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Chapter 7: Problem 29

Which neutral atom is isoelectronic with each of the following ions? \(\mathrm{Ga}^{3+}, \mathrm{Zr}^{4+}, \mathrm{Mn}^{7+}, \Gamma, \mathrm{Pb}^{2+}\).

Short Answer

Expert verified
The neutral atoms that are isoelectronic with the given ions \(\mathrm{Ga}^{3+}, \mathrm{Zr}^{4+}, \mathrm{Mn}^{7+}, \mathrm{Pb}^{2+}\) are Zinc (Zn), Krypton (Kr), Argon (Ar), and Platinum (Pt), respectively.

Step by step solution

01

Recall the Electron Configuration of Ions

To find the electron configuration of an ion, first, write down the electron configuration of that atom in its neutral form. Then, if the ion is positively charged, remove electrons from the highest energy levels. If the ion is negatively charged, add electrons to the available energy levels.
02

Determine the Electron Configuration of the Given Ions

First, let's write down the atomic number and electron configuration of each ion in its neutral state: 1. \(\mathrm{Ga}^{3+}\): Gallium (Ga) has an atomic number of 31. Its electron configuration is \([Ar] 3d^{10} 4s^2 4p^1\). 2. \(\mathrm{Zr}^{4+}\): Zirconium (Zr) has an atomic number of 40. Its electron configuration is \([Kr] 4d^2 5s^2\). 3. \(\mathrm{Mn}^{7+}\): Manganese (Mn) has an atomic number of 25. Its electron configuration is \([Ar] 3d^5 4s^2\). 4. \(\mathrm{Pb}^{2+}\): Lead (Pb) has an atomic number of 82. Its electron configuration is \([Xe] 4f^{14} 5d^{10} 6s^2 6p^2\). Now, we will remove the electrons from each ion based on their positive charge: 1. \(\mathrm{Ga}^{3+}\): Remove 3 electrons: \([Ar] 3d^{10}\). 2. \(\mathrm{Zr}^{4+}\): Remove 4 electrons: \([Kr] 4d^{0}\) or \([Kr]\). 3. \(\mathrm{Mn}^{7+}\): Remove 7 electrons: \([Ar] 3d^0\) or \([Ar]\). 4. \(\mathrm{Pb}^{2+}\): Remove 2 electrons: \([Xe] 4f^{14} 5d^{10} 6s^0 6p^0\) or \([Xe] 4f^{14} 5d^{10}\).
03

Find Neutral Atoms with the Same Electron Configuration

Now, let's find the neutral atoms with the same electron configurations as the ions: 1. \(\mathrm{Ga}^{3+}\): \([Ar] 3d^{10}\) has the same electron configuration as Zinc (Zn). 2. \(\mathrm{Zr}^{4+}\): \([Kr]\) has the same electron configuration as Krypton (Kr). 3. \(\mathrm{Mn}^{7+}\): \([Ar]\) has the same electron configuration as Argon (Ar). 4. \(\mathrm{Pb}^{2+}\): \([Xe] 4f^{14} 5d^{10}\) has the same electron configuration as Platinum (Pt). So, the neutral atoms that are isoelectronic with the given ions are Zinc (Zn), Krypton (Kr), Argon (Ar), and Platinum (Pt) respectively.

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Key Concepts

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

Electron Configurations
Understanding electron configurations is essential for grasping the concept of isoelectronic atoms. Electron configurations describe the distribution of electrons in an atom's orbitals, which are regions around the nucleus where electrons are likely to be found.

Each electron occupies the lowest energy orbital available, filling them in a specific order: 1s, 2s, 2p, 3s, 3p, and so on. This order is dictated by the principles of quantum mechanics. You can think of it like filling up seats in a theater. The seats closest to the stage (or nucleus, in our case) are filled up first, with each notable section (s, p, d, f orbitals) representing a different part of the theater.

For example, the electron configuration of neutral gallium (Ga), with an atomic number of 31, is \[Ar\] 3d^{10} 4s^2 4p^1. This shorthand notation tells us that gallium has the same electron arrangement as argon (\[Ar\]), with additional electrons in the 3d, 4s, and 4p orbitals. When ions form, they lose or gain electrons to achieve a more stable electron configuration, often resembling the nearest noble gas.
Atomic Number
The atomic number is effectively the ID card of an element. It's unique for every element and indicates the number of protons in an atom's nucleus. Since atoms are electrically neutral, the atomic number also reveals how many electrons are in a neutral atom.

For instance, the atomic number of Mn (manganese) is 25, meaning it has 25 protons and, when neutral, 25 electrons. The beauty of the atomic number is that it gives a direct insight into the possible electron configurations an element can have. During ion formation, while the number of electrons changes, the atomic number remains the same, ensuring the element's identity is constant.
Ions and Charges
When atoms lose or gain electrons, they become ions. The number of electrons lost or gained is reflected in the ion's charge鈥攖he more electrons lost, the more positive the ion is.

