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Let's say I was dissolving $\pu{1 M}~\ce{MgSO4}$ into water and I wanted to find its $\mathrm{pH}$. I would go right to the reaction of the dissociation of $\ce{Mg(OH)2}$:

$$\ce{Mg(OH)2 <=> Mg^2+ + 2OH-}$$

The $K_\mathrm{sp}$ expression for this reaction is:

$$K_\mathrm{sp}=[\ce{Mg^2+}][\ce{OH-}]^2$$

According to wikipedia (see sources at bottom), the $K_\mathrm{sp}$ for $\ce{Mg(OH)2}$ is $\pu{5.61*10^{-12}}$

$$\pu{5.61*10^{-12}}=[\ce{Mg^2+}][\ce{OH-}]^2$$

My molarity of $\ce{MgSO4}$ will be the same as that of $\ce{Mg^2+}$, which is $\pu{1 M}$. Substitute that in.

$$\pu{5.61*10^{-12}}=[\ce{OH-}]^2$$

And then solving for $[\ce{OH-}]$ we get:

$$[\ce{OH-}]=\pu{2.37*10^{-6} M}$$

Therefore:

$$\mathrm{pOH}=5.63$$ and $$\mathrm{pH}=8.37$$

So my final solution of $\ce{MgSO4}$ will be basic. However, on stack exchange it says that the $\mathrm{pH}$ of $\ce{MgSO4}$ is between 5.5 and 6.5. The post does not explain why, but that the general consensus is that that is the range of the $\mathrm{pH}$.

What did I do wrong?

Sources: https://en.wikipedia.org/wiki/Magnesium_hydroxide

Is magnesium sulfate basic, neutral or acidic?

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    $\begingroup$ Simplified calculations which result in pH values between 6-8 (usually from extremely dilute acid/base solutions or by addtion of very weak acid/bases to water) are generally incorrect because they fail to take into consideration the autodissociation of water. Pure water starts at pH 7, and any hydroxide ions consumed by $\ce{Mg^2+}$ must cause the pH to fall below 7, as you would expect from adding an acid. Multiple previous answers here at Chem.SE touch on this point, for example here. You will have to find a slightly different equation. $\endgroup$ – Nicolau Saker Neto Jan 5 '18 at 5:08
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    $\begingroup$ Using the Ksp of $\ce{Mg(OH)_2}$ would give you the maximum concentration of $\ce{OH-}$ for a solution of a given amount of $\ce{Mg^2+}$ - it won't necessarily give you the actual concentration. (It's perfectly happy with solubility products below the Ksp value.) -- If you're getting a pH above 7.0, you have to ask yourself where the "extra" $\ce{OH-}$ is coming from. It's from water, obviously, but what's driving the "extra" splitting of the $\ce{H2O}$, and - critically - what's happening to the $\ce{H+}$ that's being generated by the auto-dissociation of water to form the extra $\ce{OH-}$? $\endgroup$ – R.M. Jan 5 '18 at 19:32
  • $\begingroup$ There is an answer here for this question. The pH is depend on the concentration of $\ce{Mg^2+}$, thus why the range of pH is given. $\endgroup$ – Mathew Mahindaratne Sep 19 '20 at 22:28
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Another aspect to be taken into account is the difference between measured solubility and solubility as calculated from the solubility product. Salts like $\ce{MgSO_4}$ are always much more soluble than what can be calculated from the solubility product. I don't have the numerical values for $\ce{MgSO_4}$, but I know the corresponding values for $\ce{CaSO_4}$, which is its neighbor in the periodic table. Calculated from $\ce{K_{sp}}$, the solubility is $4.7$ mM. The measured value, obtained by titration, is $18$ mM, as stated in J. Chem. Educ. $77, 12$, Dec. $2000$, p.$1558$

This discrepancy is due to hydrolysis. An important part of the $\ce{Ca^{2+}}$ ions react with water to produce ions like $\ce{[Ca(OH)]^{+}}$ according to the equation $$\ce{Ca^{2+} + H_2O -> [Ca(OH)]^+ + H^+}$$ $\ce{Mg^{2+}}$ should react the same way.$$\ce{Mg^{2+} + H_2O -> [Mg(OH)]^+ + H^+}$$ Simultaneously, an important part of the sulfate ions are reacting according to the following equation $$\ce{SO_4^{2-} + H_2O -> HSO_4^- + OH^-}$$ And there is also the possibility that some $\ce{CaSO_4}$ ou $\ce{MgSO_4}$ gets dissolved without being dissociated. The relative extent of these two last reactions is the reason why $\ce{MgSO_4}$ gives non neutral solutions in water.

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Your answer lies not in the solubility product but in the acidity constants of sulfuric acid and the basicity constants of $\ce{Mg(OH)2}$, though the solubility product may well come into play. You would need to solve a system of 6 equations, one for each of the:

  • 2 $\mathrm{p}K_\mathrm{a}$ values for the acid
  • Two $\mathrm{p}K_\mathrm{b}$ values for the base
  • Proton condition or charge neutrality
  • And as you will be groping in $\mathrm{pH}$, one to be sure you don't exceed the solubility product.

As sulfuric acid is 'stronger' as an acid than $\ce{Mg(OH)2}$ is as a base, you would expect the answer to be slightly on the "acid side" of neutral $\mathrm{pH}$.

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    $\begingroup$ Magnesium salts do, however, form less acidic solutions than those of most other metals. It's an example of magnesium hydroxide being in a "gray zone" (like phosphoric acid among acids) between "strong" and "weak". $\endgroup$ – Oscar Lanzi Jan 28 '18 at 20:07

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