Problem 43 - General Chemistry

Question

Determine the oxidation number of the transition element in each of the following complexes. a. \(\mathrm{K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]\) b. \(\left[\mathrm{Mo}(\mathrm{en})_{3}\right]^{3+}\) c. \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) d. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right] \mathrm{Cl}_{2}\)

Step-by-Step Solution

Answer

Ni: +2, Mo: +3, Cr: +3, Co: +3.

Step 1: Determine the oxidation number for (a)

Complex: \( \mathrm{K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right] \). The complex ion is \([\mathrm{Ni}(\mathrm{CN})_{4}]^{2-}\). Cyanide (\(\mathrm{CN}^-\)) has a charge of \(-1\) each. There are four cyanide ions: \(-1 \times 4 = -4\).Since the overall charge of the complex ion is \(-2\), let \(x\) be the oxidation number of Ni:\[ x + (-4) = -2 \]Solve for \(x\):\[ x = +2 \]The oxidation number of Ni is \(+2\).

Step 2: Determine the oxidation number for (b)

Complex: \( \left[\mathrm{Mo}(\mathrm{en})_{3}\right]^{3+} \). The complex ion is \([\mathrm{Mo}(\mathrm{en})_{3}]^{3+}\). Ethylenediamine (en) is a neutral ligand with no charge contribution.Let \(x\) be the oxidation number of Mo:\[ x + 0 = +3 \]Solve for \(x\):\[ x = +3 \]The oxidation number of Mo is \(+3\).

Step 3: Determine the oxidation number for (c)

Complex: \( \left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]^{3-} \). The complex ion is \([\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}\). Each oxalate ion (\(\mathrm{C}_2\mathrm{O}_4^{2-}\)) contributes \(-2\). There are three oxalate ions: \(-2 \times 3 = -6\).Let \(x\) be the oxidation number of Cr:\[ x + (-6) = -3 \]Solve for \(x\):\[ x = +3 \]The oxidation number of Cr is \(+3\).

Step 4: Determine the oxidation number for (d)

Complex: \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right]\mathrm{Cl}_{2} \). The complex ion is \([\mathrm{Co}(\mathrm{NH}_3)_5(\mathrm{NO}_2)]^{2+}\). The overall charge of the complex ion needs to be \(+2\) because there are two \(\mathrm{Cl}^-\) ions contributing \(-1\) each, making the compound neutral.Ammonia (\(\mathrm{NH}_3\)) is neutral, and nitrite (\(\mathrm{NO}_2^-\)) has a charge of \(-1\).Let \(x\) be the oxidation number of Co:\[ x + 0 + (-1) = +2 \]Solve for \(x\):\[ x = +3 \]The oxidation number of Co is \(+3\).

Key Concepts

Transition Metal Complexes

Transition metal complexes are fascinating chemical compounds where a central transition metal atom or ion is bonded to several surrounding molecules or ions. These surrounding groups are known as ligands. They form the inner coordination sphere of the complex. Transition metals include elements like Nickel (Ni), Molybdenum (Mo), Chromium (Cr), and Cobalt (Co), as seen in the exercises related to the complexes. These metals have unique properties that allow them to form stable complexes with various ligands.
Some intriguing aspects of transition metal complexes include:

• Variety of Ligands: Ligands can be neutral molecules like water or ammonia, or charged ions like cyanide and oxalate. The type of ligand affects the properties of the complex.
• Coordination Number: This is the number of ligand atoms bonded directly to the metal center. It affects the shape and geometry of the complex.
• Colorful Nature: Many transition metal complexes exhibit vivid colors due to electronic transitions between d-orbitals.

These complexes play crucial roles in various fields, including chemistry, biochemistry, and industrial processes.

Oxidation Number Calculation

Calculating the oxidation number of a transition metal in a complex helps in understanding the electron distribution around the metal center. It indicates how many electrons have been lost or gained by an atom to form the compound. The general steps to determine the oxidation number in complexes involve identifying the charge on each ligand and the overall charge of the complex.
Here is a simple guide to solve for oxidation numbers:

• Identify Ligand Charges: Each ligand contributes a specific charge. For example, cyanide (\( \mathrm{CN}^- \)) carries a -1 charge.
• Total Ligand Charge: Multiply the charge of each ligand by the number of such ligands.
• Overall Complex Charge: Look at the given charge of the complex ion from the formula.
• Calculate Metal Charge: Set up an equation with the unknown metal charge, solve for the metal oxidation state.

Accurate determination of oxidation states is critical, especially in coordination chemistry and redox reactions.

Coordination Compounds

Coordination compounds are a broader category that includes transition metal complexes. They consist of a central metal atom bonded to surrounding ligands, which define the complex's properties. These compounds are distinct because the bonds between metal and ligands are coordinate covalent bonds, where ligands donate electron pairs to the metal center.
Important points regarding coordination compounds include:

• Stability: Components like the metal oxidation state and ligand type influence the compound's stability.
• Structural Diversity: Coordination numbers and geometric arrangement can vary widely, resulting in diverse properties.
• Reactivity: Coordination compounds engage in various chemical reactions, including catalysis and electron transfer.

Understanding these compounds is essential, not just in inorganic chemistry, but also in materials science and medicine.

Transition Elements

Transition elements are metals located in the d-block of the periodic table. They are known for their ability to form various oxidation states and coordination complexes. These elements have partially filled d-orbitals, which allow them to exhibit unique chemical and physical properties compared to other elements. These characteristics make them ideal for forming stable complexes and participate in important chemical reactions.
Key characteristics of transition elements include:

• Variable Oxidation States: Unlike main group elements, transition elements can exhibit more than one oxidation state.
• Colored Compounds: Many compounds of transition elements are colored due to d-d electronic transitions.
• Catalytic Properties: Transition metals are widely used as catalysts in industrial processes.

Overall, transition elements are essential to many chemical processes, including the formation of transition metal complexes discussed earlier.