Final answer:
The pH of a solution saturated with Mn(OH)2 is approximately 7.15. To find the pH of a solution saturated with Mn(OH)2, we calculate the hydroxide ion concentration from the Ksp, determine the pOH, and then subtract it from 14 to get the pH.
Step-by-step explanation:
The solubility product constant (Ksp) for Mn(OH)2 is 2.0 x 10⁻¹³. To determine the pH of a solution saturated with Mn(OH)2, we need to consider the dissolution of Mn(OH)2 in water:
Mn(OH)2 (s) → Mn²+ (aq) + 2OH¯ (aq)
Since Mn(OH)2 is a sparingly soluble base, it will partially dissociate into Mn²+ and OH¯ ions. The concentration of OH¯ ions in a saturated solution can be calculated using the Ksp value:
Ksp = [Mn²+] [OH¯]²
Substituting the Ksp and solving for [OH¯], we find that [OH¯] = sqrt(Ksp/2), which gives us [OH¯] = sqrt(2.0 x 10⁻¹³/2) = 1.4 x 10⁻⁷ M.
To find the pH, we can use the fact that pH + pOH = 14. Taking the negative logarithm of [OH¯], we get pOH = -log10(1.4 x 10⁻⁷) ≈ 6.85. Subtracting pOH from 14, we find pH ≈ 7.15.
Since each mole of Mn(OH)2 produces two moles of OH-, we can set up the expression for Ksp as (Ksp) = [Mn2+][OH-]2 = (s)(2s)2 = 4s3, where s is the solubility of Mn(OH)2. Solving for s, we find the concentration of OH- ions. The pOH can then be calculated using the formula pOH = -log[OH-], and pH is found by subtracting the pOH from 14 (pH = 14 - pOH). This gives us the pH of the saturated Mn(OH)2 solution.