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Chapter 23: Problem 62

For each of the following metals, write the electronic configuration of the atom and its \(3+\) ion: (a) Fe, (b) Mo, (c) Co. Draw the crystal-field energy-level diagram for the \(d\) orbitals of an octahedral complex, and show the placement of the \(d\) electrons for each \(3+\) ion, assuming a weak-field complex. How many unpaired electrons are there in each case?

Short Answer

Expert verified
The electronic configurations of the 3+ ions are: Fe3+: \(3d^5\); Mo3+: \(4d^2\); Co3+: \(3d^6\). In an octahedral weak-field complex, the d-orbitals are filled as follows: Fe3+: \(t_{2g}^5 e_g^0\), Mo3+: \(t_{2g}^2 e_g^0\), and Co3+: \(t_{2g}^6 e_g^0\). There are no unpaired electrons in Fe3+ and Co3+, while Mo3+ has 2 unpaired electrons.

Step by step solution

01

(Step 1: Find the electronic configuration of each element)

First, we'll write the electronic configuration for each metal atom: (a) Fe: Z=26, electronic configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6\) (b) Mo: Z=42, electronic configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^5\) (c) Co: Z=27, electronic configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7\)
02

(Step 2: Determine the electronic configuration of each element's 3+ ion)

Now, we'll find the electronic configuration of each 3+ ion: (a) Fe3+: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5\) (b) Mo3+: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 4d^2\) (c) Co3+: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^6\)
03

(Step 3: Draw the crystal-field energy-level diagram for the d-orbitals of an octahedral complex)

For an octahedral complex, the d-orbitals split into two categories: \(e_g\) orbitals (dx²-y² and d~z²~) at higher energy levels, and \(t_{2g}\) orbitals (dxy, d~x~z, and d~y~z) at lower energy levels. In a weak-field complex, the energy gap between these orbitals isn't significant, so the electrons will occupy low-energy orbitals following Hund's Rule, prioritizing maximum unpaired electrons filling the orbitals in order.
04

(Step 4: Show the placement of d electrons for each 3+ ion, assuming a weak-field complex)

We'll now fill the d-electrons based on the weak-field energy split in an octahedral complex: (a) Fe3+: Since we have 5 d-electrons, they will completely fill the \(t_{2g}\) orbitals, leaving 0 unpaired electrons. The electron configuration for Fe3+ will be: \(t_{2g}^5 e_g^0\) (b) Mo3+: Having 2 d-electrons, they will fill the two lowest-energy orbitals in the \(t_{2g}\) set. The electron configuration for Mo3+ will be: \(t_{2g}^2 e_g^0\) (c) Co3+: With 6 d-electrons, they will occupy all the orbitals in the \(t_{2g}\) set and one electron will be in the \(e_g\) set. The electron configuration for Co3+ will be: \(t_{2g}^6 e_g^0\)
05

(Step 5: Find the number of unpaired electrons in each ion)

Lastly, we'll identify any unpaired electrons present in each 3+ ion: (a) Fe3+: 0 unpaired electrons (b) Mo3+: 2 unpaired electrons (c) Co3+: 0 unpaired electrons Hence, there are no unpaired electrons in Fe3+ and Co3+, while the Mo3+ ion has 2 unpaired electrons.

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Most popular questions from this chapter

Determine if each of the following complexes exhibits geometric isomerism. If geometric isomers exist, determine how many there are. (a) tetrahedral $\left[\mathrm{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right],(\mathbf{b})$ square-pla- \(\operatorname{nar}\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-},(\mathbf{c})\) octahedral $\left[\mathrm{Fe}(o \text { -phen })_{2} \mathrm{Cl}_{2}\right]^{+} .$

Draw the structure for $\mathrm{Pt}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\left(\mathrm{NH}_{3}\right)_{2}$ and use it to answer the following questions: (a) What is the coordination number for platinum in this complex? (b) What is the coordination geometry? (c) What is the oxidation state of the platinum? (d) How many unpaired electrons are there? [Sections 23.2 and 23.6\(]\)

The square-planar complex $\left[\mathrm{Pt}(\mathrm{en}) \mathrm{Cl}_{2}\right]$ only forms in one of two possible geometric isomers. Which isomer is not observed: cis or trans?

If the lobes of a given \(d\) -orbital point directly at the ligands, will an electron in that orbital have a higher or lower energy than an electron in a \(d\) -orbital whose lobes do not point directly at the ligands?

The lanthanide contraction explains which of the following periodic trends? (a) The atomic radii of the transition metals first decrease and then increase when moving horizontally across each period. (b) When forming ions the period 4 transition metals lose their \(4 s\) electrons before their \(3 d\) electrons. (c) The radii of the period 5 transition metals (Y-Cd) are very similar to the radii of the period 6 transition metals (Lu-Hg).
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