Calculate the Ksp of a saturated solution of Mg(OH)2 upon titration with 0.0100 HCl in the presence of phenolphthalein indicator utilizing the data below.

mL saturated Mg(OH)2 titrated - 1382
mL of 0.0100 M HCl to endpoint - 38.7

Please help me and show how you solve this.

Let's work in millimoles. mols = L x M and millimols = mL x M

millimols HCl used = mL x M = 38.7 x 0.01 = 0.387
So millimoles OH = 0.387
(OH^-) in molarity = millimoles/mL = 0.387/1382 = ?approx 3E-4 but that's an estimate.
......................Mg(OH)2 ==> Mg^2+ + 2OH^-
.......................solid..............(3E-4)/2....3E-4

Plug the concns of Mg and OH into the Ksp expression and solve for Ksp.
Post your work if you get stuck.

To calculate the Ksp of Mg(OH)2, we need to first determine the moles of HCl that reacted with Mg(OH)2. Then, we can use stoichiometry to find the moles of Mg(OH)2 that dissolved in the solution.

1. Calculate the moles of HCl titrated:
moles HCl = concentration of HCl × volume of HCl
moles HCl = 0.0100 M × 38.7 mL = 0.0100 mol

2. Use the balanced chemical equation to find the moles of Mg(OH)2:
Mg(OH)2 + 2HCl -> MgCl2 + 2H2O
From the equation, we see that the ratio of Mg(OH)2 to HCl is 1:2.
Therefore, moles of Mg(OH)2 = 0.0100 mol/2 = 0.00500 mol

3. Convert the volume of saturated Mg(OH)2 solution to liters:
volume of saturated Mg(OH)2 = 1382 mL = 1382 × 10^-3 L = 1.382 L

4. Calculate the concentration of Mg(OH)2 in the saturated solution:
concentration of Mg(OH)2 = moles of Mg(OH)2 / volume of saturated solution
concentration of Mg(OH)2 = 0.00500 mol / 1.382 L = 0.00362 M

5. Use the concentration of Mg(OH)2 to calculate the Ksp:
Ksp = [Mg2+][OH^-]^2
In a saturated solution of Mg(OH)2, the concentration of Mg2+ and OH^- are the same.
Therefore, Ksp = [Mg2+][OH^-]^2 = (0.00362 M)(0.00362 M)^2 = 4.95 × 10^-8

So, the Ksp of a saturated solution of Mg(OH)2 is 4.95 × 10^-8.

To calculate the Ksp of a saturated solution of Mg(OH)2, you need to determine the concentration of OH- ions at equilibrium. This can be done by using the volume of HCl required to reach the endpoint of the titration in the presence of phenolphthalein indicator.

Let's break down the steps to solve this problem:

Step 1: Find the moles of HCl used in the titration.
To do this, multiply the volume of HCl used (38.7 mL) by its molarity (0.0100 M) to get the moles of HCl used.

moles of HCl = volume of HCl (L) × molarity of HCl (mol/L)
= 0.0387 L × 0.0100 mol/L
= 0.000387 mol

Step 2: Determine the moles of OH- ions reacted.
Since HCl is a strong acid, it reacts completely with OH- ions in a 1:1 ratio. Therefore, the moles of OH- ions reacted are equal to the moles of HCl used.

moles of OH- = moles of HCl
= 0.000387 mol

Step 3: Calculate the concentration of OH- ions in the saturated solution.
To find the volume of the saturated solution, subtract the volume of HCl used from the volume of Mg(OH)2 titrated.

volume of saturated solution = volume of Mg(OH)2 titrated - volume of HCl used
= 1382 mL - 38.7 mL
= 1343.3 mL

Convert the volume to liters:

volume of saturated solution = 1343.3 mL × (1 L/1000 mL)
= 1.3433 L

Now, divide the moles of OH- ions by the volume of the saturated solution to obtain its concentration:

concentration of OH- = moles of OH- / volume of saturated solution
= 0.000387 mol / 1.3433 L
= 2.88 × 10^-4 M

Step 4: Calculate the Ksp.
The Ksp expression for Mg(OH)2 is: Ksp = [Mg2+][OH-]^2.

Since Mg(OH)2 is a strong electrolyte, it ionizes completely to 1 mol of Mg2+ and 2 moles of OH- ions:

[Mg2+] = 1 × [OH-]^2

Substitute the calculated concentration of OH- ions into the expression:

Ksp = [Mg2+] × [OH-]^2
= 1 × (2.88 × 10^-4 M)^2
= 8.2944 × 10^-8

Therefore, the Ksp of a saturated solution of Mg(OH)2 is 8.2944 × 10^-8.