Problem 45 - General Chemistry

Question

Consider the complex ion \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{-}\). a. What is the oxidation state of the metal atom? b. Give the formula and name of each ligand in the ion. C. What is the coordination number of the metal atom? d. What would be the charge on the complex if all ligands were chloride ions?

Step-by-Step Solution

Answer

a. +3, b. NH3 (ammine), Cl^- (chloride), C2O4^{2-} (oxalate), c. 6, d. -3 charge if all were chlorides.

Step 1: Determine Oxidation State

In the complex ion \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{-}\), \(\mathrm{NH}_3\) is a neutral ligand, \(\mathrm{Cl}^-\) has a charge of -1, and \(\mathrm{C_2O_4}^{2-}\) (oxalate) has a charge of -2. Let the oxidation state of \(\mathrm{Cr}\) be \(x\). The equation is: \[ x + 2(0) + 2(-1) + (-2) = -1 \] Solving gives \(x = +3\). The oxidation state of chromium is +3.

Step 2: Identify Ligands and their Formulas

The ligands in the complex are: - \(\mathrm{NH}_3\) (ammine), a neutral ligand.- \(\mathrm{Cl}^-\) (chloride), which is negatively charged.- \(\mathrm{C_2O_4}^{2-}\) (oxalate), a bidentate ligand with a -2 charge.

Step 3: Determine Coordination Number

The coordination number is the number of ligand donor atoms bonded to the central metal atom. - \(\mathrm{NH}_3\) coordinates with 2 nitrogen atoms.- \(\mathrm{Cl}^-\) coordinates with 2 chlorine atoms.- \(\mathrm{C_2O_4}^{2-}\) coordinates with 2 oxygen atoms. Total = 2 + 2 + 2 = 6, so the coordination number is 6.

Step 4: Calculate Complex Charge with Chloride Ligands

If all ligands were chloride ions, replace \(\mathrm{NH}_3\) and \(\mathrm{C_2O_4}^{2-}\) with \(\mathrm{Cl}^-\). So the total count of \(\mathrm{Cl}^-\) ions becomes 1 (from each \(\mathrm{NH}_3\))\times 2 + 1 \(\mathrm{from Cl}\) \times 2 + 1 (each oxygen from \(\mathrm{C_2O_4}^{2-}\) counts as two chloride), resulting in a total of 6 chloride ions. Using the formula:\[ \text{Charge} = +3 + 6(-1) = -3 \]The charge on the complex would be -3.

Key Concepts

Oxidation State Determination

In coordination chemistry, finding the oxidation state of a metal within a complex is crucial for understanding its chemical behavior. The oxidation state tells us how many electrons the metal atom has gained or lost, which in turn influences its reactivity and interactions with other molecules.
The oxidation state in a coordination complex can be determined by considering the charges on the ligands and the overall charge of the complex. In this exercise, the complex ion is \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{-}\). Here's how you can find the oxidation state of the chromium (Cr) metal:

• Ammonia (\(\mathrm{NH}_3\)) is a neutral ligand, meaning it does not contribute any charge.
• Chloride (\(\mathrm{Cl}^{-}\)) carries a -1 charge; with two chlorides present, they contribute a total of -2.
• Oxalate (\(\mathrm{C}_2\mathrm{O}_4^{2-}\)) has a -2 charge itself.

We create an equation to account for these, letting "x" define the oxidation state of chromium:\[ x + 2(0) + 2(-1) + (-2) = -1 \]Upon solving, we find \(x = +3\). Thus, chromium has an oxidation state of +3.

Coordination Number

The coordination number in a complex indicates how many ligand atoms are directly bonded to the central metal atom. It's an important characteristic because it affects the geometry and, consequently, the properties of the complex.
For our complex \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{-}\), the coordination number is determined by counting each atom from the ligands attaching to Cr.

• Each ammonia (\(\mathrm{NH}_3\)) molecule provides one nitrogen atom that coordinates with chromium. With two \(\mathrm{NH}_3\), the contribution is 2.
• Each chloride ion (\(\mathrm{Cl}^-\)) provides one coordinating atom. With two chlorides, we get another 2.
• The oxalate ion (\(\mathrm{C}_2\mathrm{O}_4^{2-}\)) is a bidentate ligand, meaning it uses two donor atoms (oxygen atoms in this case). Thus, it contributes 2 to the coordination number.

Adding them together, \(2 + 2 + 2 = 6\), the coordination number for this chromium complex is 6.

Ligands in Coordination Complexes

Ligands are ions or molecules that bind to a central metal atom or ion in a coordination complex. They are crucial because they define the properties and stability of the complex, including the shape and electrons involved.
For the complex ion \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{-}\), several ligands are present, each with distinct characteristics:

• \(\mathrm{NH}_3\) (Ammonia): A neutral, monodentate ligand, meaning it binds through one donor atom (nitrogen).
• \(\mathrm{Cl}^-\) (Chloride): A negatively charged, monodentate ligand that coordinates through one donor atom (chlorine) and contributes to the overall charge.
• \(\mathrm{C}_2\mathrm{O}_4^{2-}\) (Oxalate): A bidentate ligand, providing two coordination points through oxygen atoms, making it versatile in forming stable complexes.

Understanding these ligands is essential as they not only determine the coordination number and geometry but also influence how the complex interacts with other substances in reactions.