INFORMATION:

[HCl] = 0.1388 M
We placed 0.5 g Ca(OH)2 in 100 mL of the following solutions:
Flask A: Distilled Water (7.4 mL of HCl needed to titrate)
Flask B: 0.05 NaOH (12.1 mL of HCl needed to titrate)
Flask C: 0.025 NaOH (10.8 mL of HCl needed to titrate)
Flask D: 0.0125 NaOH (8.9 mL of HCl needed to titrate)
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QUESTION is to calculate the following for each flask:

[OH-]eq from titration
[OH-]0 from original solution
[OH-] from Ca(OH2)
[Ca2+]eq from Ca(OH)2
Ksp = [Ca2+]eq * [OH-]eq

Please teach me how to get answers for one of the flasks, then I could finish the rest :)

You don't have units on the NaOH. 0.05 what? 0.025 what? 0.0125 what? And that may not be all the what? If those are M then what are the volumes? If they are grams that's ok.

Of course! Let's go step by step to get the answers for Flask A.

Step 1: Calculate the moles of HCl used for titration.
To do this, we will first convert the volume of HCl used in titration from milliliters to liters:
Volume of HCl used = 7.4 mL = 7.4 * 10^(-3) L
Since the concentration of HCl is given as 0.1388 M, we can use the formula:
moles of HCl = concentration of HCl * volume of HCl used
moles of HCl = 0.1388 M * 7.4 * 10^(-3) L

Step 2: Convert the moles of HCl used to moles of OH-.
In the neutralization reaction between HCl and Ca(OH)2, 1 mole of HCl reacts with 2 moles of OH-. Therefore, the moles of OH- present in the solution is twice the moles of HCl used in titration.
moles of OH- = 2 * moles of HCl

Step 3: Calculate the concentration of OH- in the equilibrium solution.
The equilibrium concentration of OH- can be found by dividing the moles of OH- by the volume of the solution in liters.
[OH-]eq = moles of OH- / volume of solution

Step 4: Calculate the initial concentration of OH- in the original solution.
The original solution is created by dissolving 0.5 g of Ca(OH)2 in 100 mL of the solution. We need to calculate the moles of Ca(OH)2 and then convert it to moles of OH-.
First, we convert grams of Ca(OH)2 to moles:
moles of Ca(OH)2 = mass of Ca(OH)2 / molar mass of Ca(OH)2
molar mass of Ca(OH)2 = (40.08 g/mol) + 2 * (1.01 g/mol) + 2 * (16.00 g/mol)
Next, we calculate the moles of OH-:
moles of OH- from Ca(OH)2 = 2 * moles of Ca(OH)2
Finally, we find the concentration of OH-:
[OH-]0 = moles of OH- from Ca(OH)2 / volume of solution

Step 5: Calculate the concentration of Ca2+ in the equilibrium solution.
Since Ca(OH)2 completely dissociates in water, the concentration of Ca2+ in solution will be the same as the concentration of OH-.
[Ca2+]eq = [OH-]eq

Step 6: Calculate the Ksp value.
Ksp = [Ca2+]eq * [OH-]eq

Now, you can follow these steps for Flask A and then apply the same process for the remaining flasks (B, C, and D) to find the respective values for each flask.