Problem 9 - Chemistry and Chemical Reactivity

Question

Give the oxidation number of the metal ion in each of the following compounds. (a) \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{SO}_{4}\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (b) \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) (d) \(\mathrm{Cr}(\mathrm{en})_{2} \mathrm{Cl}_{2}\)

Step-by-Step Solution

Answer

(a) +2, (b) +3, (c) +3, (d) +2.

Step 1: Analyzing compound (a)

For the compound \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{SO}_{4}\), break it into its components. The sulfate ion \(\mathrm{SO}_4^{2-}\) has a charge of \(-2\). The ammonia ligand \(\left(\mathrm{NH}_{3}\right)\) is neutral (charge = 0), so the total charge of \([\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}]\) complex has to be \(+2\). Given \([\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}]\) is neutralizing the sulfate ion, the oxidation number of \(\mathrm{Mn}\) is \(+2\).

Step 2: Analyzing compound (b)

In \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\), the \(\mathrm{K}_3\) has a total charge of \(+3\) (since each K has \(+1\)). The cyanide ion \(\mathrm{CN}^{-}\) has a charge of \(-1\). Since there are six cyanide ions, their total charge is \(-6\). Therefore, the \([\mathrm{Co}(\mathrm{CN})_{6}]^{3-}\) complex must balance this out to be a net charge of \(-3\). Thus, \(\mathrm{Co}\) must have an oxidation number of \(+3\).

Step 3: Analyzing compound (c)

In \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\), considering the \(\mathrm{Cl}^{-}\) outside the bracket has a charge of \(-1\). Inside, four ammonia \(\left(\mathrm{NH}_3\right)\) are neutral and each chlorine \(\left(\mathrm{Cl}\right)\) has a \(-1\) charge. Hence the charge on the complex \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_{4} \mathrm{Cl}_2\right]\) must be \(+1\) to balance the \(\mathrm{Cl}^{-}\) outside, meaning \(\mathrm{Co}\) has an oxidation number of \(+3\).

Step 4: Analyzing compound (d)

For \(\mathrm{Cr}(\mathrm{en})_{2} \mathrm{Cl}_{2}\), recognize that the ethylenediamine (en) ligand is neutral. The two chloride ions \(\mathrm{Cl}^{-}\) contribute a total charge of \(-2\). The entire compound is neutral, so \(\mathrm{Cr}\) must balance the \(-2\) from the chlorides. Therefore, the oxidation number of \(\mathrm{Cr}\) is \(+2\).

Key Concepts

Coordination Compounds

Coordination compounds are fascinating structures formed by the combination of metal ions and ligands. A central metal atom or ion is surrounded by molecules or ions called ligands. These structures are typically enclosed in square brackets. For example, in \([\mathrm{Co}(\mathrm{CN})_{6}]^{3-}\), cobalt is the central metal, with cyanide ions as ligands. Coordination compounds have unique properties and are often colorful due to the electronic transitions within the d orbitals of transition metals.

• The central metal is the core around which the compound is built.
• Ligands, which are atoms or molecules that donate pairs of electrons, bind to the central metal.
• Coordination compounds can act as single units in reactions.

Understanding these compounds is crucial in fields like chemistry and materials science, given their application in catalysis and pharmaceuticals.

Ligand Charges

Ligand charges play a crucial role in determining the overall charge of coordination compounds. Ligands can be neutral or charged. For instance, ammonia \(\left(\mathrm{NH}_3\right)\) is a neutral ligand, while cyanide \(\left(\mathrm{CN}^-\right)\) carries a negative charge.

• Neutral ligands do not impact the compound's net charge, simplifying oxidation number calculations.
• Charged ligands, such as \(\mathrm{Cl}^-\), directly influence the overall charge of the compound.

To find the oxidation number of the metal, sum the charges of all ligands and compare it with the known charge of the whole coordination complex.

Transition Metals

Transition metals are the central stars in coordination compounds. They include familiar elements like chromium, cobalt, and manganese. These metals have partially filled d orbitals, allowing them to form complex shapes with various ligands.

• They can exhibit multiple oxidation states, which makes them versatile in forming compounds.
• The element's position in the periodic table and its electron configuration can help predict likely oxidation states.

Transition metals are essential in many chemical processes, serving as catalysts and forming stable coordination compounds. This versatility comes from their ability to donate and accept electrons.

Charge Balancing

Charge balancing is a fundamental principle in understanding coordination compounds. It ensures that the sum of all charges in a compound equals the net charge indicated.

• Each ion or molecule involved in the compound must contribute to this balance.
• The oxidation number of the metal is determined by ensuring the sum of the ligand charges and the metal's oxidation state equals the overall charge.

For example, if a compound is neutral, the sum of all positive and negative charges must equal zero. By understanding how ligands and transition metals interact, you can easily balance charges and determine oxidation states.