Question

The first ionization energy (IE) of potassium is lower than the first IE for calcium, but the second IE of calcium is lower than the second IE of potassium. Use an electron configuration or size argument to explain this trend in ionization energies.

Short answer

Potassium has a lower first ionization energy than calcium because it has one less electron in the highest energy level, reducing electron-electron repulsion. Calcium has a lower second ionization energy than potassium because after losing one electron it does not yet have a noble gas configuration, whereas potassium does.

Step-by-step solution

Understanding First Ionization Energy

First ionization energy (IE1) is the energy required to remove the most loosely held electron from an atom of an element in its gaseous state. For potassium (K), the electron configuration is [Ar] 4s^1 and for calcium (Ca), it is [Ar] 4s^2. Since potassium only has one electron in the 4s orbital and calcium has two, with both being equally shielded by the same core electrons, the single electron in potassium is easier to remove due to less electron-electron repulsion.

Comparing the Electron Configurations for IE1

For IE1, we compare the ease of removing the single electron in the 4s orbital of both elements. Potassium has an electron configuration of [Ar] 4s^1, which is a single electron state. It requires less energy to remove this one electron due to the absence of electron-electron repulsion in the 4s orbital, as opposed to calcium, which has two electrons in the 4s orbital. This extra electron causes a slight repulsion, making it slightly harder to remove one electron and hence a higher IE1.

Understanding Second Ionization Energy

Second ionization energy (IE2) is the energy needed to remove a second electron from an atom after the first has been removed. After losing its first electron, potassium becomes [Ar], a noble gas configuration, which is very stable. In contrast, after losing one electron, calcium becomes [Ar] 4s^1, which still has one more electron to lose before achieving noble gas stability.

Comparing the Electron Configurations for IE2

Calcium, after losing one electron ([Ar] 4s^1), will lose its second electron more easily than potassium ([Ar]) will lose its second electron. This is because calcium still does not have a noble gas configuration after the first ionization, whereas potassium does. Elements tend to reach a stable noble gas configuration, and since calcium is one electron away from this after the first ionization, the second ionization energy is lower than that of potassium.

Key concepts

Electron Configuration

The electron configuration of an atom describes how the electrons are arranged within orbitals, subshells, and shells. The configuration is influenced by the principles of quantum mechanics, which dictate the most stable arrangements of electrons. For instance, the 'Aufbau principle' proposes that electrons fill lower energy levels before moving to higher ones, thereby creating a foundation for understanding electron distribution around the nucleus.

In the context of potassium (K) and calcium (Ca), we look at their electron configurations, which are [Ar] 4s¹ and [Ar] 4s², respectively. The notation [Ar] indicates that both elements have the same electron configuration as argon in their inner shells, and the difference arises in the outermost 4s subshell. Potassium has a single electron in this subshell, while calcium has two. This difference plays a pivotal role in determining their respective ionization energies.

First Ionization Energy

First ionization energy (IE1) is a measure of the energy required to remove the outermost electron from an isolated, gaseous atom. It is a critical indicator of an element’s reactivity and is often influenced by nuclear charge, electron shielding, and the distance of the outermost electron from the nucleus. A higher IE1 means that it's generally harder to remove an electron due to a stronger attraction between the electron and the nucleus.

In our comparison between potassium and calcium, potassium's IE1 is lower. This is because with its electron configuration of [Ar] 4s¹, the single electron experiences minimal electron-electron repulsion and is therefore easier to remove. In contrast, calcium's IE1 is slightly higher because the two electrons in the 4s subshell experience some level of repulsive force, requiring more energy to remove one of them.

Second Ionization Energy

Second ionization energy (IE2) is defined as the energy needed to remove a second electron from an atom, after the first has already been removed. It is generally higher than the first ionization energy because removing a second electron from a positively charged ion is more difficult as the effective nuclear charge acting on the remaining electrons has increased.

For potassium, after it loses its first electron, it achieves a noble gas configuration ([Ar]). This makes the removal of a further electron very difficult, resulting in a high second ionization energy. In contrast, for calcium, once it loses one electron ([Ar] 4s¹), it still remains one electron away from the noble gas configuration, which means it's more willing to lose that second electron, thus, a lower IE2 compared to that of potassium.

Electron-Electron Repulsion

Electron-electron repulsion is a fundamental concept explaining why electrons within the same orbital or subshell affect each other’s energies. Electrons are negatively charged, and like charges repel one another according to Coulomb's law. This repulsion can influence an atom's energy levels and thus its ionization energy.

In a multi-electron atom like calcium, the two electrons in the 4s orbital repel each other, making it easier to remove one of them compared to a situation where no repulsion is present. This repulsion is one of the reasons for the lower first ionization energy observed in calcium when compared to potassium, which does not have electron-electron repulsion in its valence subshell since it contains only a single electron.