---
title: "A student compares lattice-energy trends for alkaline earth oxide and chloride solids. The ionic radii for the relevant ions in comparable coordination environments are shown below.  | Ion | Ionic radius, \\(r\\) (\\(\\text{pm}\\)) | |—|—:| | \\(\\text{Mg}^{2+}\\) | \\(72\\) | | \\(\\text{Ca}^{2+}\\) | \\(100\\) | | \\(\\text{O}^{2-}\\) | \\(140\\) | | \\(\\text{Cl}^{-}\\) | \\(181\\) |  The student models the magnitude of the dominant attraction between neighboring ions using the index  \\[ I=\\dfrac{|z_+z_-|}{r_++r_-} \\]  where a larger value of \\(I\\) predicts a larger lattice-energy magnitude. Assume that other structural factors are comparable within each cation replacement. Which statement correctly predicts whether \\(\\text{CaO}\\rightarrow\\text{MgO}\\) or \\(\\text{CaCl}_2\\rightarrow\\text{MgCl}_2\\) produces the larger increase in the modeled lattice-energy magnitude and gives the correct justification?"
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url: "https://nerd-notes.com/ubq/120038/"
date_modified: "2026-08-21T08:40:52+00:00"
---

# A student compares lattice-energy trends for alkaline earth oxide and chloride solids. The ionic radii for the relevant ions in comparable coordination environments are shown below.

| Ion | Ionic radius, \(r\) (\(\text{pm}\)) |
|—|—:|
| \(\text{Mg}^{2+}\) | \(72\) |
| \(\text{Ca}^{2+}\) | \(100\) |
| \(\text{O}^{2-}\) | \(140\) |
| \(\text{Cl}^{-}\) | \(181\) |

The student models the magnitude of the dominant attraction between neighboring ions using the index

\[
I=\dfrac{|z_+z_-|}{r_++r_-}
\]

where a larger value of \(I\) predicts a larger lattice-energy magnitude. Assume that other structural factors are comparable within each cation replacement. Which statement correctly predicts whether \(\text{CaO}\rightarrow\text{MgO}\) or \(\text{CaCl}_2\rightarrow\text{MgCl}_2\) produces the larger increase in the modeled lattice-energy magnitude and gives the correct justification?

A student compares lattice-energy trends for alkaline earth oxide and chloride solids. The ionic radii for the relevant ions in comparable coordination environments are shown below.

| Ion | Ionic radius, \(r\) (\(\text{pm}\)) |
|---|---:|
| \(\text{Mg}^{2+}\) | \(72\) |
| \(\text{Ca}^{2+}\) | \(100\) |
| \(\text{O}^{2-}\) | \(140\) |
| \(\text{Cl}^{-}\) | \(181\) |

The student models the magnitude of the dominant attraction between neighboring ions using the index

\[
I=\dfrac{|z_+z_-|}{r_++r_-}
\]

where a larger value of \(I\) predicts a larger lattice-energy magnitude. Assume that other structural factors are comparable within each cation replacement. Which statement correctly predicts whether \(\text{CaO}\rightarrow\text{MgO}\) or \(\text{CaCl}_2\rightarrow\text{MgCl}_2\) produces the larger increase in the modeled lattice-energy magnitude and gives the correct justification?

- **A.** The replacement \(\text{CaCl}_2\rightarrow\text{MgCl}_2\) produces the larger increase because the larger radius of \(\text{Cl}^{-}\) makes the \(28\text{ pm}\) decrease in cation radius a larger fractional change in ion separation.
- **B.** The replacement \(\text{CaCl}_2\rightarrow\text{MgCl}_2\) produces the larger increase because the greater polarizability of \(\text{Cl}^{-}\) strengthens the Coulombic attraction more than the charge on \(\text{O}^{2-}\) does.
- **C.** The replacement \(\text{CaO}\rightarrow\text{MgO}\) produces the larger increase because the ionic charge of \(\text{Mg}^{2+}\) is greater than the ionic charge of \(\text{Ca}^{2+}\).
- **D.** The replacement \(\text{CaO}\rightarrow\text{MgO}\) produces the larger increase because \(|(+2)(-2)|\) is twice \(|(+2)(-1)|\), and the same \(28\text{ pm}\) decrease in cation radius produces a larger change in reciprocal separation for the smaller oxide ion pairs.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120038/*