What is the solubility of M(OH)2 in pure water?

The generic metal hydroxide M(OH)2 has Ksp = 1.45×10^−18.

A)What is the solubility of M(OH)2 in pure water?

B)What is the solubility of M(OH)2 in a 0.202M solution of M(NO3)2?

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What is the solubility of M(OH)2 in pure water?

The generic metal hydroxide M(OH)2 has Ksp = 1.45×10^−18.

A)What is the solubility of M(OH)2 in pure water?

B)What is the solubility of M(OH)2 in a 0.202M solution of M(NO3)2?

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The equilibrium will be :

M(OH)2 <---> M2+ + 2OH-

and the requirement for equilibrium is that

Ksp = [M2+] [ OH-]^2

Let x = mole/L M(OH)2 that dissolve in water

We would get x mol/L M2+ and 2x mol/L OH-

Substitute these in the Ksp expression

1.45 x 10^-18 = x ( 2x)^2 = 4x^3

x = 7.13 x 10^-7 M

M(NO3)2 is a strong electrolyte:

M(NO3)2 >> M2+ + 2NO3-

[M2+] = 0.202 M

At equilibrium

[M2+] = x+0.202

[OH-] = 2x

1.45 x 10^-18 = ( x+0.202) (2x)^2

Since x has to be small compared to 0.202 we can assume:

x+ 0.202 = 0.202

1.45 x 10^-18 = 0.202 (4x^2)

x = 1 x 10^-9 M

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Dr. A's answer for both parts A and B are CORRECT.

Part B is where most people are having trouble with, but the truth is that MasteringChemistry doesn't accept 1.0 x 10^-9 or something of the sort. If you're using a standard scientific calculator, then you may not be able to see all of the digits that your calculator gives you due to the sheer amount of zeroes that consumes your entire display. In that case, MULTIPLY your answer by 1000 (or something similar) to find the rest of the digits.

For instance, my TI-30X gave me 0.000000002, which 2 x 10^-9. This answer was marked as incorrect. If I multiply by 1000, I see that it's actually 0.000001846. So, I typed in 1.846 x 10^-9 as my answer, and it was marked as correct. :D

Maybe you shouldn't be so quick to downvote someone who has received 95% of the best answers for 45895 of his answers.