Problem 66 - Chemistry

Question

No element has a negative second electron affinity. That is, the process \(\mathrm{A}^{-}(\mathrm{g})+\mathrm{e}^{-} \longrightarrow \mathrm{A}^{2-}(g)\) is unfavorable for every ele- ment. Suggest a reason.

Step-by-Step Solution

Answer

The second electron affinity is unfavorable due to increased electron-electron repulsion within the negatively charged ion.

Step 1: Understanding Electron Affinity

Electron affinity is the amount of energy released when an electron is added to a neutral atom in the gaseous state to form a negative ion. The first electron affinity tends to be negative, indicating an exothermic process as energy is released.

Step 2: Analyzing the Second Electron Affinity

The second electron affinity refers to the addition of an electron to a negatively charged ion. This process typically requires energy, as it involves adding a negatively charged electron to an already negatively charged ion, which leads to electron-electron repulsion.

Step 3: Explaining Unfavorable Nature of Second Electron Affinity

This unfavorable nature arises from electrostatic repulsion. Introducing another electron into an already negative ion increases electron-electron repulsion, making the process endothermic and thus requiring energy input. Consequently, the second electron affinity is positive for all elements, indicating an unfavorable process.

Key Concepts

Second Electron Affinity

When discussing electron affinities, the focus often starts with the first electron affinity, where energy is typically released. This process adds an electron to a neutral atom, forming a negatively charged ion. However, when it comes to the second electron affinity, things change. This process involves adding an electron to an already negatively charged ion. It is not only less common but also requires a deep dive to understand why it always demands energy input. Here's why:

• Adding a second electron to a negative ion involves overcoming the inherent repulsive forces between like charges.
• This repulsion makes it necessary to put energy into the system to get the second electron to bond with the ion.
• Therefore, the term for the second electron affinity is positive, indicating an endothermic reaction.

These factors contribute to why no elements have a negative second electron affinity, thus making it a consistently unfavorable process.

Electron-Electron Repulsion

Electron-electron repulsion is a key factor in understanding the second electron affinity. It is all about the repulsive forces that occur when two negatives try to approach each other. In the case of adding an electron to an already negative ion:

• The existing negative charge of the ion repels the added electron, due to the principle that like charges repel each other.
• This repulsive force requires additional energy to be overcome, hence making the electron addition process energetically demanding.
• The resulting electron cloud becomes more compact, increasing the repulsion from inner electrons as well as the newly added one.

Thus, the electron-electron repulsion plays a fundamental role in making the second electron affinity an endothermic process.

Endothermic Processes

In an endothermic process, energy is absorbed rather than released. This is a crucial factor when looking at second electron affinities, as they do not release energy, but require it. Here is what makes this process endothermic:

• Breaking down the required energy input: overcoming electron-electron repulsion is the main energy-consuming action.
• Endothermicity is indicated by a positive energy value, meaning energy isn't released but instead needs to be absorbed by the system to proceed.
• As the negative ion gains another electron, it becomes less stable and requires more energy to maintain this extra electron in its orbit.

Due to these absorption requirements, endothermic processes like the second electron affinity highlight why this addition of electrons isn't energetically favorable.