Problem 60 - Chemistry: The Central Science

Question

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?

Step-by-Step Solution

Answer

The electronic configurations for the given metals and their $3+$ ions are: (a) Fe: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶; Fe³⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵; 3 unpaired electrons in weak-field octahedral complex. (b) Mo: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁵; Mo³⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 4d¹; 1 unpaired electron in weak-field octahedral complex. (c) Co: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷; Co³⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶; 4 unpaired electrons in weak-field octahedral complex.

Step 1: Know the Atomic Numbers

To determine the electronic configuration of the metals and their ions, we need to know their atomic numbers. (a) Fe (Iron) has an atomic number of 26. (b) Mo (Molybdenum) has an atomic number of 42. (c) Co (Cobalt) has an atomic number of 27.

Step 2: Write Electron Configurations for Atoms

Using the atomic numbers, write the electronic configurations for the atoms. (a) Fe (Iron): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ (b) Mo (Molybdenum): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁵ (c) Co (Cobalt): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷

Step 3: Write Electron Configurations for 3+ Ions

Remove three electrons from each atom to form 3+ ions and write the electronic configurations. (a) Fe³⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ (b) Mo³⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 4d¹ (c) Co³⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶

Step 4: Draw Crystal-Field Energy-Level Diagram for Octahedral Complex

In an octahedral complex, the d orbitals split into two sets due to crystal field effects: the triplet t2g and the doublet eg. Assuming a weak-field complex, the ligands do not cause any change in the order of electron filling. We use the aufbau principle (place electrons in the lowest energy levels first, then move to the next higher energy levels) and Hund's rule (every orbital in a subshell must have one electron before adding the second one) to fill in the d electrons for each 3+ ion.

Step 5: Show Placement of d Electrons for Each 3+ Ion

Fill in the d electrons in the crystal-field energy-level diagram according to aufbau principle and Hund's rule. (a) Fe³⁺: 3d⁵ - For t2g orbitals: ↑, ↑, ↑ - For eg orbitals: no electrons (b) Mo³⁺: 4d¹ - For t2g orbitals: ↑ - For eg orbitals: no electrons (c) Co³⁺: 3d⁶ - For t2g orbitals: ↑↓, ↑↓, ↑ - For eg orbitals: no electrons

Step 6: Count Unpaired Electrons for Each 3+ Ion

Count the unpaired electrons in the t2g and eg orbitals for each 3+ ion. (a) Fe³⁺: 3 unpaired electrons (b) Mo³⁺: 1 unpaired electron (c) Co³⁺: 4 unpaired electrons