Question

Arrange the atoms and/or ions in the following groups in order of decreasing size. a. \(\mathrm{O}, \mathrm{O}^{-}, \mathrm{O}^{2-}\) b. \(\mathrm{Fe}^{2+}, \mathrm{Ni}^{2+}, \mathrm{Zn}^{2+}\) c. \(\mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{Cl}^{-}\)

Short answer

The short answer based on the given step-by-step solution is: a) O²⁻ > O⁻ > O b) Fe²⁺ > Ni²⁺ > Zn²⁺ c) Cl⁻ > K⁺ > Ca²⁺

Step-by-step solution

Group a: O, O⁻, O²⁻

1. Recall the periodic trend in the atomic radii. Atomic radii generally decrease across a period (from left to right) and increase down a group (from top to bottom) in the periodic table. 2. Consider the effect of adding electrons. When an ion gains electrons and acquires a negative charge, the increased electron repulsion causes the ion to expand compared to a neutral atom. Thus, anions are larger than their parent atoms. 3. Arrange the atoms and ions according to size. Based on points 1 and 2, we can conclude that O²⁻ is the largest ion in this group, followed by O⁻, and finally, the neutral O atom. So, the order of decreasing size is: O²⁻ > O⁻ > O.

Group b: Fe²⁺, Ni²⁺, Zn²⁺

1. Recall the periodic trend in the atomic radii in transition metals. Transition metals experience fewer variations in atomic radii compared to other elements as their outer electrons occupy the d-orbitals. However, moving across a period still leads to a smaller atomic radius due to increased nuclear charge. 2. Compare the charge of the ions. All the ions in this group have the same charge of +2. Therefore, the effective nuclear charge is not the main determining factor for their sizes. 3. Determine the position of the elements in the periodic table. Fe, Ni, and Zn are all transition metals in period 4. Fe is the farthest to the left, followed by Ni and then Zn. 4. Arrange the ions according to size. Since the transition metal ions have the same charge and are in the same period, we use the periodic trend in atomic radii, which states that atomic size decreases across a period. Therefore, the order of decreasing size is: Fe²⁺ > Ni²⁺ > Zn²⁺.

Group c: Ca²⁺, K⁺, Cl⁻

1. Identify the relative positions of the elements in the periodic table. All three elements, Ca, K, and Cl, are found in period 4. Moving across the period from left to right, K comes first, followed by Ca, and finally Cl. 2. Consider the charges of the ions. Ca²⁺ has a +2 charge, K⁺ has a +1 charge, and Cl⁻ has a -1 charge. In general, cations are smaller and anions are larger than their respective neutral atoms. 3. Analyze the effects of the charges. The K⁺ ion is larger than the Ca²⁺ ion due to the difference in charge, even though Ca is farther to the right of K in the periodic table. Meanwhile, Cl⁻ is larger than the neutral Cl atom and all of the cations due to its negative charge. 4. Arrange the ions according to size. Taking into account the position of the elements in the periodic table and the charges of the ions, we can arrange the ions in the order of decreasing size as follows: Cl⁻ > K⁺ > Ca²⁺.