Common Ion
At some other temperature, a solid sample of Ca(OH)2 is shaken with 0.0100 M CaCl2.
Once equilibrated, some solid Ca(OH)2 remains undissolved.
The solution is filtered and a 10.00 mL sample requires 12.96 mL of 0.0150 M HCl to neutralize it.
1. Calculate the value for Ksp of Ca(OH)2 from this data.
2.What is the molarity of Ca(OH)2 which is dissolved in this solution?
3.What is the solubility of Ca(OH)2 in this solution, in g/100mL?
You have two equilibria occurring in the solution.
Ca(OH)2 --> Ca^2+ + 2OH^- and
CaCl2 ==> Ca^2+ + 2Cl^-
The first one is limited solubility. The second one is 100% ionized. So
...................Ca(OH)2 ==Ca^2+ + 2OH^-
I......................solid............0...........0
C......................-x................x...........2x
E......................solid.............x..........2x where
Ksp for Ca(OH)2 = (Ca^2+)(OH^-)^2. For the CaCl2, we have
.................CaCl2 ==> Ca^2+ + 2Cl^-
I.............0.0100M...........0.............0
C...........-0.0100..........0.0100.....0.0200
E................0.0...........0.0100......0.0200
Therefore, Ksp for Ca(OH)2 = (Ca^2+)(OH^-)^2
You know (Ca^2+) = 0.0100 from CaCl2 and x from CaCl2 to make 0.0100 + x so Ksp = (0.0100 + x)(2x)^2. The titration with HCl determines the (OH-)
HCl + OH^- ==> H2O + Cl^-
mols HCl used = M x L = 0.1500 M x 0.01296 L = 0.001944 moles for a 10.00 mL sample. (OH^-) in mols/L = 0.001944 x (1000 mL/10.00 mL) = 0.1944 M = 2x
Plug that in for Ksp expression and solve for Ksp. This is answer to 1.
You shouldn't have any trouble with question 2 and 3.
1. Well, well, looks like we have some chemistry going on here. To determine the value of Ksp for Ca(OH)2, we need to use the neutralization data. The reaction between Ca(OH)2 and HCl is:
Ca(OH)2 + 2HCl → CaCl2 + 2H2O
Since 12.96 mL of 0.0150 M HCl is required to neutralize a 10.00 mL sample of the solution, we can use the stoichiometry of the reaction to find the moles of Ca(OH)2 in the original 10.00 mL sample.
Moles of HCl = Molarity × Volume (L)
Moles of Ca(OH)2 = 0.5 × Moles of HCl (from the balanced equation)
2. To find the molarity of Ca(OH)2 dissolved in the solution, we divide the moles of Ca(OH)2 by the final volume of the solution (10.00 mL).
Molarity of Ca(OH)2 = Moles of Ca(OH)2 / Volume (L)
3. The solubility of Ca(OH)2 in the solution can be calculated by converting the molarity to grams of Ca(OH)2 per 100 mL of solution.
Solubility of Ca(OH)2 = Molarity of Ca(OH)2 × Molar Mass of Ca(OH)2 × 100 / Volume (mL)
Now, I know these calculations might not be as funny as my jokes, but hey, it's chemistry!
To calculate the value for Ksp of Ca(OH)2 and solve the other related questions, we'll need to follow a series of steps. Let's break it down:
Step 1: Write the balanced equation for the reaction.
Ca(OH)2 (s) ↔ Ca2+ (aq) + 2OH- (aq)
Step 2: Calculate the concentration of Ca2+ ions.
From the given information, we know that the volume of CaCl2 is not enough to completely dissolve the Ca(OH)2. Therefore, after reaching equilibrium, the concentration of Ca2+ can be assumed to be equal to the concentration of CaCl2.
Concentration of Ca2+ (C1) = 0.0100 M
Step 3: Calculate the number of moles of Ca2+ in the 10.00 mL solution.
