Question

Identify each statement as true or false: (a) Cations are larger than their corresponding neutral atoms. (b) Li \(^{+}\) is smaller than Li. (c) \(\mathrm{Cl}^{-}\) is bigger than \(\mathrm{I}^{-}.\)

Short answer

(a) False, cations are smaller than their corresponding neutral atoms. (b) True, Li \(^{+}\) is smaller than Li. (c) False, Cl\(^{-}\) is smaller than I\(^{-}\).

Step-by-step solution

(Statement a) Cations are larger than their corresponding neutral atoms.

In general, a cation is formed when an atom loses one or more electrons, resulting in a positive charge. When an electron is lost, the remaining electrons are attracted more strongly by the nucleus, leading to a decrease in the size of the atom. Hence, cations are smaller than their corresponding neutral atoms. Therefore, the given statement is false.

(Statement b) Li \(^{+}\) is smaller than Li.

Li \(^{+}\) ion is formed when a neutral lithium atom loses its one valence electron. As explained in statement a, when an atom loses an electron, the size of the atom generally decreases due to increased attraction by the nucleus. Thus, Li \(^{+}\) is indeed smaller than its neutral counterpart Li. Therefore, the given statement is true.

(Statement c) Cl\(^{-}\) is bigger than I\(^{-}\).

Anions are formed when an atom gains one or more electrons, resulting in a negative charge. When an electron is gained, the size of the atom generally increases due to the addition of an electron in the outer shell and increased electron-electron repulsion. In general, the size of atoms increases down a group in periodic table. Since Iodine (I) is in the same group as Chlorine (Cl) but is below it in the periodic table, I\(^{-}\) is expected to be larger than Cl\(^{-}\). Therefore, the given statement is false. Now, let's summarize our results: (a) False, cations are smaller than their corresponding neutral atoms. (b) True, Li \(^{+}\) is smaller than Li. (c) False, Cl\(^{-}\) is smaller than I\(^{-}\).

Key concepts

Cation vs Anion Size

Understanding the relative sizes of cations and anions is critical, both in general chemistry and many of its practical applications. A cation is an atom that has lost one or more electrons, thus having a positive charge. Now, why does losing an electron make the atom smaller? Consider the balance of forces within an atom. Electrons are repelled by each other (due to electron-electron repulsion) but attracted by the positively charged nucleus. When an electron is removed to form a cation, such as with Li⁺, there are fewer electrons pushing against each other, and the effective nuclear charge (the net positive charge felt by the electrons) increases. This stronger attraction pulls the remaining electrons closer to the nucleus, resulting in a smaller atomic radius.

In contrast, an anion is an atom that has gained one or more electrons, leading to a negative charge. Additional electrons increase electron-electron repulsion which makes the electron cloud expand, as the electrons try to maintain as much distance from each other as possible under the circumstances. Therefore, anions like Cl^- are larger than their neutral counterparts.

It’s a common misconception to believe anions would be smaller because they possess a 'negative' designation; however, the key concept here is to look at electron addition and its repulsive effects. To remember this, one might think of anions as 'adding on' size with the extra electrons, whereas cations contract due to the loss.

Trends in the Periodic Table

The periodic table is like a road map of the elements, providing a wealth of information about their properties, including atomic size. A fundamental trend is that atomic size increases down a group and decreases across a period from left to right. Down a group, new electron shells are added, increasing the size of the atom despite the increase in nuclear charge. Therefore, an element at the bottom of a group, such as iodine (I), is generally larger than elements above it, like chlorine (Cl).

This trend is reversed across a period, where an increase in the effective nuclear charge due to addition of protons pulls electrons closer, leading to a smaller atomic size. For ions like Cl^- and I^- within the same group, I^- will be larger because it is lower on the table despite both having an extra electron. These trends underpin important aspects of chemistry, especially regarding elements' reactivity and the nature of the bonds they form. A clear grasp of these often-predictable patterns allows students and scientists alike to anticipate and explain the behavior of different elements in various chemical contexts.

Electron-Electron Repulsion

Electron-electron repulsion is an often underestimated force that plays a significant role in determining the size and shape of an atom or ion. Understanding this concept not only helps with determining the ionic radii but also with molecular geometry and bond angles in compounds. Electrons are negatively charged and, as such, repel one another. In an atom or an ion, this repulsion among electrons must be balanced by the attractive force of the positively charged nucleus to form a stable structure.

When an atom gains an electron to become an anion, this addition increases electron-electron repulsion which in turn, increases the size of the electron cloud. Conversely, when an atom loses an electron to become a cation, there's less electron-electron repulsion, and the remaining electrons are held more tightly by the nucleus, resulting in a smaller atom. The battle between attraction to the nucleus and the repulsion among electrons shapes the chemistry of the elements, including how they bond and interact with each other. This balance of forces can be quite complex, with variations occurring due to the presence of other atoms or ions, the number of electrons involved, and environmental factors such as temperature and pressure.