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Chapter 8: Problem 14

The ions \(\mathrm{Na}^{+}\) and \(\mathrm{Mg}^{2+}\) occur in chemical compounds, but the ions \(\mathrm{Na}^{2+}\) and \(\mathrm{Mg}^{3+}\) do not. Explain.

Short Answer

Expert verified
The ions \(\mathrm{Na}^{2+}\) and \(\mathrm{Mg}^{3+}\) are unstable as they require extra energy to form, disrupting stable electron configurations.

Step by step solution

01

Understanding Ion Formation

Ions are atoms or molecules that have gained or lost one or more electrons, giving them a net positive or negative charge. For example, \(\mathrm{Na}^{+}\) and \(\mathrm{Mg}^{2+}\) lose electrons to reach stable electron configurations. \(\mathrm{Na}^{+}\) loses one electron and \(\mathrm{Mg}^{2+}\) loses two electrons.
02

Electron Configuration

Sodium (\(\mathrm{Na}\)) has an electron configuration of \[1s^2 2s^2 2p^6 3s^1\]. When it loses one electron to form \(\mathrm{Na}^{+}\), it achieves a stable electron configuration similar to neon, \[1s^2 2s^2 2p^6\]. Magnesium (\(\mathrm{Mg}\)) has an electron configuration of \[1s^2 2s^2 2p^6 3s^2\]. By losing two electrons, \(\mathrm{Mg}^{2+}\) also achieves a stable neon-like electron configuration.
03

Stability of Higher Charge States

Attempting to create \(\mathrm{Na}^{2+}\) would mean removing a second electron from a stable, noble gas-like configuration, which requires a lot of energy and is highly unstable. Similarly, creating \(\mathrm{Mg}^{3+}\) would require removing an additional electron from the stable \(\mathrm{Mg}^{2+}\) configuration, again requiring much energy and leading to instability.
04

Chemical Configuration and Stability

In chemical compounds, stability is achieved when ions have electron configurations similar to noble gases, making them energetically favorable. \(\mathrm{Na}^{+}\) and \(\mathrm{Mg}^{2+}\) are stable due to their electron configuration, while \(\mathrm{Na}^{2+}\) and \(\mathrm{Mg}^{3+}\) are unstable because they disrupt this configuration, requiring energy that disrupts stability.

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Key Concepts

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

Electron Configuration
Every atom has a unique arrangement of electrons around its nucleus, known as its electron configuration. Electrons fill the lowest energy levels available, starting with the innermost shells and moving outward.
Sodium (\( \mathrm{Na} \)) has an electron configuration of \[1s^2 2s^2 2p^6 3s^1\], while magnesium (\( \mathrm{Mg} \)) is \[1s^2 2s^2 2p^6 3s^2\]. These configurations provide insight into how these elements interact chemically.
  • For sodium, losing one electron (the lone 3s electron) achieves the stable configuration of neon.
  • Magnesium achieves stability by losing two 3s electrons.

Knowing the electron configuration is crucial because it helps predict how an atom might gain stability through ionization.
Noble Gas Configuration
Atoms seek to become stable, and they achieve this by having a full outer electron shell. Noble gases naturally have this full outer shell, making them extremely stable and largely inert.
When sodium loses one electron, its electron configuration mirrors that of a noble gas, neon, with a full outer shell of eight electrons (\[1s^2 2s^2 2p^6\]). Similarly, magnesium loses two electrons to also achieve the neon-like configuration.
This tendency of elements to attain noble gas-like stability guides the formation of ions. It's often referred to as achieving an "octet" configuration because the outermost, stable shell often contains eight electrons.
Chemical Stability
Chemical stability refers to the tendency of an atom to resist changes and remain in its current state. Atoms with electron configurations similar to noble gases are stable because their outer shell is complete.
With this full outer shell, the atoms are less likely to react or form compounds under normal conditions. This explains why \( \mathrm{Na}^{+} \) and \( \mathrm{Mg}^{2+} \) are common, while \( \mathrm{Na}^{2+} \) and \( \mathrm{Mg}^{3+} \) are not.
Attempting to form ions like \( \mathrm{Na}^{2+} \) or \( \mathrm{Mg}^{3+} \) requires disrupting this completed shell, making these ions unstable and unlikely to form in nature.
Energy Requirements for Ionization
Forming an ion involves removing or adding electrons, which requires energy. The amount of energy needed depends on how stable the current electron configuration is.
Sodium, for example, needs minimal energy to lose its single 3s electron and become \( \mathrm{Na}^{+} \). However, removing a second electron to form \( \mathrm{Na}^{2+} \) disturbs its stable noble gas configuration.
Similarly, magnesium can easily form \( \mathrm{Mg}^{2+} \), but \( \mathrm{Mg}^{3+} \) would require significant energy and cause instability.
  • There is a correlation between the energy required for ionization and the stability of the resulting ion.
  • The more stable the configuration, the less energy required, thereby increasing the likelihood of the ion existing.

Understanding these requirements helps explain why certain ions form more readily than others.

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Most popular questions from this chapter

A hypothetical element, \(\mathrm{X}\), has the following ionization energy values: First ionization energy: \(900 \mathrm{~kJ} / \mathrm{mol}\) Second ionization energy: \(1750 \mathrm{~kJ} / \mathrm{mol}\) Third ionization energy: \(14,900 \mathrm{~kJ} / \mathrm{mol}\) Fourth ionization energy: \(21,000 \mathrm{~kJ} / \mathrm{mol}\) Another element, Y, has the following ionization energy values: First ionization energy: \(1200 \mathrm{~kJ} / \mathrm{mol}\) Second ionization energy: \(2500 \mathrm{~kJ} / \mathrm{mol}\) Third ionization energy: \(19,900 \mathrm{~kJ} / \mathrm{mol}\) Fourth ionization energy: \(26,000 \mathrm{~kJ} / \mathrm{mol}\) a. To what family of the periodic table would element \(\mathrm{X}\) be most likely to belong? Explain? b. What charge would you expect element \(\mathrm{X}\) to have when it forms an ion? c. If you were to place elements \(X\) and \(Y\) into the periodic table, would element \(Y\) be in the same period as element \(X\) ? If not in the same period, where might they be relative to each other in the periodic table? d. Would an atom of \(Y\) be smaller or larger than an atom of \(X\) ? Explain your reasoning.

Explain how \(x\) rays are produced when an electron beam falls on a metal target.

Two elements are in the same column of the periodic table, one above the other. The ground-state atom of one element has two \(s\) electrons in its outer shell, and no \(d\) electrons anywhere in its configuration. The other element has \(d\) electrons in its configuration. Identify the elements.

Zirconium is a Group IVB element in Period \(5 .\) What would you expect for the valence-shell configuration of zirconium?

Using periodic trends, arrange the following elements in order of increasing atomic radius: \(\mathrm{O}, \mathrm{P}, \mathrm{S}\).
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