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Chapter 8: Problem 20

Write electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cd}^{2+}\) , \((\mathbf{b}) \mathrm{P}^{3-},(\mathbf{c}) \mathrm{Zr}^{4+},(\mathbf{d}) \mathrm{Ru}^{3+},(\mathbf{e}) \mathrm{As}^{3-},(\mathbf{f}) \mathrm{Ag}^{+}\)

Short Answer

Expert verified
The electron configurations for the given ions are as follows: \(Cd^{2+}: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^8\) \(P^{3-}: 1s^2 2s^2 2p^6 3s^2 3p^6\) \(Zr^{4+}: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) \(Ru^{3+}: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 4d^4\) \(As^{3-}: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) \(Ag^{+}: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 4d^{10}\) Only the \(P^{3-}\) and \(As^{3-}\) ions have noble-gas configurations (Ne and Ar, respectively).

Step by step solution

01

Identify the atomic numbers of the elements

Find the atomic numbers of the elements based on their symbols in the periodic table: Cd: 48 P: 15 Zr: 40 Ru: 44 As: 33 Ag: 47
02

Write the ground-state electron configurations of the neutral atoms

Write the electron configurations for the neutral atoms using the periodic table and the standard method for writing electron configurations: Cd: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10}\) P: \(1s^2 2s^2 2p^6 3s^2 3p^3\) Zr: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^2\) Ru: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^7\) As: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3\) Ag: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^{10}\)
03

Adjust the electron configurations for given ion charges

Cd虏鈦�: Remove two electrons from the highest-energy orbital, which is the 4d orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^8\) P鲁鈦�: Add three electrons to the highest-energy orbital, which is the 3p orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6\) Zr鈦粹伜: Remove four electrons from the highest-energy orbitals, starting with the 4d and then the 5s orbitals: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^0 4d^0\) Ru鲁鈦�: Remove three electrons from the highest-energy orbitals, starting with the 4d and then the 5s orbitals: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^0 4d^4\) As鲁鈦�: Add three electrons to the highest-energy orbital, which is the 4p orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) Ag鈦�: Remove one electron from the highest-energy orbital, which is the 5s orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^0 4d^{10}\)
04

Compare the electron configurations with noble gas configurations

The electron configurations of noble gases are complete with full energy levels, and their general form is (\(n-1\)d^{10})np^6, where \(n\) is the principal quantum number of the noble gases. In our adjusted electron configurations from Step 3, the following ions match the noble gas configurations: - P鲁鈦� matches the configuration of Ne (Z=10): \(1s^2 2s^2 2p^6\) - As鲁鈦� matches the configuration of Ar (Z=18): \(1s^2 2s^2 2p^6 3s^2 3p^6\) Conclusion: Only P鲁鈦� and As鲁鈦� ions have noble-gas configurations.

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Key Concepts

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

Noble Gas Configurations
Noble gas configurations make atoms or ions more stable by having completely filled electron shells. These configurations are noted for their complete subshells, which result in minimal chemical reactivity. Noble gases, like helium, neon, and argon, have fully filled electron configurations such as:
  • Neon: \[1s^2 2s^2 2p^6\]
  • Argon: \[1s^2 2s^2 2p^6 3s^2 3p^6\]
Atoms often gain or lose electrons to achieve a noble gas configuration, which results in ion formation. This process brings them to a lower-energy, more stable state. For instance, in our exercise, the ions \(\mathrm{P}^{3-}\) and \(\mathrm{As}^{3-}\) have electron configurations that match those of neon and argon respectively, reaching stable noble gas states.
Ion Charges
Ion charges arise when atoms gain or lose electrons, altering their electron count relative to protons. This imbalance results in an overall positive or negative charge on the ion. Ions with a positive charge, known as cations, form from losing electrons, whereas negatively charged ions, or anions, result from gaining electrons.
To determine the charge, consider the number of electrons transferred compared to the neutral atom:
  • \(\mathrm{Cd}^{2+}\): Two electrons are lost, resulting in a +2 charge.
  • \(\mathrm{P}^{3-}\): Three electrons are gained, leading to a -3 charge.
  • \(\mathrm{Zr}^{4+}\): Four electrons are removed, giving a +4 charge.
  • \(\mathrm{Ru}^{3+}\): Three electrons are lost, resulting in a +3 charge.
  • \(\mathrm{As}^{3-}\): Three electrons added, leading to a -3 charge.
  • \(\mathrm{Ag}^{+}\): One electron is removed, leading to a +1 charge.
Identifying these charges helps predict ion interactions and formation of chemical compounds.
Electron Configuration of Ions
Understanding electron configurations of ions provides insight into the structure and reactivity of atoms. By identifying which electrons to remove or add based on the ion charge, we can pinpoint the resulting configuration.
For cations, electrons are removed from the highest energy orbitals first:
  • For \(\mathrm{Cd}^{2+}\), the \(5s\) electrons are removed, resulting in: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 4d^8\]
  • For \(\mathrm{Ag}^{+}\), the \(5s\) electron is removed, leading to: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 4d^{10}\]
For anions, electrons are added to the lowest energy orbitals available:
  • For \(\mathrm{P}^{3-}\), three electrons are added to the \(3p\), resulting in: \[1s^2 2s^2 2p^6 3s^2 3p^6\]
  • For \(\mathrm{As}^{3-}\), three electrons complete the \(4p\), leading to: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\]
Mastering this concept allows one to predict how ions behave in various chemical reactions and their roles in forming ionic compounds.

