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In an exam paper it says that the lattice energy of NaCl is more exothermic than MgCl [sic] as the Na+ cation has a smaller ionic radius than Mg+. Here are the resources given:enter image description hereenter image description here

What is the reasoning for for Na+ having a smaller ionic radius even though Mg+ has a higher proton number?

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    $\begingroup$ Mg+ is not a thing at all. $\endgroup$ Oct 16, 2018 at 4:47
  • $\begingroup$ It was part of a CIE A - level chemistry exam $\endgroup$ Oct 16, 2018 at 5:14
  • $\begingroup$ I'd agree with Ivan. You must be making a mistake. It should be $\ce{Mg^{2+}}$ and $\ce{MgCl2}$. $\endgroup$
    – MaxW
    Oct 16, 2018 at 5:51
  • $\begingroup$ In the exam I think it was asked as hypothetical situation, so hypothetically how would you reason the ionic radius of Mg+? $\endgroup$ Oct 16, 2018 at 5:55
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    $\begingroup$ We wouldn't. It makes no sense. $\endgroup$ Oct 16, 2018 at 6:01

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We actually do mean $\ce{Mg^+}$ here. The idea is to show what factors are involved when an alkaline earth metal forms stable compounds with $\ce{M^{2+}}$ ions whereas an alkali metal favors $\ce{M^+}$. In this case, as pointed out in some of the comments, $\ce{Mg^+}$ is bulked up by the electron that remains in the relatively diffuse, loosely held $3s$ subshell. You need to remove that electron, making $\ce{Mg^{2+}}$, to get a compact ion that gives good lattice energies in ionic crystals.

Scandium monosulfide

Although $\ce{MgCl}$ and monatomic $\ce{Mg^+}$ are not real materials, the case of scandium monosulfude, $\ce{ScS}$ is instructive. A simple ionic model proposing $\ce{Sc^{2+}}$ and $\ce{S^{2-}}$ would require the scandium to retain a valence electron in an outer-shell orbital, apparently $3d$. In an early-group metal such orbitals are diffuse and, if occupied, would inhibit tight binding of the oppositely charged ions. Instead, according to Ref. [1] which identifies $\ce{ScS}$ as a metallic conductor, the extra electron per scandium atom is delocalized into a conduction band. This allows the sulfide ions to bind tightly with compact $\ce{Sc^{3+}}$. Thus scandium monosulfide is stable not as a conventional ionic salt, but as a compound that combines ionic and metallic characteristics.

Reference

Dismukes, J. P.; White, J. G. (1964). "The Preparation, Properties, and Crystal Structures of Some Scandium Sulfides in the Range Sc2S3-ScS". Inorg. Chem. 3 (9): 1220–1228. https://doi.org/10.1021/ic50019a004

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    $\begingroup$ Just out of interest Magnesium(I) compounds are known, but they are of the form [Mg-Mg]2+ rather than a bare Mg+ - so more like Mercury than Sodium. See pubs.rsc.org/en/content/articlelanding/2011/dt/… , and in a way this furthers the similarity between Mg and Zn. $\endgroup$
    – Ian Bush
    Oct 16, 2018 at 10:24
  • $\begingroup$ Not just magnesium. Wikipedia also documents similar dimers for other alkaline earth metals. Such dimers, of course, are easily oxidized to +2 monatomic ions. $\endgroup$ Oct 16, 2018 at 11:14

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