Problem 45 - Chemistry The Molecular Science

Question

Consider the complex ion \(\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2} \mathrm{Cl}_{2}\right]^{3-}\). (a) Identify the ligands and their charges (if any). (b) Determine the charge on the central metal ion. (c) Determine the formula and charge of the complex ion in which the \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) ions were replaced by \(\mathrm{NH}_{3}\) molecules.

Step-by-Step Solution

Answer

Ligands: \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\) (oxalate), \(\mathrm{Cl}^{-}\). Co is +3. New complex: \([\mathrm{Co}(\mathrm{NH}_{3})_{2} \mathrm{Cl}_{2}]^{+}\).

Step 1: Identify the ligands and their charges

The complex ion \([\mathrm{Co}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2} \mathrm{Cl}_{2}\right]^{3-}\) contains the following ligands: 1. Oxalate \((\mathrm{C}_{2}\mathrm{O}_{4}^{2-})\): Each oxalate ion carries a charge of -2. 2. Chloride \((\mathrm{Cl}^{-})\): Each chloride ion carries a charge of -1.

Step 2: Calculate the total charge of ligands

The total charge of the ligands can be calculated by adding up their individual charges:- Two oxalate ions contribute a total charge of \(2 \times (-2) = -4\).- Two chloride ions contribute a total charge of \(2 \times (-1) = -2\).Thus, the total charge of all the ligands is \((-4) + (-2) = -6\).

Step 3: Determine the charge on the central metal ion

Given that the overall charge of the complex ion \([\mathrm{Co}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2} \mathrm{Cl}_{2}\right]^{3-}\) is -3, we can find the charge on the cobalt ion by balancing the total charge of the ligands and the complex:Let the charge of the cobalt ion be \(x\). Then, we have \(x + (-6) = -3\).Solving for \(x\), we find \(x = -3 + 6 = +3\).Thus, the charge on the central metal ion (Co) is +3.

Step 4: Replacement of oxalate ions with ammonia molecules

Replacing the \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\) ions with \(\mathrm{NH}_{3}\), which is a neutral ligand, does not alter the total auxiliary ligand charge as ammonia contributes no charge. The new complex ion becomes \[\mathrm{Co}(\mathrm{NH}_{3})_{2} \mathrm{Cl}_{2}\].

Step 5: Determine the charge of the new complex ion

The new complex \[\mathrm{Co}(\mathrm{NH}_{3})_{2} \mathrm{Cl}_{2}\] contains two neutral ammonia molecules and two negatively charged chloride ions:- Two chloride ions contribute a total charge of \(2 \times (-1) = -2\).The cobalt ion retains its charge of +3, so the overall charge of the complex ion is \(3 - 2 = +1\).Therefore, the charge of the complex ion is +1.

Key Concepts

Understanding Ligands

In coordination chemistry, ligands are molecules or ions that bind to a central metal atom or ion. They donate pairs of electrons to form coordinate covalent bonds. Ligands are vital in the formation of complex ions because they directly influence the stability and reactivity of the complex.Consider the given complex ion \( \left[\mathrm{Co}(\mathrm{C}_{2}\mathrm{O}_{4})_{2} \mathrm{Cl}_{2}\right]^{3-} \). In this complex:

• Oxalate \( (\mathrm{C}_{2}\mathrm{O}_{4}^{2-}) \) acts as a bidentate ligand, meaning it can form two bonds with the central metal ion with its two negatively charged oxygen atoms.
• Chloride \( (\mathrm{Cl}^{-}) \) is a monodentate ligand, contributing one electron pair for bonding to the metal ion.

These ligands add specificity to the structure and properties of the complex ion.

Complex Ion Charge

The charge of a complex ion is critical in understanding its overall reactivity and formation. It results from the cumulative charges of both the central metal ion and surrounding ligands.For \( \left[\mathrm{Co}(\mathrm{C}_{2}\mathrm{O}_{4})_{2} \mathrm{Cl}_{2}\right]^{3-} \), the complex ion overall has a \( -3 \) charge. To calculate this:

• The total charge contributed by the ligands, two oxalate ions and two chloride ions, is \( -6 \); \( -4 \) from oxalates and \( -2 \) from chlorides.
• If the total ligand charge is offset by the central cobalt ion's positive charge, the resulting net charge becomes \( -3 \).

Thus, understanding each component's charge aids in correctly determining the overall charge of the complex ion.

Cobalt Ion Charge

The central metal ion, in this case cobalt, plays a crucial role in determining the characteristics of a complex ion. The charge of the cobalt ion needs to balance with that of its ligands to result in the net charge of the complex ion.Given:

• Total charge of \( \left[\mathrm{Co}(\mathrm{C}_{2}\mathrm{O}_{4})_{2} \mathrm{Cl}_{2}\right]^{3-} \) is \( -3 \).
• Ligand charge contribution is \( -6 \).

We can set up the equation \( x + (-6) = -3 \), where \( x \) is the charge of the cobalt ion. Solving gives: \( x = +3 \). This indicates that the cobalt ion contributes a positive \( +3 \) charge within the complex.

Role of Oxalate Ion

Oxalate ions are essential in coordination chemistry due to their bidentate nature, allowing them to form two bonds with the metal center. Oxalate (\(\mathrm{C}_2\mathrm{O}_4^{2-}\)) carries a net negative charge of \( -2 \). In the complex ion, \( \left[\mathrm{Co}(\mathrm{C}_{2}\mathrm{O}_{4})_{2} \mathrm{Cl}_{2}\right]^{3-} \), each oxalate ion forms two chelate rings with the cobalt ion, lending stability.The overall contribution of two oxalate ions is \( 2 \times (-2) = -4 \). This charge is critical in balancing the total charge in the complex, indicating how the combination of oxalate ions helps achieve the required structural stability and charge balance in coordination complexes.

Function of Ammonia Ligand

Ammonia molecules are common neutral ligands in coordination chemistry. Unlike many anionic ligands, ammonia does not contribute to the charge of the complex. Instead, it provides lone pairs of electrons for bonding to the metal ion.For example, replacing oxalate ions with ammonia in the complex \( \left[\mathrm{Co}(\mathrm{NH}_3)_{2} \mathrm{Cl}_2\right] \), you get:

• The ammonia molecules, being neutral, do not alter the charge characteristics, so no charge is contributed by ammonia.
• After substitution, the complex retains the cobalt ion's charge \( +3 \) and the chlorides \( -2 \), resulting in an overall charge of \( +1 \).

This example highlights ammonia's neutrality, making it valuable when designing complexes with specific charge and bonding needs.