How Does pH Affect the Solubility of Mg(OH)2?

[jesuslovesu]

Homework Statement

What is the solubility of Mg(OH)2 in a solution buffered at pH 8.80.

Homework Equations

The Attempt at a Solution

The answer is .45 M or 26 g/L but I can't get that for some reason.

I can find the concentration of hydroxide [OH-] = 6.3 x 10-6
Mg(OH)2 -> Mg+2 + 2OH-
...0+x,...6.3x10-6 + 2x

1.8x10-11 = x(6.3x10-6 + 2x)^2

x = 1.65 x 10-4 M (neglecting the 6.3 x10-6)
I've also tried solving the cubic with similar results.
Does anyone where I went wrong?

 

[Borek]

Solution is buffered. [OH-] is not 6.3x10-6 + 2x but JUST 6.3x10-6.

 

[Blueshift5]

Your attempt at solving the problem is correct. The solubility of Mg(OH)2 in a solution buffered at pH 8.80 is indeed 1.65 x 10-4 M or 26 g/L. The discrepancy in your results may be due to rounding errors or slight variations in the given values. It is also possible that the answer given to you is incorrect. I would suggest double checking your calculations and the given values to determine the source of the discrepancy.