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Ksp: Metal Hydroxides

Skills to develop

• Estimate the pH of the solution due to precipitate of a metal hydroxide.
• Calculate the maximum metal ion concentration when the pH is known.
• Explain behavior of amphoteric metal hydroxides

Ksp: Metal Hydroxides

Most metal hydroxides are insoluble, some such as Ca(OH)2, Mg(OH)2, Fe(OH)2, Al(OH)3 etc are sparingly soluble. However, alkali metal hydroxides CsOH, KOH, and NaOH are very soluble, making them strong bases. When dissolved, these hydroxides are completely ionized. Since the hydroxide concentration, [OH-], is an integrated property of the solution, the solubility of metal hydroxide depends on pH, pOH or [OH-].

Alkali metal hydroxides LiOH, NaOH, KOH, CsOH are soluble, and their solutions are basic. Hydroxides of alkali earth metals are much less soluble. For example, quicklime (CaO) reacts with water to give slaked lime, which is slightly soluble.

```  CaO     +  H2O = Ca(OH)2
quicklime        slaked lime (slightly soluble)
```
Milk of magnesia is Mg(OH)2 (Ksp = 7e-12) suspension. In an acidic solution such as the stomach juice, the following reaction takes place, Mg(OH)2 + H+ = Mg2+ + 2 H2O

Thus, it can neutralize excess acid in the stomach.

Example 1

Calculate the maximum concentration of Mg2+ in a solution which contains a buffer so that pH = 3 at 298 K.

Solution

As usual, we write the equilibrium equation so that we can write the concentration below the formula. If we do not know the concentration, we assume it to be a variable x.
``` Mg(OH)2  =  Mg2+  +  2 OH-
x         1e-11
```
Ksp = x (1e-11)2 = 7e-12 Solving for x results in x = 7e10

Discussion
This value certainly is too large, unrealistic.

Example 2

Calculate the pH of a saturated Mg(OH)2 solution.

Solution

We assume the concentration to be x M of Mg(OH), and note that [OH- = 2 x,

Mg(OH)2 = Mg2+ + 2 OH-
x       2 x
Ksp = x (2 x)2 = 7e-12
Solving for x; x = 1.2e-4
[OH] = 2.4e-4
pOH = 3.62
pH = 14 - 3.62 = 10.38

Discussion
The pH of a saturated lime, Ca(OH)2, solution is about 10.0.

Amphoteric Hydroxides

Not all metal hydroxides behave the same way - that is precipitate as hydroxide solids. Metal hydroxides such as Fe(OH)3 and Al(OH)3 react with acids and bases, and they are called amphoteric hydroxide. In reality, Al(OH)3 should be formulated as Al(H2O)3(OH)3, and this neutral substance has a very low solubility. It reacts in the following way as [H+] increases. Al(H2O)3(OH)3 + H3O+ = Al(H2O)4(OH)2+ + HOH
Al(H2O)4(OH)2+ + H3O+ = Al(H2O)5(OH)2+ + H2O
Al(H2O)5(OH)2+ + H3O+ = Al(H2O)63+ + H2O

When the pH increases, the following reactions take place

Al(H2O)3(OH)3 + OH- = Al(H2O)2(OH)4- + H2O
Al(H2O)2(OH)4- + OH- = Al(H2O)(OH)52- + H2O
Al(H2O)(OH)52- + OH- = Al(OH)63- + H2O

The charged species are soluble in water. As a result, amphoteric hydroxides dissolve in acidic and basic solutions.

Confidence Building Questions

• Assume the pH of gastric juice to be 2. Calculate the maximum [Mg2+].

Consider...

We assume the temperature to be 298 K, which is too low.
[Mg2+] = 7e-12 / (1e-12)2 = ?
This value is unrealistically large. The result is correct, but meaningless.

• Calculate the pH of a 0.10 M NH3 solution.

Consider...

[OH-] = (0.10*1.8e-5)1/2 = 1.34e-3
[H+] = 1e-14 / 1.34e-3 = 7.5e-12, pH = ?
This value is required for the calculation in next question. Better yet, remember that [OH-] = 1.34e-4.

• Calculate the maximum [Fe2+] in a 0.10 M NH3 solution. Give the value in M