Problem 157 - Introductory Chemistry Atoms First

Question

Write the ground-state electron configuration for each of the following atoms or ions. Which have a valence-shell octet? (a) \(\mathrm{Ca}^{+}\) (b) Li (c) \(\mathrm{P}^{3-}\) (d) \(\mathrm{Ar}^{+}\) (e) \(\mathrm{Si}^{2+}\)

Step-by-Step Solution

Answer

The ground-state electron configurations are as follows: (a) \(\mathrm{Ca}^{+}\): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s¹ (no octet). (b) Li: 1s², 2s¹ (no octet). (c) \(\mathrm{P}^{3-}\): 1s², 2s², 2p⁶, 3s², 3p⁶ (octet). (d) \(\mathrm{Ar}^{+}\): 1s², 2s², 2p⁶, 3s², 3p⁵ (no octet). (e) \(\mathrm{Si}^{2+}\): 1s², 2s², 2p⁶, 3s² (no octet). Only the \(\mathrm{P}^{3-}\) ion has a valence-shell octet.

Step 1: (a) Determine the electron configuration for \(\mathrm{Ca}^{+}\)

The atom Calcium (Ca) has 20 electrons. Since it loses one electron as \(\mathrm{Ca}^{+}\), it has 19 electrons. So, the electron configuration is: 1s², 2s², 2p⁶, 3s², 3p⁶, 4s¹. The valence shell has only 1 electron, so it doesn't have an octet.

Step 2: (b) Determine the electron configuration for Li

The atom Lithium (Li) has 3 electrons. So, the electron configuration is: 1s², 2s¹. The valence shell has only one electron, so it doesn't have an octet.

Step 3: (c) Determine the electron configuration for \(\mathrm{P}^{3-}\)

The atom Phosphorus (P) has 15 electrons. Since it gains three electrons as \(\mathrm{P}^{3-}\), it has 18 electrons. So, the electron configuration is: 1s², 2s², 2p⁶, 3s², 3p⁶. The valence shell has 8 electrons, so it has an octet.

Step 4: (d) Determine the electron configuration for \(\mathrm{Ar}^{+}\)

The atom Argon (Ar) has 18 electrons. Since it loses one electron as \(\mathrm{Ar}^{+}\), it has 17 electrons. So, the electron configuration is: 1s², 2s², 2p⁶, 3s², 3p⁵. The valence shell has 7 electrons, so it doesn't have an octet.

Step 5: (e) Determine the electron configuration for \(\mathrm{Si}^{2+}\)

The atom Silicon (Si) has 14 electrons. Since it loses two electrons as \(\mathrm{Si}^{2+}\), it has 12 electrons. So, the electron configuration is: 1s², 2s², 2p⁶, 3s². The valence shell has 2 electrons, so it doesn't have an octet.

Key Concepts

Valence Shell

The valence shell of an atom is the outermost shell of electrons. This is where all the action happens in chemistry. The electrons in this shell are called valence electrons. They play a key role in forming bonds and determining the chemical behavior of an atom.

• Valence electrons can participate in forming chemical bonds.
• The number of valence electrons affects how an atom reacts with others.

For example, in the ion \( \mathrm{Ca}^{+} \), calcium loses one electron, leaving it with a valence shell of just one electron in the 4s orbital. This is why it does not have an octet.

Octet Rule

The octet rule is a chemical guideline that suggests atoms are most stable when they have eight electrons in their valence shell. This rule explains why atoms form ions or covalent bonds.

• Atoms with fewer than 8 electrons tend to gain, lose, or share electrons to achieve a complete octet.
• It is a key factor in predicting molecule stability and chemical reactivity.

For example, \( \mathrm{P}^{3-} \) gains three electrons to achieve a stable octet of 8 valence electrons, resulting in the electron configuration of \( 1s^2, 2s^2, 2p^6, 3s^2, 3p^6 \).

Ions

Ions are atoms or molecules that carry a charge due to the loss or gain of electrons. Understanding ions is crucial to grasping many chemical reactions and properties.

• Cations are positively charged ions formed when an atom loses electrons.
• Anions are negatively charged ions, created by gaining electrons.

In the case of \( \mathrm{Ar}^{+} \), the atom loses one electron to become a cation, resulting in the electron configuration \( 1s^2, 2s^2, 2p^6, 3s^2, 3p^5 \), leaving seven valence electrons instead of eight.

Electron Gain and Loss

Atoms strive for stability, often achieved by gaining or losing electrons. This electron movement is central to ion formation and the octet rule.

• Atoms will lose electrons to become positively charged cations.
• They will gain electrons to become negatively charged anions.

For example, lithium (\( \mathrm{Li} \)) loses one electron to form a \( \mathrm{Li}^{+} \) ion with an electron configuration of \( 1s^2 \) instead of \( 1s^2, 2s^1 \), thus going from three electrons to two. Similarly, silicon (\( \mathrm{Si}^{2+} \)) loses two electrons, resulting in a configuration of \( 1s^2, 2s^2, 2p^6, 3s^2 \) with just two electrons in the valence shell.