---
title: "A student compares the dissolution of the hypothetical ionic solids \\(\\text{MZ(s)}\\) and \\(\\text{NZ(s)}\\) in water.  \\[ \\text{MZ(s)} \\rightarrow \\text{M}^{+}\\text{(aq)}+\\text{Z}^{-}\\text{(aq)} \\]  \\[ \\text{NZ(s)} \\rightarrow \\text{N}^{+}\\text{(aq)}+\\text{Z}^{-}\\text{(aq)} \\]  For \\(1\\text{ mol}\\) of each solid, the lattice-separation enthalpies are equal, and the hydration contributions from \\(\\text{Z}^{-}\\) are identical. In the diagram, the first-shell hydration radius is the distance from the center of a cation to the center of a surrounding water oxygen atom.  Based on the particulate diagram, which statement correctly compares the cation hydration enthalpies and the enthalpies of solution?"
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url: "https://nerd-notes.com/ubq/120063/"
date_modified: "2026-08-21T08:41:07+00:00"
---

# A student compares the dissolution of the hypothetical ionic solids \(\text{MZ(s)}\) and \(\text{NZ(s)}\) in water.

\[
\text{MZ(s)} \rightarrow \text{M}^{+}\text{(aq)}+\text{Z}^{-}\text{(aq)}
\]

\[
\text{NZ(s)} \rightarrow \text{N}^{+}\text{(aq)}+\text{Z}^{-}\text{(aq)}
\]

For \(1\text{ mol}\) of each solid, the lattice-separation enthalpies are equal, and the hydration contributions from \(\text{Z}^{-}\) are identical. In the diagram, the first-shell hydration radius is the distance from the center of a cation to the center of a surrounding water oxygen atom.

Based on the particulate diagram, which statement correctly compares the cation hydration enthalpies and the enthalpies of solution?

A student compares the dissolution of the hypothetical ionic solids \(\text{MZ(s)}\) and \(\text{NZ(s)}\) in water.

\[
\text{MZ(s)} \rightarrow \text{M}^{+}\text{(aq)}+\text{Z}^{-}\text{(aq)}
\]

\[
\text{NZ(s)} \rightarrow \text{N}^{+}\text{(aq)}+\text{Z}^{-}\text{(aq)}
\]

For \(1\text{ mol}\) of each solid, the lattice-separation enthalpies are equal, and the hydration contributions from \(\text{Z}^{-}\) are identical. In the diagram, the first-shell hydration radius is the distance from the center of a cation to the center of a surrounding water oxygen atom.

Based on the particulate diagram, which statement correctly compares the cation hydration enthalpies and the enthalpies of solution?

![A grayscale particulate diagram with a legend first: a small solid-gray disk represents \(\text{M}^{+}\), a larger solid-gray disk represents \(\text{N}^{+}\), and each bent water molecule consists of \(1\) open circle for \(\text{O}\) bonded to exactly \(2\) smaller solid-black circles for \(\text{H}\). Panel I contains exactly \(1\) \(\text{M}^{+}\) at the center and exactly \(6\) water molecules equally spaced around it; each \(\text{O}\) end points toward the cation, and the oxygen centers lie on a dashed circle. Panel II contains exactly \(1\) \(\text{N}^{+}\) at the center and exactly \(6\) identically sized, identically oriented water molecules on a larger dashed circle. Place the single relation \(r_M<r_N\) beneath the panels. Use no gridlines. No other particles, labels, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787301666-k6WToM.jpg)

- **A.** \(\Delta H_{\mathrm{hyd}}(\text{M}^{+})<\Delta H_{\mathrm{hyd}}(\text{N}^{+})\) and \(\Delta H_{\mathrm{soln}}(\text{MZ})<\Delta H_{\mathrm{soln}}(\text{NZ})\), because the shorter cation–oxygen distance for \(\text{M}^{+}\) produces stronger ion-dipole attractions and greater energy release during hydration.
- **B.** \(\Delta H_{\mathrm{hyd}}(\text{M}^{+})<\Delta H_{\mathrm{hyd}}(\text{N}^{+})\) and \(\Delta H_{\mathrm{soln}}(\text{MZ})<\Delta H_{\mathrm{soln}}(\text{NZ})\), because the smaller cation is more polarizable and therefore forms stronger London dispersion forces with water.
- **C.** \(\Delta H_{\mathrm{hyd}}(\text{M}^{+})<\Delta H_{\mathrm{hyd}}(\text{N}^{+})\), but \(\Delta H_{\mathrm{soln}}(\text{MZ})=\Delta H_{\mathrm{soln}}(\text{NZ})\), because the equal lattice-separation enthalpies cancel the difference between the hydration enthalpies.
- **D.** \(\Delta H_{\mathrm{hyd}}(\text{M}^{+})=\Delta H_{\mathrm{hyd}}(\text{N}^{+})\) and \(\Delta H_{\mathrm{soln}}(\text{MZ})=\Delta H_{\mathrm{soln}}(\text{NZ})\), because the cations have equal charges and equal numbers of water molecules in their first hydration shells.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120063/*