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Chapter 9: Problem 20

The radii of the species \(\mathrm{S}, \mathrm{S}^{+}\), and \(\mathrm{S}^{-}\) decrease in the following order: a. \(\mathrm{S}^{+}>\mathrm{S}>\mathrm{S}^{-}\) b. \(\mathrm{S}^{+}>\mathrm{S}>\mathrm{S}\) c \(\mathrm{S}>\mathrm{S}^{-}>\mathrm{S}^{+}\) d. \(\mathrm{S}>\mathrm{S}^{+}>\mathrm{S}^{-}\) e. \(\mathrm{S}^{-}>\mathrm{S}>\mathrm{S}^{+}\)

Short Answer

Expert verified
e. \(\mathrm{S}^{-} > \mathrm{S} > \mathrm{S}^{+}\)

Step by step solution

01

Understand the Problem

We are asked to determine the order of radii for S, S^+, and S^-. We need to consider how the addition or removal of electrons affects the size of an atom or ion.
02

Review Ion Size Concepts

Adding an electron to an atom increases its size due to increased electron-electron repulsion. Removing an electron generally decreases the size due to a reduction in repulsion and an increase in effective nuclear charge.
03

Analyze Ion Sizes for Sulfur

Sulfur (S) gains an electron to become S^- and loses an electron to become S^+. When S becomes S^-, the added electron increases the size due to repulsion. When S loses an electron to become S^+, the size decreases because there is less repulsion among the remaining electrons.
04

Determine the Order of Sizes

Based on the analysis, the order of sizes is based on the idea: S^- will be the largest due to extra electron repulsion, followed by S as it has a usual electron number, and S^+ will be the smallest because of reduced repulsion.
05

Select the Correct Option

From the given options, e. \(\mathrm{S}^{-} > \mathrm{S} > \mathrm{S}^{+}\) corresponds to our determined order. This reflects the changes in size due to electron gain and loss.

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Key Concepts

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

Electron Configuration
Electron configuration refers to the arrangement of electrons in an atom or ion. This configuration is crucial because it influences the chemical properties and reactivity of an element. For the element Sulfur (S), the electron configuration is typically represented as \(1s^2 2s^2 2p^6 3s^2 3p^4\). This indicates that sulfur has 16 electrons, filling up to the 3p orbital.
  • When sulfur gains an electron to form \(S^-\), its electron configuration becomes \(1s^2 2s^2 2p^6 3s^2 3p^5\), meaning an extra electron is added to the 3p orbital.
  • Conversely, when sulfur loses an electron to form \(S^+\), its configuration is \(1s^2 2s^2 2p^6 3s^2 3p^3\), indicating a loss of one electron from the 3p orbital.
Thus, changes in electron configuration directly affect the size and properties of the ion, as seen in its ionic radii.
Ionization
Ionization is the process by which an atom or molecule gains or loses electrons, thus forming an ion. This process affects not just the charge but also the size of the atom. Removing an electron from an atom results in a positive ion, while adding an electron leads to a negative ion.
  • In the case of sulfur, losing an electron results in \(S^+\), which has a reduced size compared to neutral sulfur, because the loss of an electron decreases electron-electron repulsion.
  • Gaining an electron for sulfur produces \(S^-\), leading to an increase in size due to added electron repulsion.
Understanding ionization helps explain the trend in ionic radii: \(S^- > S > S^+\). This trend reflects how electron gain and loss impact the atomic structure and radius.
Atomic Structure
The atomic structure of an element describes how its protons, neutrons, and electrons are arranged. These subatomic particles determine numerous properties, including ionic radii. The nucleus contains protons, which have a positive charge and defined by the element's atomic number, and neutrons, which are neutral. Electrons circle the nucleus in designated orbitals according to quantum mechanical principles.
  • Sulfur's atomic number is 16, meaning it has 16 protons and, in its neutral state, 16 electrons.
  • Electrons are distributed among different energy levels or shells. The configuration impacts how tightly electrons are held, influencing things like radius and ion size.
The structure dictates essential interactions such as electron-electron repulsion and nuclear attraction, which in turn modify an element鈥檚 or ion鈥檚 size.
Effective Nuclear Charge
The concept of effective nuclear charge is crucial for understanding atomic size. It refers to the net positive charge experienced by an electron in a multi-electron atom. This charge is "effective" because electrons are subject to both attraction toward the nucleus and repulsion from other electrons.
  • In a sulfur atom, as electrons are removed (such as in \(S^+\)), the effective nuclear charge increases because there are fewer electron-electron repulsions. This increase causes the remaining electrons to be pulled closer to the nucleus, reducing the atomic radius.
  • Conversely, when an electron is added to form \(S^-\), there is more electron-electron repulsion, reducing the effectiveness of nuclear attraction which generally increases the radius.
Therefore, effective nuclear charge plays a significant role in explaining why ionic radii decrease with positive charge and increase with negative charge: \(S^+\) experiences higher effective nuclear charge than neutral \(S\), which in turn is more than \(S^-\).

