Problem 29 - Chemistry: The Central Science

Question

Which neutral atom is isoelectronic with each of the following ions? \(\mathrm{Ga}^{3+}, \mathrm{Zr}^{4+}, \mathrm{Mn}^{7+}, \Gamma, \mathrm{Pb}^{2+}\).

Step-by-Step Solution

Answer

The neutral atoms that are isoelectronic with the given ions \(\mathrm{Ga}^{3+}, \mathrm{Zr}^{4+}, \mathrm{Mn}^{7+}, \mathrm{Pb}^{2+}\) are Zinc (Zn), Krypton (Kr), Argon (Ar), and Platinum (Pt), respectively.

Step 1: Recall the Electron Configuration of Ions

To find the electron configuration of an ion, first, write down the electron configuration of that atom in its neutral form. Then, if the ion is positively charged, remove electrons from the highest energy levels. If the ion is negatively charged, add electrons to the available energy levels.

Step 2: Determine the Electron Configuration of the Given Ions

First, let's write down the atomic number and electron configuration of each ion in its neutral state: 1. \(\mathrm{Ga}^{3+}\): Gallium (Ga) has an atomic number of 31. Its electron configuration is \([Ar] 3d^{10} 4s^2 4p^1\). 2. \(\mathrm{Zr}^{4+}\): Zirconium (Zr) has an atomic number of 40. Its electron configuration is \([Kr] 4d^2 5s^2\). 3. \(\mathrm{Mn}^{7+}\): Manganese (Mn) has an atomic number of 25. Its electron configuration is \([Ar] 3d^5 4s^2\). 4. \(\mathrm{Pb}^{2+}\): Lead (Pb) has an atomic number of 82. Its electron configuration is \([Xe] 4f^{14} 5d^{10} 6s^2 6p^2\). Now, we will remove the electrons from each ion based on their positive charge: 1. \(\mathrm{Ga}^{3+}\): Remove 3 electrons: \([Ar] 3d^{10}\). 2. \(\mathrm{Zr}^{4+}\): Remove 4 electrons: \([Kr] 4d^{0}\) or \([Kr]\). 3. \(\mathrm{Mn}^{7+}\): Remove 7 electrons: \([Ar] 3d^0\) or \([Ar]\). 4. \(\mathrm{Pb}^{2+}\): Remove 2 electrons: \([Xe] 4f^{14} 5d^{10} 6s^0 6p^0\) or \([Xe] 4f^{14} 5d^{10}\).

Step 3: Find Neutral Atoms with the Same Electron Configuration

Now, let's find the neutral atoms with the same electron configurations as the ions: 1. \(\mathrm{Ga}^{3+}\): \([Ar] 3d^{10}\) has the same electron configuration as Zinc (Zn). 2. \(\mathrm{Zr}^{4+}\): \([Kr]\) has the same electron configuration as Krypton (Kr). 3. \(\mathrm{Mn}^{7+}\): \([Ar]\) has the same electron configuration as Argon (Ar). 4. \(\mathrm{Pb}^{2+}\): \([Xe] 4f^{14} 5d^{10}\) has the same electron configuration as Platinum (Pt). So, the neutral atoms that are isoelectronic with the given ions are Zinc (Zn), Krypton (Kr), Argon (Ar), and Platinum (Pt) respectively.

Key Concepts

Electron Configurations

Understanding electron configurations is essential for grasping the concept of isoelectronic atoms. Electron configurations describe the distribution of electrons in an atom's orbitals, which are regions around the nucleus where electrons are likely to be found.

Each electron occupies the lowest energy orbital available, filling them in a specific order: 1s, 2s, 2p, 3s, 3p, and so on. This order is dictated by the principles of quantum mechanics. You can think of it like filling up seats in a theater. The seats closest to the stage (or nucleus, in our case) are filled up first, with each notable section (s, p, d, f orbitals) representing a different part of the theater.

For example, the electron configuration of neutral gallium (Ga), with an atomic number of 31, is \[Ar\] 3d^{10} 4s^2 4p^1. This shorthand notation tells us that gallium has the same electron arrangement as argon (\[Ar\]), with additional electrons in the 3d, 4s, and 4p orbitals. When ions form, they lose or gain electrons to achieve a more stable electron configuration, often resembling the nearest noble gas.

Atomic Number

The atomic number is effectively the ID card of an element. It's unique for every element and indicates the number of protons in an atom's nucleus. Since atoms are electrically neutral, the atomic number also reveals how many electrons are in a neutral atom.

For instance, the atomic number of Mn (manganese) is 25, meaning it has 25 protons and, when neutral, 25 electrons. The beauty of the atomic number is that it gives a direct insight into the possible electron configurations an element can have. During ion formation, while the number of electrons changes, the atomic number remains the same, ensuring the element's identity is constant.

Ions and Charges

When atoms lose or gain electrons, they become ions. The number of electrons lost or gained is reflected in the ion's charge—the more electrons lost, the more positive the ion is.

Consider the \[Ga^{3+}\] ion. Gallium originally has 31 electrons, but as a 3+ ion, it's lost 3 electrons, so it only has 28 left. In contrast, a hypothetical \[Ga^{3-}\] ion would have gained 3 electrons, having a total of 34. These changes in electron number drastically alter electron configurations, which lead to similarities with neutral atoms of other elements - hence, the term isoelectronic. It's all about balance; elements often lose or gain electrons to achieve a noble gas configuration, which is the epitome of electronic stability in chemistry.