When salts dissolve in water, the anions, cations, and strongly polar water molecules undergo hydration reactions, resulting in the formation of hydrated ions with a specific number of coordinated water molecules.
For example, from Ref 1:

Table S2. Diameter of hydrated ions.

Ions Hydrated diameters/nm
$\ce{K+}$ 0.66
$\ce{Cl-}$ 0.66
$\ce{Na+}$ 0.72
$\ce{Ca^{2+}}$ 0.82
$\ce{Mg^{2+}}$ 0.86
$\ce{Al^{3+}}$ 0.95
$\ce{SO4^{2-}}$ 1.00

BTW, please post the research paper that the data comes from.


  1. Yixin Yang, Guorong Li, Dan Ouyang, Zongwei Cai, Zian Lin, Dual-activation interfacial polymerization based anionic covalent organic framework nanofiltration membrane for high-flux dye separation, Chemical Engineering Journal, Volume 456, 2023, 141008, ISSN 1385-8947, https://doi.org/10.1016/j.cej.2022.141008.

2 Answers 2


The data you share (source of the table?) are poor; neither is there a reference what the author considers as hydrated cation -- because different coordination geometries require different volume, nor the method to determine the these dimensions.

In PAC, Persson for example compiles the following data (in Angstrom) from the literature about the distance between center/metal cation $\ce{M}$ and oxygen $\ce{O}$ of the water ligand:

aqua complex $\ce{M-O}$ distance $\ce{M^{n+}}$' ions radius/A Shannon Configuration
$\ce{Li(H2O)^+_4}$ 1.95 0.61 0.59 Tetrahedron
$\ce{Li(H2O)^+_6}$ 2.10 0.76 0.76 Octahedron
$\ce{Na(H2O)^+_6}$ 2.43 1.09 1.02 Octahedron
$\ce{K(H2O)^+_8}$ 2.48* 1.50* 1.51 Square antiprism
$\ce{Mg(H2O)^{2+}_6}$ 2.10 0.76 0.72 Octahedron
$\ce{Ca(H2O)^{2+}_8}$ 2.46 1.12 1.12 Square antiprism
$\ce{Al(H2O)^{3+}_6}$ 1.89 0.55 0.535 Octahedron

(Persson2010, distances marked by an asterisk were determined in the solid state)

Recording the position of protons can be difficult (because the time scale of the proton exchanges vs the one of the analytic technique, very low diffraction power vs X-ray diffraction, etc.).

In a separate publication, Mähler and Perrson derive from Large Angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR)

It was found that the average Li−O distance in $\ce{Li(H2O)^+_4}$ was $\pu{1.942 Å}$ for 36 observed structures,and this number did not change noticeably if other neutral homo- or heteroleptic monodentate oxygen donor non-ether complexes were allowed. The Li−O distance of $\ce{Li(H2O)^+_6}$ is $\pu{2.134 Å}$ as an average for 10 observed structures.

X-ray diffraction indeed is one, but not the sole technique to determine the ions' dimension. As pointed out in a comment by @poutnik, ion mobility can complement the insight. Hayamizu et al. for instance monitored the diffusion of $\ce{Li(H2O)^+_x}$ by solution NMR spectroscopy, and determine an effective Stokes radius of $\ce{Li+}$ in diluted aqueous solutions of about $\pu{300 pm}$ ($ = \pu{3 Å}$).

enter image description here

The authors visualize the effective (Stokes) radii of a few ions with the following figure:

enter image description here

(Hayamizu et al.)

Persson, I. Hydrated Metal Ions in Aqueous Solution: How Regular Are Their Structures? Pure Appl. Chem. 2010, 82, 1901–1917. https://doi.org/10.1351/PAC-CON-09-10-22 (open access).

Mähler, J.; Persson, I. A Study of the Hydration of the Alkali Metal Ions in Aqueous Solution. Inorg. Chem. 2012, 51, 425–438. https://doi.org/10.1021/ic2018693 (open access).

Hayamizu, K.; Chiba, Y.; Haishi, T. Dynamic Ionic Radius of Alkali Metal Ions in Aqueous Solution: A Pulsed-Field Gradient NMR Study. RSC Adv. 2021, 11, 20252–20257. https://doi.org/10.1039/D1RA02301B (open access).

You might miss valuable literature references if you skip a keyword like ionic radii e.g.,

Marcus, Y. Ionic Radii in Aqueous Solutions. Chem. Rev. 1988, 88, 1475–1498. https://doi.org/10.1021/cr00090a003.

Conway, B. E.; Ayranci, E. Effective Ionic Radii and Hydration Volumes for Evaluation of Solution Properties and Ionic Adsorption. J. Solution Chem. 1999, 28, 163–192. https://doi.org/10.1023/A:1021702230117.


The Hydrated Radius of Lithium ion is 76pm. Thus the Hydrated Diameter should be 152pm (I think so).

I got this table from toppr.com

  • 4
    $\begingroup$ Your answer doesn't state the origin of the data. $\endgroup$
    – Buttonwood
    Feb 5 at 10:50

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