Number of moles of Ca2+ (n1) = Concentration (C1) × Volume (V1)
= 0.0100 M × 0.01000 L
= 0.000100 mol
Step 4: Calculate the number of moles of OH- ions in the 10.00 mL solution.
Since the stoichiometric coefficient of OH- ions in the balanced equation is 2, the number of moles of OH- ions (n2) will be twice that of moles of Ca2+.
Number of moles of OH- (n2) = 2 × Number of moles of Ca2+ (n1)
= 2 × 0.000100 mol
= 0.000200 mol
Step 5: Calculate the number of moles of OH- ions per liter (mol/L) in the solution.
Number of moles of OH- ions per liter (Molarity of OH-) = Number of moles of OH- (n2) / Volume of solution (V2)
= 0.000200 mol / (10.00 mL / 1000)
= 0.00200 mol/L
Step 6: Calculate the concentration of OH- ions (C2) in the solution.
Concentration of OH- ions (C2) = 0.00200 mol/L
Step 7: Calculate the concentration of H+ ions (C3) in the solution.
From the given information, we know that 12.96 mL of 0.0150 M HCl is needed to neutralize 10.00 mL of the solution.
According to the balanced equation for acid-base neutralization:
H+ (aq) + OH- (aq) → H2O (l)
The stoichiometry of the reaction is 1:1, which means that the number of moles of H+ ions (n3) will be equal to the number of moles of OH- ions (n2) present in the solution.
Number of moles of H+ (n3) = Number of moles of OH- (n2)
= 0.000200 mol
Step 8: Calculate the concentration of H+ ions (C3) in the solution.
Concentration of H+ ions (C3) = Number of moles of H+ (n3) / Volume of HCl (V3)
= 0.000200 mol / (12.96 mL / 1000)
= 0.0154 mol/L
Step 9: Calculate the concentration of OH- ions using the concentration of H+ ions in the solution.
Since the reaction is an acid-base neutralization, the concentration of OH- ions can be calculated using the equation Kw = [H+][OH-].
Kw is the equilibrium constant for water, which is 1.0 × 10^-14 at 25°C.
[H+] × [OH-] = 1.0 × 10^-14
0.0154 mol/L × [OH-] = 1.0 × 10^-14
[OH-] = (1.0 × 10^-14) / (0.0154 mol/L)
≈ 6.49 × 10^-13 mol/L
Step 10: Calculate the solubility of Ca(OH)2.
Since Ca(OH)2 dissociates into one Ca2+ ion and two OH- ions, the solubility of Ca(OH)2 (S) can be calculated using the concentration of OH- ions.
Solubility of Ca(OH)2 (S) = [OH-] × 2
≈ 6.49 × 10^-13 mol/L × 2
≈ 1.30 × 10^-12 mol/L
Step 11: Convert the solubility to g/100mL.
The molar mass of Ca(OH)2 is 40.08 g/mol.
Solubility (S) in g/L = Solubility (S) in mol/L × Molar mass (MM)
Solubility (S) = 1.30 × 10^-12 mol/L × 40.08 g/mol
≈ 5.21 × 10^-11 g/L
To convert g/L to g/100mL:
Solubility (S) = Solubility (S) in g/L × 100 / Volume of solution (V)
= 5.21 × 10^-11 g/L × (100/10)
≈ 5.21 × 10^-10 g/100mL
Now, let's summarize the answers to the different questions:
1. The value of Ksp for Ca(OH)2 is calculated to be approximately 6.49 x 10^-13.
2. The molarity of Ca(OH)2 dissolved in the solution is approximately 0.00200 mol/L.
3. The solubility of Ca(OH)2 in the solution is approximately 5.21 x 10^-10 g/100mL.
By the way, in question 1 you have a grammar error. That should be
"1. Calculate the value for Ksp of Ca(OH)2 from THESE data."
Data is plural but this is singular. These is plural.