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.

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.

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

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.

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-)

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.