Problem 60 - A Complete Resource Book in Chemistry for JEE Main

Question

The oxidation state of Mo in its oxo-complex species \(\left[\mathrm{Mo}_{2} \mathrm{O}_{4}\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{2-}\) is (a) \(+2\) (b) \(+3\) (c) \(+4\) (d) \(+5\)

Step-by-Step Solution

Answer

The oxidation state of Mo is +3.

Step 1: Determine the Charge Balance

The given complex is \(\left[\mathrm{Mo}_{2}\mathrm{O}_{4}\left(\mathrm{C}_{2}\mathrm{H}_{4}\right)_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right]^{2-}\). The entire complex carries a charge of \(-2\). We need to balance this charge with the oxidation states of the component ions and ligands.

Step 2: Assign Known Oxidation States

Oxygen generally has an oxidation state of \(-2\), and each \(\mathrm{O}\) contributes \(-2\) in the complex. There are 4 oxygen atoms, hence contributing \(-8\) in total. \(\mathrm{H}_{2}\mathrm{O}\) and \(\mathrm{C}_{2}\mathrm{H}_{4}\) are neutral ligands, contributing \(0\) to the oxidation state.

Step 3: Set Up the Equation

Using the information from the previous steps, express the sum of oxidation states as \(2x\) (for the two molybdenum atoms) and solve:\[2x + (-8) + 0 = -2\]

Step 4: Solve for Oxidation State of Molybdenum

Simplify and solve the equation:1. \(2x - 8 = -2\)2. \(2x = 6\)3. \(x = +3\)Thus, the oxidation state of each molybdenum atom (Mo) is \(+3\).

Key Concepts

Molybdenum Complexes

Molybdenum complexes are coordination compounds that include molybdenum, a transition metal, bound to various ligands. These complexes are important in many chemical reactions and have significant roles in catalysis and industrial processes. Molybdenum can form a variety of coordination numbers and geometries, making it versatile in complex formation.

• Molybdenum often exhibits oxidation states ranging from "+2" to "+6," allowing it to participate in diverse chemical environments.
• In coordination chemistry, ligands can be organic, such as ethylene (\( \mathrm{C}_2 \mathrm{H}_4 \)) or inorganic, like oxo-ligands (\( \mathrm{O}^{2-} \)).
• The bonding and stability of these complexes depend on the type of ligands and the oxidation state of molybdenum.

Understanding how molybdenum interacts with its ligands is essential for predicting the complex's behavior in reactions. This knowledge assists in industrial and laboratory synthesis of molybdenum chemicals.

Oxo-Complex Analysis

Oxo-complexes are coordination compounds that include oxo-ligands, typically oxygen atoms with a "+2" oxidation state. The analysis of these complexes involves understanding the role of oxo-ligands and how they influence the properties of the complex.

• Oxo-ligands are highly electronegative, which strongly influences the electron distribution within the complex.
• These ligands often stabilize the high oxidation states of metal centers, such as molybdenum in our example.
• Analyzing the contribution of oxo-ligands helps in determining the overall charge and stability of the complex.

In the given molybdenum complex, \( \mathrm{Mo}_2\mathrm{O}_4 \) represents an integral part where each oxygen contributes significantly to the overall oxidation state calculation. Recognizing the behavior of these ligands allows for more precise calculation of the metal's oxidation state.

Charge Balance in Coordination Compounds

Charge balance in coordination compounds is a fundamental concept in determining the oxidation states of the metal centers. This involves balancing the net charge of the entire compound with the known and unknown oxidation states of its individual components.

• Identify the charge on the complex. For \( \left[\mathrm{Mo}_2\mathrm{O}_4\left(\mathrm{C}_2\mathrm{H}_4\right)_2\left(\mathrm{H}_2\mathrm{O}\right)_2\right]^{2-} \), the overall charge is "+2," affecting how we balance individual oxidation states.
• Assign known oxidation states to all identifiable parts (like oxo-ligands with "-2") and figure out the unknown ones (molybdenum in this case).
• Create an equation setting the sum of these charges equal to the total compound charge and solve for each unknown.

By understanding charge balance, we determine that in our exercise, molybdenum holds an oxidation state of "\(+3\)" based on the known and calculated values. This process highlights how intrinsic charge properties guide the chemistry of the complex.