Problem 62 - Chemistry An Atoms First Approach

Question

Write equations for the stepwise formation of each of the following complex ions. a. \(\mathrm{CoF}_{6}^{3-}\) b. \(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\)

Step-by-Step Solution

Answer

The stepwise formation equations for the given complex ions are: a. Hexafluorocobaltate(III) ion \(\mathrm{CoF}_{6}^{3-}\) 1. \(\mathrm{[Co(H_{2}O)_6]^{3+} + F^{-} \rightarrow [CoF(H_{2}O)_5]^{2+} + H_{2}O}\) 2. \(\mathrm{[CoF(H_{2}O)_5]^{2+} + F^{-} \rightarrow [CoF_2(H_{2}O)_4]^{+} + H_{2}O}\) 3. \(\mathrm{[CoF_2(H_{2}O)_4]^{+} + F^{-} \rightarrow [CoF_3(H_{2}O)_3]^{0} + H_{2}O}\) 4. \(\mathrm{[CoF_3(H_{2}O)_3]^{0} + F^{-} \rightarrow [CoF_4(H_{2}O)_2]^{-} + H_{2}O}\) 5. \(\mathrm{[CoF_4(H_{2}O)_2]^{-} + F^{-} \rightarrow [CoF_5(H_{2}O)]^{2-} + H_{2}O}\) 6. \(\mathrm{[CoF_5(H_{2}O)]^{2-} + F^{-} \rightarrow [CoF_6]^{3-} + H_{2}O}\) b. Tetraamminezinc(II) ion \(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\) 1. \(\mathrm{[Zn(H_{2}O)_6]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})(H_{2}O)_5]^{2+} + H_{2}O}\) 2. \(\mathrm{[Zn(NH_{3})(H_{2}O)_5]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})_2(H_{2}O)_4]^{2+} + H_{2}O}\) 3. \(\mathrm{[Zn(NH_{3})_2(H_{2}O)_4]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})_3(H_{2}O)_3]^{2+} + H_{2}O}\) 4. \(\mathrm{[Zn(NH_{3})_3(H_{2}O)_3]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})_4(H_{2}O)_2]^{2+} + H_{2}O}\)

Step 1: Identify the central metal ion and ligands

In this complex, the central metal ion is cobalt (Co) with an oxidation state of +3, and the ligands are six fluoride ions (F\(^-\)).

Step 2: Write the stepwise formation equations

The fluoride ligands will replace water molecules in Co\(^{3+}\)'s coordination sphere. We will start with the hexaaquacobalt(III) ion, \(\mathrm{[Co(H_{2}O)_6]^{3+}}\), and replace each water molecule with a fluoride ion: 1. \(\mathrm{[Co(H_{2}O)_6]^{3+} + F^{-} \rightarrow [CoF(H_{2}O)_5]^{2+} + H_{2}O}\) 2. \(\mathrm{[CoF(H_{2}O)_5]^{2+} + F^{-} \rightarrow [CoF_2(H_{2}O)_4]^{+} + H_{2}O}\) 3. \(\mathrm{[CoF_2(H_{2}O)_4]^{+} + F^{-} \rightarrow [CoF_3(H_{2}O)_3]^{0} + H_{2}O}\) 4. \(\mathrm{[CoF_3(H_{2}O)_3]^{0} + F^{-} \rightarrow [CoF_4(H_{2}O)_2]^{-} + H_{2}O}\) 5. \(\mathrm{[CoF_4(H_{2}O)_2]^{-} + F^{-} \rightarrow [CoF_5(H_{2}O)]^{2-} + H_{2}O}\) 6. \(\mathrm{[CoF_5(H_{2}O)]^{2-} + F^{-} \rightarrow [CoF_6]^{3-} + H_{2}O}\) b. Tetraamminezinc(II) complex ion (\(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\))

Step 1: Identify the central metal ion and ligands

In this complex, the central metal ion is zinc (Zn) with an oxidation state of +2, and the ligands are four ammonia molecules (NH\(_3\)).

Step 2: Write the stepwise formation equations

The ammonia ligands will replace water molecules in Zn\(^{2+}\)'s coordination sphere. We will start with the hexaaquazinc(II) ion, \(\mathrm{[Zn(H_{2}O)_6]^{2+}}\), and replace each water molecule with an ammonia molecule: 1. \(\mathrm{[Zn(H_{2}O)_6]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})(H_{2}O)_5]^{2+} + H_{2}O}\) 2. \(\mathrm{[Zn(NH_{3})(H_{2}O)_5]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})_2(H_{2}O)_4]^{2+} + H_{2}O}\) 3. \(\mathrm{[Zn(NH_{3})_2(H_{2}O)_4]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})_3(H_{2}O)_3]^{2+} + H_{2}O}\) 4. \(\mathrm{[Zn(NH_{3})_3(H_{2}O)_3]^{2+} + NH_{3} \rightarrow [Zn(NH_{3})_4(H_{2}O)_2]^{2+} + H_{2}O}\) Note that we only showed the replacement of four water molecules by ammonia molecules because the final complex ion has four NH\(_3\) ligands.