Consider the \[Ga^{3+}\] ion. Gallium originally has 31 electrons, but as a 3+ ion, it's lost 3 electrons, so it only has 28 left. In contrast, a hypothetical \[Ga^{3-}\] ion would have gained 3 electrons, having a total of 34. These changes in electron number drastically alter electron configurations, which lead to similarities with neutral atoms of other elements - hence, the term isoelectronic. It's all about balance; elements often lose or gain electrons to achieve a noble gas configuration, which is the epitome of electronic stability in chemistry.

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Most popular questions from this chapter

Which of the following statements about effective nuclear charge for the outermost valence electron of an atom is incorrect? (i) The effective nuclear charge can be thought of as the true nuclear charge minus a screening constant due to the other electrons in the atom. (ii) Effective nuclear charge increases going left to right across a row of the periodic table. (iii) Valence electrons screen the nuclear charge more effectively than do core electrons. (iv) The effective nuclear charge shows a sudden decrease when we go from the end of one row to the beginning of the next row of the periodic table. (v) The change in effective nuclear charge going down a column of the periodic table is generally less than that going across a row of the periodic table.

Zinc in its 2+ oxidation state is an essential metal ion for life. \(\mathrm{Zn}^{2+}\) is found bound to many proteins that are involved in biological processes, but unfortunately \(\mathrm{Zn}^{2+}\) is hard to detect by common chemical methods. Therefore, scientists who are interested in studying \(\mathrm{Zn}^{2+}\)-containing proteins frequently substitute \(\mathrm{Cd}^{2+}\) for \(\mathrm{Zn}^{2+}\), since \(\mathrm{Cd}^{2+}\) is easier to detect. (a) On the basis of the properties of the elements and ions discussed in this chapter and their positions in the periodic table, describe the pros and cons of using \(\mathrm{Cd}^{2+}\) as a \(\mathrm{Zn}^{2+}\) substitute. (b) Proteins that speed up (catalyze) chemical reactions are called enzymes. Many enzymes are required for proper metabolic reactions in the body. One problem with using \(\mathrm{Cd}^{2+}\) to replace \(\mathrm{Zn}^{2+}\) in enzymes is that \(\mathrm{Cd}^{2+}\) substitution can decrease or even eliminate enzymatic activity. Can you suggest a different metal ion that might replace \(\mathrm{Zn}^{2+}\) in enzymes instead of \(\mathrm{Cd}^{2+}\) ? Justify your answer.

(a) The measured \(\mathrm{Bi}-\mathrm{Br}\) bond length in bismuth tribromide, \(\mathrm{BiBr}_{3}\), is \(2.63 \AA\). Based on this value and the data in Figure 7.8, predict the atomic radius of Bi. (b) Bismuth tribromide is soluble in acidic solution. It is formed by treating solid bismuth(III) oxide with aqueous hydrobromic acid. Write a balanced chemical equation for this reaction. (c) While bismuth(III) oxide is soluble in acidic solutions, it is insoluble in basic solutions such as \(\mathrm{NaOH}(a q)\). Based on these properties, is bismuth characterized as a metallic, metalloid, or nonmetallic element? (d) Treating bismuth with fluorine gas forms \(\mathrm{BiF}_{5}\). Use the electron configuration of \(\mathrm{Bi}\) to explain the formation of a compound with this formulation. (e) While it is possible to form \(\mathrm{BiF}_{5}\) in the manner just described, pentahalides of bismuth are not known for the other halogens. Explain why the pentahalide might form with fluorine but not with the other halogens. How does the behavior of bismuth relate to the fact that xenon reacts with fluorine to form compounds but not with the other halogens?

Some metal oxides, such as \(\mathrm{Sc}_{2} \mathrm{O}_{3}\), do not react with pure water, but they do react when the solution becomes either acidic or basic. Do you expect \(\mathrm{Sc}_{2} \mathrm{O}_{3}\) to react when the solution becomes acidic or when it becomes basic? Write a balanced chemical equation to support your answer.

In the chemical process called electron transfer, an electron is transferred from one atom or molecule to another. (We will talk about electron transfer extensively in Chapter 20.) A simple electron transfer reaction is $$ \mathrm{A}(g)+\mathrm{A}(g) \longrightarrow \mathrm{A}^{+}(g)+\mathrm{A}^{-}(g) $$ In terms of the ionization energy and electron affinity of atom A, what is the energy change for this reaction? For a representative nonmetal such as chlorine, is this process exothermic? For a representative metal such as sodium, is this process exothermic?
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