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Chapter 2: Problem 20

Give the ground-state electron configuration and number of unpaired electrons expected for each of the following ions: (a) \(\mathrm{Sn}^{2+}\); (b) \(\mathrm{Cr}^{3+}\); (c) \(\mathrm{Ba}^{2+}\) (d) \(\mathrm{P}^{3-}\).

Short Answer

Expert verified
Ground-state electron configurations and unpaired electrons: (a) \rm{Sn^{2+}}: [Kr]4d^{10}5s^{2}5p^{0}, 0 unpaired electrons; (b) \rm{Cr^{3+}}: [Ar]3d^{3}, 3 unpaired electrons; (c) \rm{Ba^{2+}}: [Xe], 0 unpaired electrons; (d) \rm{P^{3-}}: [Ne]3s^{2}3p^{6}, 0 unpaired electrons.

Step by step solution

01

Identify Ground-State Configuration of Neutrals

Before finding the electron configuration for the ions, identify the electron configuration for the neutral atoms. Tin (Sn) has an atomic number of 50, Chromium (Cr) 24, Barium (Ba) 56, and Phosphorus (P) 15.
02

Adjust for Ion Charge

Subtract or add electrons corresponding to the ion charge. (a) Sn will lose 2 electrons. (b) Cr will lose 3 electrons. (c) Ba will lose 2 electrons. (d) P will gain 3 electrons.
03

Determine Electron Configuration for Ions

Write the electron configurations for the resulting ions, keeping in mind the Aufbau principle, Hund's rule, and the Pauli exclusion principle. For transition metals, remove electrons from the highest energy orbital, generally from the s orbitals before the d orbitals.
04

Determine the Number of Unpaired Electrons

Examine the electron configurations to see if any orbitals have unpaired electrons. Electrons in the same orbital must have opposite spins.

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Key Concepts

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

Ground-State Electron Configuration
Understanding the ground-state electron configuration of an atom or ion is critical for predicting its chemical behavior. In its ground-state, an atom's electrons are arranged in the energetically lowest available orbitals. This state reflects the most stable configuration of electrons.

During the ground-state configuration, electrons fill subshells in an order dictated by their energy levels. The energy of the subshells increases from 1s to 2s, to 2p, and so forth. Each electron is placed into the lowest energy orbital available, following the Aufbau principle, which is further guided by Hund's rule and the Pauli exclusion principle.
Unpaired Electrons
Unpaired electrons are those that exist alone in an orbital without a corresponding electron of opposite spin. These electrons have important implications for an atom's magnetic properties and chemical reactivity.

Atoms with unpaired electrons tend to be paramagnetic, meaning they are attracted to magnetic fields, whereas atoms with all paired electrons are diamagnetic and weakly repel magnetic fields. Identifying unpaired electrons involves looking at an atom's electron configuration and considering each orbital within a subshell. If there's an orbital with only one electron, that electron is unpaired.
Aufbau Principle
The Aufbau principle is a fundamental concept that guides the electron filling order in an atom's orbitals. The term 'Aufbau' is German for 'building up', which illustrates how electrons populate orbitals from lower to higher energy as the atom's electron configuration develops.

According to the Aufbau principle, one must fill orbitals starting with the lowest energy level, such as the 1s orbital, and then proceed to fill higher energy levels like 2s, 2p, and so on. Electron configurations start at the ground state of an atom and can shift when electrons are added or removed in the formation of ions.
Hund's Rule
Hund's rule addresses how electrons populate subshells of the same energy—also known as degenerate orbitals—and emphasizes the minimization of electron repulsion. It states that electrons will fill an empty orbital before they pair up in an already occupied one.

This means that within a particular subshell (such as 2p or 3d), electrons are spread out into as many orbitals as possible with parallel spins before doubling up. This behavior reduces repulsion between electrons, which is lower when they are in separate orbitals rather than sharing one.
Pauli Exclusion Principle
The Pauli exclusion principle is a quantum mechanical principle which states that no two electrons can have the same set of four quantum numbers. In essence, an orbital can hold a maximum of two electrons, and they must have opposite spins, represented as 'up' (\r\( \uparrow \r\)) and 'down' (\r\( \downarrow \r\)).

This principle is crucial when writing electron configurations because it dictates that once an orbital has two electrons, it is filled, and any additional electrons must move to the next available orbital. The interplay of the Pauli exclusion principle with the Aufbau principle and Hund's rule allows for the prediction of electron configurations of atoms and ions.

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Most popular questions from this chapter

An important principle in chemistry is the isolobal analogy. This very simple principle states that chemical fragments with similar valence orbital structures can replace one another in molecules. For example, \(\cdot \dot{\mathrm{C}}-\mathrm{H}\) and \(\cdot \dot{\mathrm{S}}-\mathrm{H}\) are isolobal fragments, each having three electrons with which to form bonds in addition to the bond to \(\mathrm{H}\). An isolobal series of molecules would be HCCH, HCSiH, HSiSiH. Similarly, a lone pair of electrons can be used to replace a bond so that - \(\mathrm{N}\) : is isolobal with \(\cdot \dot{\mathrm{C}}-\mathrm{H}\) with the lone pair taking the place of the \(\mathrm{C}-\mathrm{H}\) bond. The isolobal set here is \(\mathrm{HCCH}, \mathrm{HCN}\), NN. (a) Draw the Lewis structures for the molecules HCCH, HCSiH, HSiSiH, HCN, and NN. (b) Using the isolobal principle, draw Lewis structures for molecules based on the structure of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), in which one or more \(\mathrm{CH}\) groups are replaced with \(\mathrm{N}\) atoms.

In each of these ions and compounds, an atom violates the octet rule. Identify the atom and explain the deviation from the octet rule: (a) \(\mathrm{BeCl}_{2}\); (b) \(\mathrm{ClO}_{2}\).

Write the Lewis structure of (a) \(\mathrm{OCl}_{2}\); (b) \(\mathrm{PBr}_{3}\); (c) \(\mathrm{GeH}_{4}\); (d) \(\mathrm{GaCl}_{3}\)

Which \(\mathrm{M}^{2+}\) ions (where \(\mathrm{M}\) is a metal) are predicted to have the following ground-state electron configurations: (a) [Ar] \(3 \mathrm{~d}^{7}\); (b) \([\mathrm{Kr}] 4 \mathrm{~d}^{7}\); (c) \([\mathrm{Kr}] 4 \mathrm{~d}^{10} 5 \mathrm{~s}^{2}\); (d) \([\mathrm{Xe}] 4 \mathrm{f}^{14} 5 \mathrm{~d}^{10}\) ?

Write the most likely charge for the ions formed by each of the following elements: (a) S; (b) Te; (c) Rb; (d) Ga; (c) Cd.
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