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Most popular questions from this chapter

Which of the following contains both ionic and covalent bonds in the same compound? a. \(\mathrm{BaCO}_{3}\) b. \(\mathrm{MgCl}_{2}\) c. \(\mathrm{BaO}\) d. \(\mathrm{H}_{2} \mathrm{~S}\) e. \(\mathrm{SO}_{4}^{2-}\)

Write resonance descriptions for the following: a. \(\mathrm{NO}_{2}^{-}\) b. \(\mathrm{FNO}_{2}\)

When atoms of the hypothetical element \(\mathrm{X}\) are placed together, they rapidly undergo reaction to form the \(\mathrm{X}_{2}\) molecule: $$\mathrm{X}(g)+\mathrm{X}(g) \longrightarrow \mathrm{X}_{2}(g)$$ a. Would you predict that this reaction is exothermic or endothermic? Explain. b. Is the bond energy of \(X_{2}\) a positive or a negative quantity? Why? c. Suppose \(\Delta H\) for the reaction is \(-500 \mathrm{~kJ} / \mathrm{mol}\). Estimate the bond energy of the \(\mathrm{X}_{2}\) molecule. d. Another hypothetical molecular compound, \(\mathrm{Y}_{2}(g)\), has a bond energy of \(750 \mathrm{~kJ} / \mathrm{mol}\), and the molecular compound \(\mathrm{XY}(g)\) has a bond energy of \(1500 \mathrm{~kJ} / \mathrm{mol}\). Using bond-energy information, calculate \(\Delta H\) for the following reaction. $$\mathrm{X}_{2}(g)+\mathrm{Y}_{2}(g) \longrightarrow 2 \mathrm{XY}(g)$$ e. Given the following information, as well as the information previously presented, predict whether or not the hypothetical ionic compound \(\mathrm{AX}\) is likely to form. In this compound, \(\mathrm{A}\) forms the \(\mathrm{A}^{+}\) cation, and \(\mathrm{X}\) forms the \(\mathrm{X}^{-}\) anion. Be sure to justify your answer. Reaction: \(\mathrm{A}(g)+\frac{1}{2} \mathrm{X}_{2}(g) \longrightarrow \mathrm{AX}(s)\) The first ionization energy of \(\mathrm{A}(\mathrm{g})\) is \(400 \mathrm{~kJ} / \mathrm{mol}\). The electron affinity of \(\mathrm{X}(g)\) is \(-525 \mathrm{~kJ} / \mathrm{mol}\). The lattice energy of \(\mathrm{AX}(s)\) is \(100 \mathrm{~kJ} / \mathrm{mol}\). f. If you predicted that no ionic compound would form from the reaction in part e, what minimum amount of \(\mathrm{AX}(s)\) lattice energy might lead to compound formation?

Give resonance descriptions for the following: a. \(\mathrm{SeO}_{2}\) b. \(\mathrm{N}_{2} \mathrm{O}_{4}\)

Use Lewis symbols to represent the electron transfer between the following atoms to give ions with noble-gas configurations: a. \(\mathrm{Mg}\) and \(\mathrm{S}\) b. \(\mathrm{Ba}\) and \(\mathrm{I}\)
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