[Halogen876]

Hello,

I am having problems with this question:

Mg(OH)₂ forms a suspension in water. 8.00g of Mg(OH)₂ is dissolved in 100.0mL of water. The Ksp of Mg(OH)₂ is 5.6E-12.

a) what mass of Mg(OH)₂ is actually dissolved in the water? I got this part fine (6.5E-4g)

b) What is the pH? I got this as well (10.35).

c) To what volume would the pH need to be lowered to dissolve all of the Mg(OH)₂ (assume no volume change). I know the answer is 8.31 but this does not make sense to me because if you are dissolving more base, the pH should be going up, not down so I am very confused about how to approach this question.

Any assistance would be greatly appreciated.

Thanks!

[mjc123]

a) is incorrect, check it again.
c) How do you know it's 8.31? I get a different answer.
As you lower the pH by adding acid, base dissolves by reaction to give its conjugate acid:
Mg(OH)₂(s) + 2H⁺(aq)  Mg²⁺(aq) + 2H₂O
so dissolving Mg(OH)₂ doesn't generate more OH^- in solution - in fact the reverse, as more Mg²⁺ means less OH^- by Ksp.

[Halogen876]

Thank you for the reply. I understand now about how it would become more acidic. That makes sense but I'm not sure how to set up the math. I know the answer is 8.31 because the question is from a textbook and that answer is provided, as is the answer to part (a). I calculated the answer for (a) and got the textbook's answer but do you think the textbook answers are wrong? I see that for (c) the Ksp expression would now have less hydroxide but I just don't know how much less. Any more clarification would be appreciated!

[AWK]

a & b are OK!
c - assume all Mg(OH)₂ is dissoloved and calculate concentration of Mg²⁺.
From Ksp you can find concentration of OH^- then pH. Your pH is reasonable.

[mjc123]

Actually your answers are right - I didn't spot the "100 ml of water" and was calculating it per litre. That would also make the pH in part c correct - I was out by 0.5.
Sorry!

[Halogen876]

I got it! Thank you both so much for your input - it is very much appreciated! If anyone else is reading this and wants any more details of how I did it, please feel free to ask me.