Ca has an atomic radius of $197\mathrm{~pm}$ and a Pauling electronegativity of $1.00$.

Mg has an atomic radius of $197\mathrm{~pm}$ and a Pauling electronegativity of $1.31$.

Since Mg is smaller and has a higher electronegativity, one would think Mg would have a smaller hydrated radius than Ca, but it doesn't. Would someone explain to me why this isn't so? I have read an explanation pertaining to charge density, but I'm not understanding why Ca would have a larger charge density if it is bigger with less electronegativity.

The goal of understanding this is to understand why the addition of Ca to soil will make it drain better and be looser, less sticky, etc. And conversely, why highly respected agricultural consultants say soils high in Mg (low in Ca) are "sticky". Any help in understanding this would be well appreciated.


Charge density is a measure of electrical charge per volume. It is independent from electronegativity, and increases with the number of charges of an ion and with decreasing radius, because a smaller ion has also a smaller volume. The number of charges for $\ce{Ca^{2+}}$ and $\ce{Mg^{2+}}$ is the same (+2), but $\ce{Mg^{2+}}$ has the smaller atomic radius. Its charge is therefore distributed over a smaller volume, and the charge density is higher.

The hydrated radius of an ion can somewhat differ from its atomic radius, because it is influenced by the charge density. If the ion charge is concentrated in a smaller volume, it exerts stronger attractive forces on the dipoles of water molecules, which results in the formation of a larger hydration shell. The smaller $\ce{Mg^{2+}}$ attracts more water dipoles and forms a larger hydration shell. Hence, its hydrated radius can be bigger than that of $\ce{Ca^{2+}}$, which has a larger atomic radius but a smaller hydrate shell.


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