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Chapter 23: Problem 56

Give the number of (valence) \(d\) electrons associated with the central metal ion in each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), (b) \(\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}\) (c) \(\mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\) (d) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{ClO}_{4}\), (e) \([\mathrm{Sr}(\mathrm{EDTA})]^{2-}\)

Short Answer

Expert verified
The number of d-electrons for the central metal ions in the given complexes are: (a) Fe(III) - 2 d-electrons (b) Mn(II) - 3 d-electrons (c) Ag(I) - 9 d-electrons (d) Cr(III) - 2 d-electrons (e) Sr(II) - 0 d-electrons

Step by step solution

01

Identify the central metal ion in each complex

The central metal ion is the atom bonded to the ligands in the complex. (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\): Fe (b) \(\left[\mathrm{Mn}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}\): Mn (c) \(\mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\): Ag (d) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{ClO}_{4}\): Cr (e) \([\mathrm{Sr}(\mathrm{EDTA})]^{2-}\): Sr
02

Determine the oxidation state of the central metal ion

Use the charges of the ligands and counterions to find the charge on the metal ion in each case: (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\): The \(\mathrm{CN^{-}}\) ligand has a charge of -1, so Fe has an oxidation state of +3. (b) \(\left[\mathrm{Mn}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}\): The \(\mathrm{NO_3^{-}}\) counterions have a charge of -1. The complex has a charge of +2, so Mn has an oxidation state of +2. (c) \(\mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\): The \(\mathrm{CN^{-}}\) ligand has a charge of -1, so Ag has an oxidation state of +1. (d) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{ClO}_{4}\): The \(\mathrm{Br^{-}}\) ligand has a charge of -1, and the \(\mathrm{ClO_4^{-}}\) counterion has a charge of -1. The complex has a charge of +1, so Cr has an oxidation state of +3. (e) \([\mathrm{Sr}(\mathrm{EDTA})]^{2-}\): EDTA is a hexadentate ligand and has a charge of -4, so Sr has an oxidation state of +2.
03

Calculate the number of d-electrons for each metal ion

Subtract the oxidation state from the group number to find the number of d-electrons: (a) Fe: Group 8, has 5 d-electrons in the ground state. Therefore, \(5 - 3 = 2\) d-electrons in the Fe(III) ion. (b) Mn: Group 7, has 5 d-electrons in the ground state. Therefore, \(5 - 2 = 3\) d-electrons in the Mn(II) ion. (c) Ag: Group 11, has 10 d-electrons in the ground state. Therefore, \(10 - 1 = 9\) d-electrons in the Ag(I) ion. (d) Cr: Group 6, has 5 d-electrons in the ground state. Therefore, \(5 - 3 = 2\) d-electrons in the Cr(III) ion. (e) Sr: Group 2, has 0 d-electrons in the ground state. Therefore, \(0 - 2 = 0\) d-electrons in the Sr(II) ion. Thus, the number of d-electrons for: (a) Fe(III) is 2 (b) Mn(II) is 3 (c) Ag(I) is 9 (d) Cr(III) is 2 (e) Sr(II) is 0

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Central Metal Ion
In coordination chemistry, the central metal ion is the pivot around which the entire complex is formed. This ion is typically a transition metal characterized by its ability to adopt multiple oxidation states and to be surrounded by ligands—a group of atoms, ions, or molecules that donate at least one pair of electrons to the metal ion to form a coordination bond.

The variety of transition metals and their electron configurations makes them particularly interesting. They can form numerous coordination compounds with diverse properties and applications. For example, iron (Fe) in hemoglobin is key to transporting oxygen in our blood, while platinum (Pt) compounds are used in chemotherapy to treat cancer.

It's crucial to identify the central ion accurately, as it influences the complex's electronic structure and reactivity. Transition metals have d-orbitals which can accommodate electrons, and these d-electrons are paramount in determining the complex's magnetic, optical, and chemical behavior. Understanding the central metal ion also assists students in predicting the geometry and stability of a complex.
Oxidation State Determination
Determining the oxidation state of a central metal ion in coordination complexes is an essential step in understanding a complex's chemical nature. The oxidation state is formally the charge an atom would have if all bonds to atoms of different elements were completely ionic.

To find the oxidation state, one must consider the overall charge of the complex and the charge of each ligand surrounding the metal ion. For instance, in a complex like \[\mathrm{Mn}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}\], the six water molecules are neutral ligands, but the two nitrate ions carry a \-1 charge each. The compound is neutral overall, so the oxidation state of manganese (Mn) must neutralize the negative charges carried by the ligands, leading to a +2 oxidation state for Mn.

This step of oxidation state determination is critical since the metal's oxidation state can influence the color, reactivity, and magnetism of the complex. Many common oxidation states for transition metals correspond with distinct colors, aiding in the identification of complexes. Students should practice using this concept, as it is one of the fundamentals of inorganic chemistry.
Coordination Complexes
A coordination complex consists of a central metal ion surrounded by molecules or anions, known as ligands. These ligands can be monodentate, attaching to the metal at a single attachment point, or polydentate, with multiple points of attachment to the metal.

The arrangement of ligands around the central metal ion is determined by the ligands' size, charge, and electron-donating capability, as well as the size and oxidation state of the central metal ion. This arrangement is referred to as the complex's 'geometry'. Common geometries include octahedral, square planar, and tetrahedral, each associated with specific electronic configurations and properties.