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Most popular questions from this chapter

Calculate the formal charge on the indicated atom in each of the following molecules or ions: (a) the central oxygen atom in \(\mathrm{O}_{3},\) (b) phosphorus in \(\mathrm{PF}_{6}^{-},(\mathbf{c})\) nitrogen in \(\mathrm{NO}_{2}\) (d) iodine in ICl_\(\mathrm{ICl}_{3},\) (e) chlorine in \(\mathrm{HClO}_{4}\) (hydrogen is bonded to \(\mathrm{O} )\)

Ammonium chloride, \(\mathrm{NH}_{4} \mathrm{Cl},\) is a very soluble salt in water. (a) Draw the Lewis structures of the ammonium and chloride ions. (b) Is there an \(\mathrm{N}-\) Cl bond in solid ammonium chloride? (c) If you dissolve 14 gof ammonium chloride in 500.0 \(\mathrm{mL}\) of water, what is the molar concentration of the solution? (d) How many grams of silver nitrate do you need to add to the solution in part (c) to precipitate all of the chloride as silver chloride?

You and a partner are asked to complete a lab entitled "Oxides of Ruthenium" that is scheduled to extend over two lab periods. The first lab, which is to be completed by your partner, is devoted to carrying out compositional analysis. In the second lab, you are to determine melting points. Upon going to lab you find two unlabeled vials, one containing a soft yellow substance and the other a black powder. You also find the following notes in your partner's notebook Compound \(1 : 76.0 \%\) Ru and 24.0\(\%\) O (by mass), Compound \(2 : 61.2 \%\) Ru and 38.8\(\%\) O (by mass). (a) What is the empirical formula for Compound 1\(?\) (b) What is the empirical formula for Compound 2\(?\) Upon determining the melting points of these two compounds, you find that the yellow compound melts at \(25^{\circ} \mathrm{C}\) , while the black powder does not melt up to the maximum temperature of your apparatus, \(1200^{\circ} \mathrm{C}\) . (c) What is the identity of the yellow compound? (d) What is the identity of the black compound? (e) Which compound is molecular? (f) Which compound is ionic?

Some chemists believe that satisfaction of the octet rule should be the top criterion for choosing the dominant Lewis structure of a molecule or ion. Other chemists believe that achieving the best formal charges should be the top criterion. Consider the dihydrogen phosphate ion, \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) , in which the \(\mathrm{H}\) atoms are bonded to \(\mathrm{O}\) atoms. (a) What is the predicted dominant Lewis structure if satisfying the octet rule is the top criterion? (b) What is the predicted dominant Lewis structure if achieving the best formal charges is the top criterion?

What is the Lewis symbol for each of the following atoms or ions? (a) \(\mathrm{K},\) (b) As, (c) \(\mathrm{Sn}^{2+},(\mathbf{d}) \mathrm{N}^{3-}\) .
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