Question

The electron affinities of the elements from aluminum to chlorine are \(-44,-120,-74,-200.4\), and \(-384.7 \mathrm{~kJ} / \mathrm{mol}\), respectively. Rationalize the trend in these values.

Short answer

The electron affinity trend from aluminum to chlorine can be rationalized by considering the effective nuclear charge (Z_eff) and the stability of half-filled orbitals. As we move across the period, Z_eff generally increases, leading to more negative electron affinity values. However, at phosphorus, the 3p orbital is already half-filled, providing extra stability and making it less energetically favorable to add an electron. This results in a less negative electron affinity for phosphorus compared to silicon and sulfur. Overall, the trend in electron affinity is: more negative from Al to Si, less negative from Si to P, and more negative from P to Cl.

Step-by-step solution

Identify the elements and their positions on the periodic table

The elements with the given electron affinities are aluminum (Al), silicon (Si), phosphorus (P), sulfur (S), and chlorine (Cl). These elements are in Period 3 of the periodic table. Their group numbers are as follows: - Aluminum (Al): Group 13 - Silicon (Si): Group 14 - Phosphorus (P): Group 15 - Sulfur (S): Group 16 - Chlorine (Cl): Group 17

Examine the trend in electron affinity values

We are given the electron affinity values as: Al (-44 kJ/mol), Si (-120 kJ/mol), P (-74 kJ/mol), S (-200.4 kJ/mol), and Cl (-384.7 kJ/mol). The overall trend in these values is: - First, the electron affinity becomes more negative from Al to Si; - Then, it becomes less negative from Si to P; - Finally, it becomes more negative from P to Cl.

Understand electron affinity's relationship with atomic structure and the periodic table

Electron affinity is influenced by the effective nuclear charge (Z_eff) and the distance between the nucleus and the added electron (represented by the principal quantum number n). As we move from left to right across a period, Z_eff generally increases, which means the attractive force between the nucleus and the outermost electrons becomes stronger. However, the distance (n) remains roughly the same within the same period.

Rationalize the trend in electron affinities

The Z_eff increases as we move across the period from aluminum to chlorine, which explains why the electron affinities generally become more negative. This indicates that the elements on the right side of the periodic table (such as chlorine) will have a stronger attraction for the added electrons than those on the left side (such as aluminum). However, there is an exception at the phosphorus element. This can be explained by the fact that, in phosphorus, an electron will be added to the 3p orbital, which is already half-filled (electron configuration: [Ne] 3s² 3p³) in its neutral state. A half-filled orbital is considered as extra stable, so adding an extra electron to a half-filled p orbital is less energetically favorable than adding an electron to a different element with a not half-filled orbital (like silicon or sulfur). So, considering both the increase in Z_eff and the half-filled orbital stability, the given trend in the electron affinity values can be rationalized as: more negative from Al to Si, less negative from Si to P (due to half-filled 3p orbital stability), and continuing more negative from P to Cl.

Key concepts

Periodic Table Trends

The concept of periodic table trends helps us understand various properties of elements as we move across a period or down a group. One such property is electron affinity, which is the energy change when an electron is added to a neutral atom in the gas phase. In general, as we move from left to right across a period, electron affinities become more negative, indicating a stronger attraction between the atom and the added electron.

This trend is due to an increase in effective nuclear charge (Z_eff) as more protons are added to the nucleus. Additionally, elements closer to the right have almost filled outer shells, making it energetically favorable to gain electrons. However, there are exceptions that need consideration, like the half-filled or full-filled stability observed in some elements.

Effective Nuclear Charge

The concept of effective nuclear charge ( Z_eff ) is crucial for understanding periodic trends like electron affinity. Z_eff is essentially the net positive charge experienced by an electron in a multi-electron atom. As we move from left to right across a period, the number of protons in the nucleus increases. This increase in positive charge pulls electrons closer to the nucleus.

While electrons in the inner shells shield some of this charge, the outer electrons experience a greater effective nuclear charge due to imperfect shielding. As a result, this stronger attraction makes it more energetically favorable for atoms to gain additional electrons. This is why electron affinities are typically more negative as we progress across a period in the periodic table.

Atomic Structure

Atomic structure plays a significant role in determining electron affinity. Each element's atomic structure consists of a nucleus surrounded by electrons arranged in shells or orbitals. These shells fill in a specific order, based on increasing energy levels.

For example, in the case of the third period elements mentioned—Al, Si, P, S, and Cl—the electron configuration and the filling of the 3p orbitals play a crucial role. As we move from Al to Cl, the effective nuclear charge increases, which generally leads to more negative electron affinity values. However, we observe an exception with phosphorus, where the 3p sublevel is half-filled, providing extra stability and thus requiring less energy to add another electron compared to other elements in this sequence.

Group Elements

Group elements share similar chemical and physical properties, which can also influence their electron affinities. Within a group, elements have the same number of electrons in their outer shell, which contributes to similar chemical behavior.

For instance, elements in Group 17, like chlorine, have high electron affinities due to their need to complete their valence shell of electrons and form stable negative ions. Conversely, elements from Group 13, such as aluminum, typically have lower electron affinities since gaining electrons would not fill their valence shell and doesn't increase their stability significantly.

This variation within group elements highlights how electron affinity is not only dependent on atomic structure and effective nuclear charge, but also on how the electron configuration contributes to an element's tendency to gain electrons for achieving stability.