Problem 33 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

The atomic radii of Cl, S, and K are approximately 97 pm, 100 pm, and 227 pm, respectively. Therefore, the order of increasing atomic size is Cl < S < K. The most common ions are \(Cl^{-}\), \(S^{2-}\), and \(K^{+}\), with ionic radii of 167 pm, 184 pm, and 133 pm, respectively. The order of increasing ionic size is \(K^{+}\) < \(Cl^{-}\) < \(S^{2-}\). The differences in the orders are due to the formation of ions altering the size of the elements: Cl and S become larger when forming anions, while K becomes smaller when forming the cation \(K^{+}\).

Step 1: Look up atomic radii for each element

Refer to a periodic table or an atomic radius chart to find the atomic radii of Sulfur (S), Chlorine (Cl), and Potassium (K). The atomic radii are approximately: - Sulfur (S): 100 pm - Chlorine (Cl): 97 pm - Potassium (K): 227 pm

Step 2: List the elements in order of increasing atomic radii

We can now list the elements in order of increasing size: Chlorine (Cl) < Sulfur (S) < Potassium (K) (b) Comparing ionic sizes

Step 1: Identify the most common ions of each element

The most common ions for the given elements are: - Sulfur (S): \(S^{2-}\) - Chlorine (Cl): \(Cl^{-}\) - Potassium (K): \(K^{+}\)

Step 2: Look up ionic radii for each ion

Refer to a periodic table or an ionic radius chart to find the ionic radii of \(S^{2-}\), \(Cl^{-}\), and \(K^+\). The ionic radii are approximately: - \(S^{2-}\): 184 pm - \(Cl^{-}\): 167 pm - \(K^{+}\): 133 pm

Step 3: List the ions in order of increasing ionic radii

We can now list the ions in order of increasing size: \(K^{+}\) < \(Cl^{-}\) < \(S^{2-}\) (c) Explain any differences in the orders of the atomic and ionic sizes

Step 1: Compare the orders of atomic and ionic sizes

We have found that: The order of atomic radii: Cl < S < K The order of ionic radii: \(K^{+}\) < \(Cl^{-}\) < \(S^{2-}\)

Step 2: Explain the differences

The atomic radius of an element increases as we go down the periodic table (due to the addition of electron shells). However, the ionic radius varies depending on the charge of the ion. In the case of Cl and S, both gain electrons and become larger when forming anions. When Chlorine gains 1 electron to form \(Cl^{-}\), its repulsion between valence electrons increases causing an increase in its ionic radius. On the other hand, Potassium loses an electron to form the cation \(K^{+}\), resulting in a decrease in its ionic radius. The loss of an electron causes less-electron repulsion and more attraction between the remaining electrons and nucleus, which lead to a smaller ionic radius. These differences account for the difference in the order of atomic and ionic radii.