How can magnesium hydroxide be a strong base and be sparingly soluble at the same time?

Question

A strong base means it completely dissociates forming $\ce{OH^-}$ ions when added to aqueous solution. Sparingly soluble means it dissolves very little when added to aqueous solution.

Yet magnesium hydroxide is said to be both. These two properties seem to contradict each other. How can this be?

A very similar question was asked (What does it mean to say that a strong base is only slightly soluble?), the most relevant answer states that

Some strong bases like calcium hydroxide aren't very soluble in water. That doesn't matter - what does dissolve is still 100% ionised into calcium ions and hydroxide ions. Calcium hydroxide still counts as a strong base because of that 100% ionisation.

But I don't understand the difference — how can something dissolve and not be ionised? (wouldn't that imply a covalent structure like glucose?)

Answer 1

I think we should not conflate "solubility" with "dissociation". They are different phenomena. The former has to do with a molecule breaking away from the other solute molecules and forming interactions with the solvent. The latter is a process which occurs after dissolution, whereby the solute molecules break apart to form ions, separately solvated by the solvent molecules. For a simple covalent substance, the two phemomena are clearly different.

For an ionic solid, the two may seem to occur together since when a soluble ionic salt is placed in water, its ions are in fact pulled apart by water molecules. In this sense, it is dissolving and dissociating at the same time. Hence, by the Arrhenius definition of acids and bases, insoluble hydroxides such as $\ce {Mg(OH)_2}$ may not even be considered to be strong bases. Arrhenius theory would tell us that the strong base is the hydroxide ion, that is produced from the dissolultion and dissociation of the salt.

Actually, in particular for some metal oxides such as $\ce {MgO}$, the first reaction it undergoes upon contact with water is $\ce {MgO + H2O -> Mg(OH)2}$. Hence, we can rightfully say $\ce {MgO}$ is not an Arrhenius base, but it is the precursor to the weak Arrhenius base $\ce {Mg(OH)2}$.

I would like to disagree with the part of the answer you have referenced in your post because as aforementioned, dissolution and dissociation are the same phenomena for ionic salts. It is thus not correct to say that "what does dissolve is still $\ce {100}$% ionised into [ions]" and hence, say that insoluble (or sparingly soluble) ionic salts are strong bases.

To generalise, Arrhenius theory would consider soluble ionic hydroxides such as $\ce {NaOH (s)}$ to be strong bases while it would consider sparingly soluble ionic hydroxides such as $\ce {Ca(OH)2}$ to be weak bases. In other words, the strength of these metal hydroxides as bases is directly linked to their solubility and this makes perfect sense since dissolution and dissociation for an ionic salt are the same process.

Answer 2

Whether magnesium hydroxide is a strong or weak base is a matter of disagreement. Usually it is considered a weak base because of its low solubility.

Whether it's a strong or weak base in terms of dissociation is not completely known. IUPAC reports a single $\mathrm{p}K_\mathrm{b}$ value, generally between 2 and 3, based on hydrolysis measurements. But because the hydrolysis is dominated by the reaction

$$\ce{Mg^{2+} + H2O <=> H^+(aq) + MgOH^+},$$

this says that only the second dissociation constant is (slightly) weak.

The first dissociation constant could be stronger, but magnesium hydroxide has very little solubility in solutions that would be sufficiently alkaline (probably $\mathrm{pH} > 12)$ to equilibrate the first dissociation of the hydroxide. Both dissociation constants are known for calcium hydroxide and heavier alkaline earth hydroxides where their binary aqueous solutions provide sufficiently alkaline $\mathrm{pH}.$

Magnesium hydroxide is, however, much stronger and more soluble than most transition metal hydroxides. This answer describes how magnesium hydroxide with its superior solubility displaces iron almost quantitatively from aqueous solution, yet an excess does not dissolve into the water.

This self-regulating property makes magnesium hydroxide (or the oxide which becomes the hydroxide in situ) and the similarly behaving calcium hydroxide especially suitable for water and soil treatment applications. A fully strong base would risk making a caustic solution.

Answer 3

Let's look at it in reverse. Were magnesium hydroxide a weak base, solutions of magnesium ion in water would hydrolyze in water removing hydroxide ions and making solutions of magnesium salts such as Epsom salts [magnesium sulfate], or magnesium chloride acidic. Quick anecdotal search says these salts give neutral solutions in water; this indicates that magnesium hydroxide is a strong base. If someone is truly interested some actual research in the literature or in the lab with some salts, DI water, a GOOD pH meter and good technique can answer this without all the hand waving.