Question

Consider the following test for a group-IV cation. \[ \text{M}^{2+} + \text{H}_2\text{S} \rightarrow \text{A (Black precipitate)} + \text{byproduct} \] \[ \text{A + aqua regia} \rightarrow \text{B + NOCl + S + H}_2\text{O} \] \[ \text{B + KNO}_2 + \text{CH}_3\text{COOH} \rightarrow \text{C + byproduct} \] The spin-only magnetic moment value of the metal complex \( \text{C} \) is \( \dots \dots \dots \) BM. (Nearest integer)

Answer 1

Correct Answer: 0

The problem requires the identification of the cation \( \text{M}^{2+} \) and its subsequent reactions to form the metal complex \( \text{C} \). This process will allow for the determination of the spin-only magnetic moment of \( \text{C} \).

Step 1: Cation Identification

The formation of a black precipitate \( \text{A} \) upon reaction of \( \text{M}^{2+} \) with \( \text{H}_2\text{S} \) indicates a metal sulfide typical of group-IV cations. \( \text{PbS} \) is a probable candidate due to its black color, suggesting \( \text{M}^{2+} \) is \( \text{Pb}^{2+} \).

Step 2: Aqua Regia Reaction

Reaction of \( \text{A} \) (\( \text{PbS} \)) with aqua regia yields product \( \text{B} \), along with \( \text{NOCl, S} \), and \( \text{H}_2\text{O} \). \( \text{PbS} \) typically produces elemental sulfur and \( \text{Pb(NO}_3\text{)}_2 \), which is \( \text{B} \).

Step 3: Formation of C

Compound \( \text{B (Pb(NO}_3\text{)}_2) \) reacts with \( \text{KNO}_2 \) and \( \text{CH}_3\text{COOH} \) to form \( \text{C} \). \( \text{Pb(CH}_3\text{COO)}_2 \) is a common complex formed in this context.

Step 4: Spin-Only Magnetic Moment Calculation

The spin-only magnetic moment \( \mu \) is calculated using \( \mu = \sqrt{n(n+2)} \) BM, where \( n \) is the number of unpaired electrons. Lead (Pb) in the +2 oxidation state has the electronic configuration [Xe]4f¹⁴5d¹⁰6s⁰6p⁰, meaning it has 0 unpaired electrons.

Therefore, \( \mu = \sqrt{0(0+2)} = 0 \) BM.

Step 5: Verification

The computed magnetic moment of \( 0 \) BM falls within the specified range (0,0), confirming the accuracy of the result and its expected parameters.

Consequently, the spin-only magnetic moment of the metal complex \( \text{C} \) is 0 BM.