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Chapter 23: Problem 60

For each of the following metals, write the electronic configuration of the atom and its \(3+\) ion: (a) \(\mathrm{Ru},(\mathbf{b}) \mathrm{Mo},(\mathbf{c}) \mathrm{Co} .\) 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 for the 3+ ions of Ru, Mo, and Co are \([Kr]4d^5\), \([Kr]4d^3\), and \([Ar]3d^6\), respectively. Assuming a weak-field complex in an octahedral crystal-field energy-level diagram, the electron placements are: 3 in t₂g and 2 in e_g for Ru³⁺, all 3 in t₂g for Mo³⁺, and 3 in t₂g and 3 in e_g for Co³⁺. The number of unpaired electrons in each ion is: 1 for Ru³⁺, 1 for Mo³⁺, and 2 for Co³⁺.

Step by step solution

01

Determine Electronic Configurations of the Metal Atoms

Find the electronic configurations for Ru, Mo, and Co using the periodic table. Use the Aufbau principle, Pauli Exclusion principle, and Hund's rule to distribute electrons. 1. Ru (Z = 44): \([Kr]5s^24d^6\) 2. Mo (Z = 42): \([Kr]5s^14d^5\) 3. Co (Z = 27): \([Ar]4s^23d^7\)
02

Determine Electronic Configurations for 3+ Ions

Determine the electronic configurations for Ru³⁺, Mo³⁺, and Co³⁺ by removing 3 electrons from their corresponding atom. 1. Ru³⁺: Remove 2 electrons from 5s orbital and 1 electron from 4d orbital: \([Kr]4d^5\) 2. Mo³⁺: Remove 1 electron from 5s orbital and 2 electrons from 4d orbital: \([Kr]4d^3\) 3. Co³⁺: Remove 2 electrons from 4s orbital and 1 electron from 3d orbital: \([Ar]3d^6\)
03

Draw Crystal-Field Energy-Level Diagram for the d Orbitals of Octahedral Complex

Draw the crystal-field energy-level diagram for the d orbitals of an octahedral complex and split the d orbitals into two sets: t₂g orbitals (lower energy) and e_g orbitals (higher energy). Under weak-field condition, electrons preferentially occupy the lower-energy orbitals (t₂g) before filling up the higher-energy orbitals (e_g).
04

Place d Electrons for 3+ Ions in the Diagram

Place the electrons in the energy-level diagram as per the configurations in Step 2, using the weak-field assumption. 1. Ru³⁺ (\([Kr]4d^5\)): 5 d electrons ⇒ 3 in t₂g and 2 in e_g 2. Mo³⁺ (\([Kr]4d^3\)): 3 d electrons ⇒ all 3 in t₂g (no electron in e_g) 3. Co³⁺ (\([Ar]3d^6\)): 6 d electrons ⇒ all 3 in t₂g and 3 in e_g
05

Count Unpaired Electrons

Count the number of unpaired electrons in each metal-ion's d orbitals. 1. Ru³⁺: 1 unpaired electron in the e_g set 2. Mo³⁺: 1 unpaired electron in the t₂g set 3. Co³⁺: 2 unpaired electrons in the e_g set So, there are 1, 1, and 2 unpaired electrons in the octahedral complexes of Ru³⁺, Mo³⁺, and Co³⁺, respectively.

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Most popular questions from this chapter

The total concentration of \(\mathrm{Ca}^{2+}\) and \(\mathrm{Mg}^{2+}\) in a sample of hard water was determined by titrating a \(0.100-\mathrm{L}\) sample of the water with a solution of EDTA \(^{4-}\). The EDTA \(^{4-}\) chelates the two cations: $$ \begin{aligned} \mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow &[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\ \mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow &[\mathrm{Ca}(\mathrm{EDTA})]^{2-} \end{aligned} $$ It requires \(31.5 \mathrm{~mL}\) of \(0.0104 \mathrm{M}[\mathrm{EDTA}]^{4-}\) solution to reach the end point in the titration. A second \(0.100-\mathrm{L}\) sample was then treated with sulfate ion to precipitate \(\mathrm{Ca}^{2+}\) as calcium sulfate. The \(\mathrm{Mg}^{2+}\) was then titrated with \(18.7 \mathrm{~mL}\) of \(0.0104 \mathrm{M}\) \([\mathrm{EDTA}]^{4-},\) Calculate the concentrations of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) in the hard water in \(\mathrm{mg} / \mathrm{L}\).

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