Chemistry: Finding Ksp for Ca(OH)2

[madeeeeee]

Homework Statement

What is the concentration of hydroxide at equilibrium in a solution that contains a mixture of .10 M sodium hydroxide and .20 M calcium chloride?

I know that the reference value for Ca(OH)2 is 6.10 x 10^-6

Equation: 2NaOH(aq) + CaCl2(aq) ---> 2NaCl(aq) + Ca(OH)2(s)

Ca(OH)2(s)----> Ca + 2OH
I -
C -
E -
Ksp = [Ca][OH]2

precipitate:
Ca: 0.20M x (1/2) = .10 M
OH: .10M x (1/2) = .05 M

My question is, is that what is the volume of the concentrations? Because i don't know how to solve this problem, please help! I have tried different ways but i keep getting a cubed root...I am really confused!

 

[Borek]

You may assume any volume you like - like 1L - if it helps you. But you don't have to.

There is an excess of calcium, so when the reaction ends you will have still a lot of calcium in the solution. Calculate its concentration, and use it to calculate concentration of OH^- that was not precipitated. This is only an approximated method, but good enough.

 

[madeeeeee]

How do I do that? Do I say Ca: .10 M + x
OH: .05 M + 2x

do I disassociate the x?

 

[Borek]

Not +x, but -x - Ca(OH)₂ precipitates, so both Ca²⁺ and OH^- are removed.

But the idea is to not use 0.05-2x - but to calculate how much Ca²⁺ was removed from the solution by precipitation assuming reaction went to completion. This is not exactly true, but knowing Ksp and [Ca²⁺] you can calculate [OH^-] and check if the assumption makes sense (that is, if amount of OH^- left in the solution is negligible in stoichiometry calculations).

 

[DeeNos]

Based on the information provided, it is not clear what the volume of the solution is. It is important to know the volume in order to calculate the concentration of hydroxide at equilibrium. Once the volume is known, the concentrations of sodium hydroxide and calcium chloride can be used to calculate the initial concentrations of calcium and hydroxide ions in the solution. From there, the Ksp equation can be used to calculate the concentration of hydroxide at equilibrium. It is also important to note that the Ksp value for Ca(OH)2 may vary slightly depending on the temperature and other factors.