Problem 47 - Chemistry The Molecular Science

Question

Determine the charge of the central metal ion in each case. (a) \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}(\mathrm{OH})\right]^{+}\) (b) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]^{+}\) (c) \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-}\)

Step-by-Step Solution

Answer

(a) Zn: +2, (b) Pt: +4, (c) Cr: +3.

Step 1: Understanding the Problem

We need to find the charge of the metal ion in each coordination complex. This involves balancing the charges between the metal ion and the ligands.

Step 2: Determining the Charge of Ligands

Identify the charge of each ligand in the coordination sphere. For (a) \(\left[\mathrm{Zn}\left(\mathrm{H}_{2}\mathrm{O}\right)_{3}(\mathrm{OH})\right]^{+}\): \(\mathrm{H}_2\mathrm{O}\) is neutral and \(\mathrm{OH}^{-}\) has a charge of -1. For (b) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3}\mathrm{Cl}_{3}\right]^{+}\): \(\mathrm{NH}_{3}\) is neutral and \(\mathrm{Cl}^{-}\) has a charge of -1 each. For (c) \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-}\): \(\mathrm{CN}^{-}\) has a charge of -1 each.

Step 3: Calculating Total Charge of Ligands

Calculate the total charge from the ligands. In (a) \(3(0) + (-1) = -1\). In (b) \(3(0) + 3(-1) = -3\). In (c) \(6(-1) = -6\).

Step 4: Solving for the Metal Ion Charge

Use the overall charge of the complex to find the charge on the metal ion. For (a) \([\mathrm{Zn}(\mathrm{H}_2\mathrm{O})_3(\mathrm{OH})]^+\), \(\text{Zn} + (-1) = +1\), thus \(\text{Zn}^{2+}\). For (b) \([\mathrm{Pt}(\mathrm{NH}_3)_3\mathrm{Cl}_3]^+\), \(\text{Pt} + (-3) = +1\), thus \(\text{Pt}^{4+}\). For (c) \([\mathrm{Cr}(\mathrm{CN})_6]^{3-}\), \(\text{Cr} - 6 = -3\), thus \(\text{Cr}^{3+}\).

Key Concepts

Metal Ion Charge

The charge of a metal ion in a coordination complex is central to understanding its chemical properties. To determine this charge: the first step is recognizing that the total complex charge is a balance of the charges from the metal ion and its bound ligands. This process involves simple arithmetic: adding or subtracting the known charges of the ligands from the complex's overall charge to solve for the metal's charge.

For example, in the complex \([\text{Zn}(\text{H}_2\text{O})_3(\text{OH})]^+\), we find that hydroxide (\