Question

Comment on the possible formation of the \(\mathrm{K}^{2+}\) ion. Why is its formation unlikely?

Short answer

The formation of ext{K}^{2+} is unlikely due to high energy costs associated with removing a second electron from a stable configuration.

Step-by-step solution

Understanding Ion Formation

When atoms lose or gain electrons, they become ions. A positive ion, or cation, forms when an atom loses electrons. Potassium ( ext{K}) usually forms ions by losing one electron.

Electron Configuration of Potassium

Potassium's atomic number is 19, meaning it has 19 electrons. Its electron configuration is ext{1s}^2 ext{2s}^2 ext{2p}^6 ext{3s}^2 ext{3p}^6 ext{4s}^1, with one electron in the 4s orbital.

Formation of ext{K}^{+} Ion

Normally, potassium loses one electron from the 4s orbital to form ext{K}^{+}, resulting in an electron configuration of ext{1s}^2 ext{2s}^2 ext{2p}^6 ext{3s}^2 ext{3p}^6, which is a stable noble gas configuration.

Attempting to Form ext{K}^{2+} Ion

To form ext{K}^{2+}, potassium would need to lose another electron, resulting in ext{1s}^2 ext{2s}^2 ext{2p}^6 ext{3s}^2 ext{3p}^5, which means entering into an incomplete 3p orbital.

Energy Considerations

Removing a second electron involves breaking into the stable noble gas core, which requires significantly more energy than removing just one electron due to increased ionization energy. The energy levels shift dramatically to unfavorable energy states.

Conclusion on Ion Formation

The formation of ext{K}^{2+} is unlikely because it requires removing an electron from a full, stable orbital, which is energetically unfavorable.

Key concepts

Electron Configuration

The electron configuration of an element describes the arrangement of electrons around the nucleus of an atom. For potassium ( K ), the atomic number is 19, indicating it has 19 electrons. These electrons are distributed across different energy levels or shells: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 . Each number and letter in this sequence tells us the number of electrons in each subshell and their positions. The 's', 'p', 'd', 'f' denote different types of orbitals, with varying energy.

Potassium's electron configuration ends with 4s^1 , which means there is one electron in the 4s orbital. This valence electron is quite loosely held, making it easier for potassium to lose it and become stabilized as a K^+ ion. Understanding these configurations helps predict how potassium and other elements will react chemically.

Potassium Ionization

Ionization refers to the process by which an atom or a molecule loses or gains electrons and forms ions. Potassium ( K ) is known for its tendency to form positive ions, called cations, by losing electrons. The ionization process for potassium typically involves losing a single electron from its outermost shell, the 4s orbital.

When potassium loses this one valence electron, it becomes K^+ . This is a stable configuration as it matches the electron configuration of argon, a noble gas. Argon has a full outer shell, which provides a stable structure. Potassium naturally prefers this state, which reflects its typical chemical behavior of losing just one electron during ionization.

The idea of potassium forming K^2+ involves losing two electrons. However, once the first electron is lost, any further ionization requires much more energy because it means disrupting a full set of electrons in the 3p orbital, moving away from a stable configuration.

Cation Stability

Stability of ions is crucial in understanding why certain ions form more readily than others. A cation's stability often depends on its electron configuration. For potassium, the stable cation is K^+ , which results from losing one electron, achieving the electron configuration of argon, a noble gas.

Noble gases are inherently stable because their valence shells are full. Thus, losing another electron to form K^2+ would result in an unstable and incomplete 3p orbital, making K^2+ far less favorable. In terms of energy, the system prefers the lower energy, more stable state of K^+ .

In chemical reactions, achieving the lowest possible energy state drives how atoms form ions. Hence, potassium's inherent cation stability is tied to reaching a noble gas configuration once it loses one electron, making further ionization unappealing and energetically costly.

Ionization Energy

The energy required to remove an electron from an atom or ion in its gaseous state is called ionization energy. For potassium, the first ionization energy is relatively low because the single electron in the 4s orbital is loosely bound and can be removed with minimal energy.

However, the second ionization energy is considerably higher. This increase is significant because it would involve breaking into a stable, filled 3p orbital. Breaking this noble gas core demands immense energy compared to removing an electron from the already incomplete 4s orbital.

So, while potassium readily loses its first electron to form K^+ , the high ionization energy needed for forming K^2+ explains why the latter is unlikely. The drastic increase in required energy for additional electron removal keeps potassium from further ionization in typical conditions, maintaining stability.