Question

Consider \(\mathrm{S}, \mathrm{Cl},\) and \(\mathrm{K}\) and their most common ions. (a) List the atoms in order of increasing size. (b) List the ions in order of increasing size. (c) Explain any differences in the orders of the atomic and ionic sizes.

Short answer

The order of S, Cl, and K atoms in increasing size is Cl < S < K, while the order of their most common ions (K^(+), Cl^(-), and S^(2-)) in increasing size is K^(+) < Cl^(-) < S^(2-). The difference in the orders of the atomic and ionic sizes is due to the gain or loss of electrons when the atoms form ions, which affects the electron-electron repulsions and the strength of the attraction between the electrons and the nucleus.

Step-by-step solution

Identify Trends in Atomic Size

To list the S, Cl, and K atoms in order of increasing size, we need to understand the trends in atomic size across the periodic table. Atomic size generally decreases as you go across a period from left to right and increases as you go down a group. Sulfur (S) is in Group 16, Period 3. Chlorine (Cl) is in Group 17, Period 3. Potassium (K) is in Group 1, Period 4.

List S, Cl, and K Atoms in Order of Increasing Size

Based on the trends in atomic size and the positions of the elements in the periodic table, below is the order of the S, Cl, and K atoms in increasing size: Cl < S < K

Determine the Most Common Ions of S, Cl, and K

To list the ions in order of increasing size, first determine the most common ions of these elements: Sulfur (S) forms S^(2-) by gaining 2 electrons. Chlorine (Cl) forms Cl^(-) by gaining 1 electron. Potassium (K) forms K^(+) by losing 1 electron.

List the Ions in Order of Increasing Size

When the atoms form ions, the size changes based on the gain or loss of electrons. For ions in the same period, the more positive the charge, the smaller the ion, and the more negative the charge, the larger the ion. So, the order of the ions in increasing size is: K^(+) < Cl^(-) < S^(2-)

Explain Differences in the Orders of the Atomic and Ionic Sizes

The differences in the orders of the atomic and ionic sizes are due to the gain or loss of electrons that occur when the atoms form ions: 1. When Cl gains 1 electron to form the Cl^(-) ion, its size increases as the additional electron increase electron-electron repulsions and the outer electrons are less strongly held to the nucleus. 2. When S gains 2 electrons to form the S^(2-) ion, its size increases even more than Cl^(-) for similar reasons. 3. When K loses 1 electron to form the K^(+) ion, its size decreases, as it loses an energy shell, and the remaining electrons experience a stronger attraction to the nucleus due to the increased number of protons. This leads to the order of ions in increasing size as K^(+) < Cl^(-) < S^(2-), which is different from the order of the atomic sizes, Cl < S < K.

Key concepts

Atomic Size

Atomic size, also known as atomic radius, refers to the distance from the center of an atom's nucleus to its outermost electrons. As you move across a period from left to right on the periodic table, atomic size generally decreases. This is because electrons are added to the same energy level while the number of protons in the nucleus increases, causing a greater pull on the electrons. On the other hand, as you move down a group, atomic size increases because each subsequent element has an additional electron shell.

Let's look at the elements sulfur ( S ), chlorine ( Cl ), and potassium ( K ). Sulfur and chlorine are in the same period (Period 3), while potassium is in the next period down (Period 4). Within a period, chlorine, being further to the right, will be smaller than sulfur due to its increased nuclear charge pulling the electron cloud closer. Potassium, located in the next period, is larger than both sulfur and chlorine due to the presence of an additional electron shell. Here is the atomic size order for Cl , S , and K :

• Cl (< smallest atomic size)
• S
• K (> largest atomic size)

Ionic Size

Ionic size refers to the size of an atom's ion, which can vary significantly from the size of the neutral atom. When atoms gain or lose electrons, they form ions, which results in changes to their size due to alterations in electron-electron repulsion and nuclear pull.

For instance, sulfur gains two electrons to form the sulfide ion ( S^{2-} ), chlorine gains one electron to become the chloride ion ( Cl^{-} ), and potassium loses one electron to become the potassium ion ( K^{+} ). Gaining electrons increases the electron cloud size because the added electrons heighten repulsion among electron pairs, which increases ionic size. Conversely, losing electrons decreases ionic size, as the reduced electron cloud feels a stronger pull from the nucleus.

Let’s order these ions based on their sizes:

• K⁺ (< smallest ionic size)
• Cl^-
• S^2- (> largest ionic size)

As K loses an entire electron shell, its resulting ion, K^{+} , is significantly smaller than any of the other ions. The cloud around Cl^{-} is larger than the neutral Cl but still smaller than S^{2-} , as S^{2-} sees a greater extent of electron-electron repulsion due to its extra negative charges.

Periodic Table Trends

The periodic table is a powerful tool that summarizes many trends of elements, including their size as atoms and ions. These trends are systematic and predictable, allowing us to infer details such as atomic and ionic size by knowing the position of an element on the table.
The trends for atomic size and ionic size are not always the same. Atoms can become larger or smaller as they convert to ions depending on whether they gain or lose electrons in the process. For example:

• Atomic size decreases across a period but increases down a group.
• Ions with positive charge ( K^{+} ) are usually smaller than their corresponding neutral atoms due to loss of electron shells.
• Negative ions ( Cl^{-} , S^{2-} ) expand in size due to increased electron repulsion.

Therefore, the periodic table helps visualize and anticipate the behavior of elements in both atomic and ionic forms by following these trends. Sulfur, chlorine, and potassium each demonstrate these principles, highlighting the order of atomic sizes (Cl < S < K) and ionic sizes (K^+ < Cl^- < S^{2-}) , which vary due to electron configuration changes.