/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 The complex \(\left[\mathrm{Mn}\... [FREE SOLUTION] | 91影视

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Chapter 24: Problem 47

The complex \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) contains five unpaired electrons. Sketch the energy-level diagram for the \(d\) orbitals, and indicate the placement of electrons for this complex ion. Is the ion a high-spin or a low-spin complex?

Short Answer

Expert verified
The energy-level diagram for the \(d\) orbitals of the complex ion \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) has all five electrons in the \(t_{2g}\) orbitals and no electrons in the \(e_g\) orbitals. The complex ion is a low-spin complex due to the presence of a strong field ligand (\(NH_3\)).

Step by step solution

01

Determine the electron configuration of the Mn2+ ion

First, we need to find the electron configuration of Mn in its 2+ oxidation state. Manganese, being the 25th element in the periodic table, has the electron configuration \([Ar] 3d^5 4s^2\). Losing two electrons will give Mn2+ the electron configuration \([Ar] 3d^5\). Thus, there are five 3d electrons to consider when placing them in the energy-level diagram.
02

Understand the energy levels and placement of d-orbitals in octahedral complexes

In octahedral complexes, the five \(d\) orbitals are split into two different energy levels due to the crystal field. The three orbitals \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) have the same energy level, while the other two orbitals, \(d_{z^2}\) and \(d_{x^2-y^2}\), have a higher energy level. The energy-level diagram would look like this in simple terms: ``` _______ (eg) (eg) | d_{z^2}, d_{x^2-y^2} _______ (t2g) (t2g) | d_{xy}, d_{xz}, d_{yz} ```
03

Identify the ligand and its effect on the crystal field.

The ligand in our complex ion is \(NH_3\), which is a strong field ligand. In the presence of a strong field ligand, the energy gap between the \(t_{2g}\) and \(e_g\) orbitals is large, which results in a low-spin complex where electrons preferentially fill the lower-energy \(t_{2g}\) orbitals before occupying the higher-energy \(e_g\) orbitals.
04

Place electrons in the energy-level diagram

Since we determined that our complex ion is a low-spin complex, we follow the rules of Hund to put the electrons in the \(d\) orbitals. ``` _______ (eg) (eg) | Empty _______ (t2g) (t2g) | 1鈫戔啌, 1鈫戔啌, 1鈫�0 ```
05

Conclusion

The energy-level diagram for the \(d\) orbitals of the complex ion \(\left[\mathrm{Mn}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) has all five electrons in the \(t_{2g}\) orbitals, and no electrons in the \(e_g\) orbitals. The complex ion is a low-spin complex due to the presence of a strong field ligand (\(NH_3\)).

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Most popular questions from this chapter

Generally speaking, for a given metal and ligand, the stability of a coordination compound is greater for the metal in the \(3+\) rather than in the \(2+\) oxidation state. Furthermore, for a given ligand the complexes of the bivalent metal ions of the first transition series tend to increase in stability in the order \(\mathrm{Mn}(\mathrm{II})<\mathrm{Fe}(\mathrm{II})<\mathrm{Co}(\mathrm{II})<\) \(\mathrm{Ni}(\mathrm{II})<\mathrm{Cu}(\mathrm{II})\). Explain how these two observations are consistent with one another and also consistent with a crystal-field picture of coordination compounds.

A Cu electrode is immersed in a solution that is \(1.00 \mathrm{M}\) in \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) and \(1.00 \mathrm{M}\) in \(\mathrm{NH}_{3} .\) When the cathode is a standard hydrogen electrode, the emf of the cell is found to be \(+0.08 \mathrm{~V}\). What is the formation constant for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} ?\)

Give brief statements about the relevance of the following complexes in living systems: (a) hemoglobin, (b) chlorophylls, (c) siderophores.

(a) A compound with formula \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) is dissolved in water, forming a solution that is approximately the same color as the solid. Immediately after forming the solution, the addition of excess \(\mathrm{AgNO}_{3}(a q)\) forms \(2 \mathrm{~mol}\) of solid \(\mathrm{AgCl}\) per mole of complex. Write the formula for the compound, showing which ligands are likely to be present in the coordination sphere. (b) After a solution of \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates \(3 \mathrm{~mol}\) of \(\mathrm{AgCl}\) per mole of complex. What has happened in the ensuing time?

The \(E^{\circ}\) values for two iron complexes in acidic solution are as follows: \(\begin{aligned}\left[\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}\right]^{3+}(a q)+\mathrm{e}^{-} & \rightleftharpoons\left[\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}\right]^{2+}(a q) & E^{\circ}=1.12 \mathrm{~V} \\\\\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} & \rightleftharpoons\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) & E^{\circ} &=0.36 \mathrm{~V} \end{aligned}\) (a) What do the relative \(E^{\circ}\) values tell about the relative stabilities of the Fe(II) and Fe(III) complexes in each case? (b) Account for the more positive \(E^{\circ}\) value for the
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