Calculate the solubility of Mn(OH)2 in grams per liter when buffered at each of the following.

(a) pH 7.7

(b) pH 9.6

(c) pH 11.3

Ksp = (Mn^2+)(OH^-)^2

Convert pH 7.7 to OH^-, then substitute into Ksp expression and solve for Mn^2+

To calculate the solubility of Mn(OH)2 in grams per liter at different pH values, we need to consider the solubility product constant (Ksp) of Mn(OH)2 and the pH equilibrium for Mn(OH)2.

The balanced equation for the dissociation of Mn(OH)2 is:
Mn(OH)2 ⇌ Mn2+ + 2OH-

The solubility product constant expression for Mn(OH)2 is:
Ksp = [Mn2+][OH-]^2

To calculate the solubility of Mn(OH)2, we need to determine the concentrations of Mn2+ and OH- ions.

(a) pH 7.7:
At pH 7.7, we assume that the solution is buffered, which means we have equal concentrations of OH- and H+ ions. Therefore, we can consider the OH- concentration as the concentration of hydroxide ions in the solution.

To calculate the OH- concentration, we can use the formula for pH:
pOH = 14 - pH

Given the pH of 7.7, the pOH would be:
pOH = 14 - 7.7 = 6.3

To convert the pOH to the OH- concentration, we can use the formula:
[OH-] = 10^(-pOH)

[OH-] = 10^(-6.3) = 5.01 x 10^(-7) M

Now, to calculate the solubility of Mn(OH)2, we can use the Ksp expression:
Ksp = [Mn2+][OH-]^2

Since the balanced equation shows that the stoichiometric ratio between Mn2+ and OH- ions is 1:2, the concentration of Mn2+ would be half of the OH- concentration:
[Mn2+] = 0.5 * [OH-]
[Mn2+] = 0.5 * 5.01 x 10^(-7)
[Mn2+] = 2.505 x 10^(-7) M

Finally, to calculate the solubility of Mn(OH)2 in grams per liter, we need to convert the concentration to grams per liter. The molar mass of Mn(OH)2 is 118.87 g/mol.
Using the equation:
Solubility (g/L) = [Mn(OH)2] (mol/L) * Molar Mass (g/mol)

Solubility = 2.505 x 10^(-7) * 118.87
Solubility ≈ 2.98 x 10^(-5) g/L

Therefore, at pH 7.7, the solubility of Mn(OH)2 is approximately 2.98 x 10^(-5) grams per liter.

You can repeat the same steps for parts (b) and (c), considering the respective pH values and following the calculations described above.