When excess solid Mg(OH)2 is shaken with 1.00 L of 1.2 M NH4Cl solution, the resulting saturated solution has pH = 9.30. Calculate the Ksp of Mg(OH)2
To calculate the solubility product constant, Ksp, of Mg(OH)2, we need to use the information given in the question. The pH of the resulting saturated solution can provide us with the concentration of hydroxide ions, which is key to determining the Ksp.
Here's how you can calculate the Ksp of Mg(OH)2:
Step 1: Write the balanced equation for the dissociation of Mg(OH)2.
Mg(OH)2(s) ⇌ Mg2+(aq) + 2OH-(aq)
Step 2: Use the concentration of hydroxide ions to calculate the concentration of Mg2+ ions.
Since Mg(OH)2 dissociates into one mole of Mg2+ and two moles of OH-, we can say that [Mg2+] = x and [OH-] = 2x in the saturated solution.
Step 3: Use the concentration of NH4Cl to find the initial concentration of NH4+ ions.
The NH4Cl solution is 1.2 M, so the initial concentration of NH4+ is 1.2 M.
Step 4: Use the pH to find the concentration of hydroxide ions [OH-].
The pH of the solution is 9.30, which means the [H3O+] concentration is 10^(-pH). Therefore, [OH-] = 1.0 x 10^(-5.3) because in a neutral solution, [H3O+] = [OH-] = 1.0 x 10^(-7).
Step 5: Use the concentration of hydroxide ions [OH-] to calculate the concentration of magnesium ions [Mg2+].
Since [OH-] = 2x, we can substitute this value into the equation to get [Mg2+] = x = 2 x 10^(-6.3).
Step 6: Use the concentrations of Mg2+ and OH- to calculate the Ksp of Mg(OH)2.
Ksp = [Mg2+][OH-]^2 = (2 x 10^(-6.3))(1.0 x 10^(-5.3))^2
Step 7: Calculate the Ksp.
Ksp = (2 x 10^(-6.3))(1.0 x 10^(-5.3))^2 ≈ 5.01 x 10^(-16)
Therefore, the Ksp of Mg(OH)2 is approximately 5.01 x 10^(-16).