Solubility question

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TheJourney

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Which of the following substances is most likely to be more soluble in 1.0M HCl than in 1.0M NaoH?

A) AgCl
B) Pb(OH)2
C) CaF2
D) HI

I picked answer choice D and got it wrong. I don't quite understand their explanation. My reasoning was that A was that like dissolves like there an acid will be soluble in acid and not soluble in a base. Also, I figure you could eliminate answer choice A due to the common ion effect? The correct answer choice is B can anyone try and make me understand this concept, thank you.
 
This has to do with solubility constants and equilibrium. Basically, in 1M NaOH, there will already be a 10^-1 concentration of OH-. So if you add another ionic compound that has OH- group(s), not as much of it will dissolve.
 
Pb(OH)2 <--> Pb+2 + 2OH-

nothing is completely insoluble, there's always a tiny quantity dissolved.

When the OH is combined with HCl, it forms water, thus removing OH from right side of the equation. Le Chatelier's principle will then force more Pb(OH)2 into Pb+2 and OH-, and the cycle repeats.
 

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