empirical formula is $CoCl_3 \cdot 5NH_3$.
• When treated with excess $AgNO_3$, 2 moles of $AgCl$ are precipitated per mole of the compound. This indicates that out of 3 chlorine atoms, 2 are present outside the coordination sphere as ionizable chloride ions, while 1 chlorine atom is inside the coordination sphere.
• Therefore, the structural formula of the compound is $[Co(NH_3)_5Cl]Cl_2$.

(b) IUPAC Name of the Compound:

• Coordination sphere: $[Co(NH_3)_5Cl]^{2+}$
• Ligands: five ammine ligands and one chlorido ligand.
• Central metal: Cobalt in +3 oxidation state (calculated as $x + 5(0) - 1 - 2 = 0 \implies x = +3$).
• IUPAC Name: Pentaamminechloridocobalt(III) chloride.

(c) Secondary Valency of the Central Metal Ion:

• Secondary valency corresponds to the coordination number of the central metal ion.
• In $[Co(NH_3)_5Cl]Cl_2$, the central cobalt ion is attached to 5 $NH_3$ molecules and 1 $Cl^-$ ion via coordinate covalent bonds.
• Therefore, the coordination number (secondary valency) = 6.

(d) Calculation of Spin-Only Magnetic Moment ($\mu$):

• Central metal ion is $Co^{3+}$.
• Atomic number of Cobalt ($Z$) = 27.
• Electronic configuration of neutral Co = $[Ar] 3d^7 4s^2$.
• Electronic configuration of $Co^{3+}$ = $[Ar] 3d^6$.
• $NH_3$ is a strong field ligand, causing pairing of electrons in $3d$ orbitals for octahedral geometry ($d^2sp^3$ hybridization).
• Number of unpaired electrons ($n$) = 0.
• Formula for spin-only magnetic moment: $\mu = \sqrt{n(n+2)}$ BM
• Substituting $n = 0$: $$\mu = \sqrt{0(0+2)} = \sqrt{0} = 0 \text{ BM}$$
• The spin-only magnetic moment of the complex is 0 BM.