In the following brown complex, the oxidation state of iron is +_____________.

$${[Fe{({H_2}O)_6}]^{2 + }} + NO \to \mathop {{{[Fe{{({H_2}O)}_5}(NO)]}^{2 + }}}\limits_{\text{Brown complex}} + {H_2}O$$

<p>To determine the oxidation state of iron in the brown complex ${[Fe({H_2}O)_5(NO)]^{2+}}$, we need to analyze the ligands and their charges, as well as the overall charge of the complex.</p> <h3><strong>Step 1: Understanding the Complex</strong></h3> <p>The complex is:</p> <p>$ {[Fe({H_2}O)_5(NO)]^{2+}} $</p> <p><p><strong>Iron (Fe):</strong> The central metal atom whose oxidation state we need to find.</p></p> <p><p><strong>Ligands:</strong></p></p> <p><p><strong>5 Water Molecules ($H_2O$)</strong>: Neutral ligands (charge = 0).</p></p> <p><p><strong>1 Nitrosyl Group (NO)</strong>: Can have different charges depending on its mode of bonding.</p></p> <h3><strong>Step 2: Assigning Charges to Ligands</strong></h3> <p><p><strong>Water ($H_2O$)</strong>: Neutral ligand, so it contributes <strong>0</strong> to the overall charge.</p></p> <p><p><strong>Nitrosyl (NO)</strong>: Can act as:</p></p> <p><p><strong>NO$^+$</strong> (nitrosonium ion) with a <strong>+1</strong> charge.</p></p> <p><p><strong>NO</strong> (neutral molecule) with <strong>0</strong> charge.</p></p> <p><p><strong>NO$^-$</strong> (nitroxide ion) with a <strong>–1</strong> charge.</p></p> <h3><strong>Step 3: Setting Up the Oxidation State Equation</strong></h3> <p>Let $ x $ be the oxidation state of Fe.</p> <p>The sum of the oxidation states of all components equals the overall charge of the complex:</p> <p>$ x + (5 \times 0) + (\text{Charge of NO}) = +2 $</p> <p>Simplifying:</p> <p>$ x + (\text{Charge of NO}) = +2 $</p> <h3><strong>Step 4: Determining the Charge of NO in the Complex</strong></h3> <p>In the <strong>brown ring complex</strong>, experimental evidence shows that the nitrosyl ligand acts as <strong>NO$^+$</strong>. This is because:</p> <p><p>The NO ligand forms a <strong>linear bond</strong> with Fe, characteristic of NO$^+$.</p></p> <p><p>The complex is known to involve a reduction of the oxidation state of Fe to an unusual value.</p></p> <p>Thus, <strong>Charge of NO = +1</strong>.</p> <h3><strong>Step 5: Calculating the Oxidation State of Fe</strong></h3> <p>Substitute the charge of NO into the equation:</p> <p>$ x + (+1) = +2 $</p> <p>Solving for $ x $:</p> <p>$ x = +2 - (+1) = +1 $</p> <p><strong>Therefore, the oxidation state of Fe in the brown complex is $ +1 $.</strong></p> <h3><strong>Conclusion</strong></h3> <p>The oxidation state of iron in ${[Fe({H_2}O)_5(NO)]^{2+}}$ is <strong>+1</strong>.</p>