Examples and Varying Geometries

  • Octahedral: \[\mathrm{Fe}\left(\mathrm{CN}\right)_{6}^{3-}\] where Fe is surrounded by six cyanide ligands.
  • Tetrahedral: \[\mathrm{Zn}\left(\mathrm{Cl}\right)_{4}^{2-}\] with the zinc ion coordinated by four chloride ions.
  • Square Planar: \[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{Cl}\right)_{2}\] often found in platinum-based anticancer drugs.
Coordination complexes play a vital role in various biological systems, catalysis, and material science. For example, chlorophyll, essential for photosynthesis, is a complex of magnesium, and many catalysts used in industrial processes are based on transition metal complexes.

Understanding coordination complexes involves an interdisciplinary approach, incorporating principles from inorganic chemistry, physical chemistry, and organic chemistry. Effective grasping of this concept allows for a deeper appreciation of the intricate dance of elements that make up the vibrant world of coordination chemistry.

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Most popular questions from this chapter

(a) Draw the structure for \(\mathrm{Pt}(\mathrm{en}) \mathrm{Cl}_{2} .\) (b) What is the coordination number for platinum in this complex, and what is the coordination geometry? (c) What is the oxidation state of the platinum? [Section 23.2]

Oxyhemoglobin, with an \(\mathrm{O}_{2}\) bound to iron, is a low-spin \(\mathrm{Fe}(\mathrm{II})\) complex; deoxyhemoglobin, without the \(\mathrm{O}_{2}\) molecule, is a high-spin complex. (a) Assuming that the coordination environment about the metal is octahedral, how many unpaired electrons are centered on the metal ion in each case? (b) What ligand is coordinated to the iron in place of \(\mathrm{O}_{2}\) in deoxyhemoglobin? (c) Explain in a general way why the two forms of hemoglobin have different colors (hemoglobin is red, whereas deoxyhemoglobin has a bluish cast). (d) A 15 -minute exposure to air containing 400 ppm of CO causes about \(10 \%\) of the hemoglobin in the blood to be converted into the carbon monoxide complex, called carboxyhemoglobin. What does this suggest about the relative equilibrium constants for binding of carbon monoxide and \(\mathrm{O}_{2}\) to hemoglobin? (e) \(\mathrm{CO}\) is a strong-field ligand. What color might you expect carboxyhemoglobin to be?

(a) What is the meaning of the term coordination number as it applies to metal complexes? (b) Give an example of a ligand that is neutral and one that is negatively charged. (c) Would you expect ligands that are positively charged to be common? Explain. (d) What type of chemical bonding is characteristic of coordination compounds? Illustrate with the compound \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}\) (e) What are the most common coordination numbers for metal complexes?

Metallic elements are essential components of many important enzymes operating within our bodies. Carbonic anhydrase, which contains \(\mathrm{Zn}^{2+}\) in its active site, is responsible for rapidly interconverting dissolved \(\mathrm{CO}_{2}\) and bicarbonate ion, \(\mathrm{HCO}_{3}^{-}\). The zinc in carbonic anhydrase is tetrahedrally coordinated by three neutral nitrogen- containing groups and a water molecule. The coordinated water molecule has a \(\mathrm{p} K_{a}\) of \(7.5,\) which is crucial for the enzyme's activity. (a) Draw the active site geometry for the \(\mathrm{Zn}(\mathrm{II})\) center in carbonic anhydrase, just writing \({ }^{4} \mathrm{~N}^{n}\) for the three neutral nitrogen ligands from the protein. (b) Compare the \(\mathrm{p} K_{a}\) of carbonic anhydrase's active site with that of pure water; which species is more acidic? (c) When the coordinated water to the \(\mathrm{Zn}(\mathrm{II})\) center in carbonic anhydrase is deprotonated, what ligands are bound to the \(\mathrm{Zn}(\mathrm{II})\) center? Assume the three nitrogen ligands are unaffected. (d) The \(\mathrm{p} K_{a}\) of \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is \(10 .\) Suggest an explanation for the difference between this \(\mathrm{p} K_{a}\) and that of carbonic anhydrase. (e) Would you expect carbonic anhydrase to have a deep color, like hemoglobin and other metal-ion containing proteins do? Explain.

The molecule methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) can act as a monodentate ligand. The following are equilibrium reactions and the thermochemical data at \(298 \mathrm{~K}\) for reactions of methylamine and en with \(\mathrm{Cd}^{2+}(a q):\) $$ \begin{array}{c} \mathrm{Cd}^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \rightleftharpoons\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q) \\ \Delta H^{\circ}=-57.3 \mathrm{~kJ} ; \quad \Delta S^{\circ}=-67.3 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-37.2 \mathrm{~kJ} \\\ \mathrm{Cd}^{2+}(a q)+2 \mathrm{en}(a q) \rightleftharpoons\left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q) \\ \Delta H^{\circ}=-56.5 \mathrm{~kJ} ; \quad \Delta S^{\circ}=+14.1 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-60.7 \mathrm{~kJ} \end{array} $$ (a) Calculate \(\Delta G^{\circ}\) and the equilibrium constant \(K\) for the following ligand exchange reaction: \(\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)+2 \operatorname{en}(a q) \rightleftharpoons\) $$ \left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) $$ Based on the value of \(K\) in part (a), what would you conclude about this reaction? What concept is demonstrated? (b) Determine the magnitudes of the enthalpic \(\left(\Delta H^{\circ}\right)\) and the entropic \(\left(-T \Delta S^{\circ}\right)\) contributions to \(\Delta G^{\circ}\) for the ligand exchange reaction. Explain the relative magnitudes. (c) Based on information in this exercise and in the "A Closer Look" box on the chelate effect, predict the sign of \(\Delta H^{\circ}\) for the following hypothetical reaction: $$ \begin{aligned} \left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q) &+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \\ \left[\mathrm{Cd}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \end{aligned} $$
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