Problem 119 - Introductory Chemistry Atoms First

Question

Which part of the following statement is true and which part is false? \(\mathrm{Mg}^{2+}\) and \(\mathrm{Na}^{+}\) have identical electron configurations, and they also have similar properties. Explain your answer fully.

Step-by-Step Solution

Answer

The first part of the statement is true, as \(\mathrm{Mg}^{2+}\) (1s² 2s² 2p⁶) and \(\mathrm{Na}^{+}\) (1s² 2s² 2p⁶) have identical electron configurations. However, the second part of the statement is false; although both ions are cations, they have different properties due to their varying charges (+2 for Mg²⁺ and +1 for Na⁺) and sizes (Mg²⁺ is smaller than Na⁺).

Step 1: Part 1: Electron configurations of Mg²⁺ and Na⁺

To verify if the \(\mathrm{Mg}^{2+}\) and \(\mathrm{Na}^{+}\) have identical electron configurations, we need to write the electron configuration of each ion. For magnesium (Mg): Its atomic number is 12, so the electron configuration of a neutral atom is 1s² 2s² 2p⁶ 3s². When Mg loses two electrons to become \(\mathrm{Mg}^{2+}\), its electron configuration becomes: 1s² 2s² 2p⁶. For sodium (Na): Its atomic number is 11, so the electron configuration of a neutral atom is 1s² 2s² 2p⁶ 3s¹. When Na loses one electron to become \(\mathrm{Na}^{+}\), its electron configuration becomes: 1s² 2s² 2p⁶. Now, comparing the electron configurations of \(\mathrm{Mg}^{2+}\) (1s² 2s² 2p⁶) and \(\mathrm{Na}^{+}\) (1s² 2s² 2p⁶), we find that they are identical. So, the first part of the statement is true.

Step 2: Part 2: Comparing properties of Mg²⁺ and Na⁺

Now we will analyze the second part of the statement, which claims that Mg²⁺ and Na⁺ have similar properties. Mg²⁺ and Na⁺ are both positive ions (cations) formed by losing electrons. However, they differ in their charge and size: - Charge: Mg²⁺ has a charge of +2, whereas Na⁺ has a charge of +1. - Size: Mg²⁺ is smaller in size compared to Na⁺ because, after losing electrons, Mg²⁺ has more protons (12) attracting the remaining electrons, while Na⁺ has fewer protons (11). These differences in charge and size lead to different chemical and physical properties: 1. Chemical properties: Even though both ions are cations, their reactivity and the stability of their compounds differ due to the difference in charge and size. 2. Physical properties: The difference in size and charge also affects their solubility, melting and boiling points, and other physical properties. From this analysis, we can conclude that even though Mg²⁺ and Na⁺ have identical electron configurations, they have different properties due to their varying charges and sizes. So, the second part of the statement is false.

Key Concepts

Cation Properties

Cations are positively charged ions that form when an atom loses electrons. This loss of electrons results in a positive charge. The properties of cations are influenced by their charge and size.

• A higher positive charge generally leads to stronger interactions with negatively charged species.
• Smaller cations typically lead to stronger attractions between the ion and its surroundings.

Cations like \(\mathrm{Mg}^{2+}\) and \(\mathrm{Na}^{+}\) differ in charge (+2 vs +1, respectively), which significantly impacts their properties. Mg²⁺, with more protons for the same number of electrons, is smaller than Na⁺ and can form stronger ionic bonds.

Electron Loss in Ions

When an atom becomes a cation, it loses electrons. This changes its electron configuration and stabilizes the ion according to the octet rule, often resembling the configuration of noble gases.
For example:

• Magnesium (Mg), with atomic number 12, loses two electrons to become \(\mathrm{Mg}^{2+}\), reducing its electron configuration to 1s² 2s² 2p⁶.
• Sodium (Na), with atomic number 11, loses one electron to become \(\mathrm{Na}^{+}\), also achieving a 1s² 2s² 2p⁶ configuration.

This identical electron configuration explains why ions like \(\mathrm{Mg}^{2+}\) and \(\mathrm{Na}^{+}\) can have similar stable structures, despite differing in other properties.

Chemical Properties of Ions

The chemical properties of ions, such as reactivity and the nature of the compounds they form, can be quite different even if they share the same electron configuration.
Consider the differences:

• \(\mathrm{Mg}^{2+}\), having a higher charge, forms more stable ionic compounds compared to \(\mathrm{Na}^{+}\).
• The greater charge density of \(\mathrm{Mg}^{2+}\) results in higher lattice energy in its compounds.

These distinctions arise from the ion’s charge and the size, affecting how they interact with other ions and molecules.

Physical Properties of Cations

Cations have distinctive physical properties based on their charge and size. These attributes dictate how ions behave in different physical contexts, such as:

• Solubility: \(\mathrm{Na}^{+}\) salts are generally more soluble in water compared to \(\mathrm{Mg}^{2+}\) salts, due to the smaller lattice energies of the former.
• Melting and boiling points: \(\mathrm{Mg}^{2+}\) compounds often have higher melting and boiling points, owing to stronger ionic bonds.

Even when two cations like \(\mathrm{Mg}^{2+}\) and \(\mathrm{Na}^{+}\) share the same electron configuration, these physical properties will differ because of the variations in charge and ionic size.