Problem 86 - Chemistry The Molecular Science

Question

Select the atom or ion in each pair that has the larger radius. (a) \(\mathrm{Cl}\) or \(\mathrm{Cl}^{-}\) (b) Ca or \(\mathrm{Ca}^{2+}\) (c) Al or \(N\) (d) \(\mathrm{Cl}^{-}\) or \(\mathrm{K}^{+}\) (e) \(\ln\) or Sn

Step-by-Step Solution

Answer

(a) \\mathrm{Cl}^-, (b) Ca, (c) Al, (d) \\mathrm{Cl}^-, (e) Sn

Step 1: Understanding Atomic and Ionic Radii

The atomic radius refers to the size of a neutral atom, which is the distance from the nucleus to the outermost electrons. Ionic radius is the measure of the size of an atom's ion. When an atom loses an electron and becomes a cation (positive ion), it usually becomes smaller. Conversely, when an atom gains an electron and becomes an anion (negative ion), it typically becomes larger.

Step 2: Comparing Atomic and Ionic Radii for Cl and Cl^-

For (a), the neutral chlorine atom Cl and the chloride ion Cl^- are compared. Cl^- is an anion because it has gained an extra electron, increasing electron-electron repulsion and thus resulting in a larger radius. Therefore, Cl^- has a larger radius than Cl.

Step 3: Comparing Atomic and Ionic Radii for Ca and Ca^{2+}

For (b), the calcium atom Ca and its cation Ca^{2+} are compared. Ca^{2+} has lost two electrons relative to neutral Ca, reducing the electron cloud and making the ion smaller than the neutral atom. Thus, Ca has a larger radius than Ca^{2+}.

Step 4: Comparing Atomic Radii for Al and N

For (c), the neutral atoms of aluminum (Al) and nitrogen (N) are compared. Aluminum is in period 3 and nitrogen in period 2, with aluminum having more shells, leading to a larger atomic radius. Therefore, Al has a larger radius than N.

Step 5: Comparing Ionic Radii for Cl^- and K^+

For (d), both Cl^- and K^+ are compared. Despite their charge differences, they each have the same number of electrons making them isoelectronic. However, Cl^- has a larger radius due to smaller nuclear charge compared to K^+. Therefore, Cl^- has a larger radius than K^+.

Step 6: Comparing Atomic Radii for I and Sn

For (e), the iodine (I) and tin (Sn) atoms are compared. Tin, with more electron shells, is located lower on the periodic table, resulting in a larger atomic radius than iodine. Thus, Sn has a larger radius than I.

Key Concepts

Atomic Radius

The atomic radius is a crucial concept in understanding the size of atoms. It refers to the distance from the nucleus to the outermost shell of electrons in a neutral atom. This size can vary widely among different elements. Generally, as you move down a group in the periodic table, the atomic radius increases. This is because each subsequent element has an additional electron shell, making the atom larger. Similarly, moving from left to right across a period, the atomic radius generally decreases. This size reduction occurs because more protons in the nucleus exert a stronger pull on the electron cloud, thereby pulling the electrons closer to the nucleus.

Ionic Radius

The ionic radius is a measure of an atom's ion size, which can differ from its atomic radius due to the gain or loss of electrons. When an atom loses electrons, it becomes a cation with a positive charge. Cations are typically smaller than their neutral atom counterparts because the loss of electrons leads to a decrease in electron-electron repulsion, thus allowing the remaining electrons to be pulled closer to the nucleus. On the other hand, anions are formed when an atom gains electrons, resulting in a negative charge. This gain of electrons increases electron-electron repulsion, causing the electron cloud to expand, and hence, anions are generally larger than their corresponding neutral atoms.

Cation and Anion Size Comparison

Cations and anions have differing sizes compared to their neutral atoms. Cations are smaller than their parent atoms because they lose electrons, which reduces the repulsion among remaining electrons and allows them to be drawn closer to the nucleus. This results in a smaller ionic radius. Conversely, anions are larger than their parent atoms because of the additional electrons, which increase repulsion within the electron cloud, causing it to expand. For example, chloride ions ( Cl^- ), which are anions, have larger radii compared to neutral chlorine atoms due to gaining an electron, which increases repulsion. Similarly, calcium ions ( Ca^{2+} ), which are cations, are smaller than neutral calcium atoms due to the loss of electrons and decrease in repulsion.

Isoelectronic Species

Isoelectronic species refer to atoms and ions that have the same number of electrons. Despite having different elements, these species share an identical electronic configuration. However, even with the same number of electrons, their sizes can differ based on their nuclear charge. For example, Cl^- and K^+ are isoelectronic, both having 18 electrons. However, Cl^- has a larger radius than K^+ . This size difference exists because Cl^- has fewer protons in its nucleus than K^+ , resulting in a weaker nuclear attraction pulling on the electron cloud. Thus, while they share the same electron count, the effective nuclear charge makes all the difference in their size.

Periodic Table Trends

Understanding periodic table trends can help predict the atomic and ionic sizes across different elements. Generally, as you move down a group, both atomic and ionic radii increase. This is because additional electron shells are added, making each consecutive element larger. On the other hand, moving across a period from left to right typically results in a decrease in atomic size, owing to the increase in nuclear charge which pulls electrons closer in tighter orbits. This trend, however, has exceptions, particularly noticeable in transition and inner transition metals, where electron-electron repulsion and orbital configurations play significant roles.