Simple Solubility problem...

[dedicate]

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The Ksp of Mg(OH)2 in water is 1.2 × 10–11 mol3/L3. If the Mg2+ concentration in an acid solution is 1.2 × 10–5, what is the pH at which Mg(OH)2 just begins to precipitate?

A . 3
B . 4
C . 5
D . 11

I know this seems simple, but I guessed to get it right, not knowing the exact route to take, but the explanation is not helpful for me! Can you explain it in a step by step process please?🙂

 

[Medmad]

The Ksp of Mg(OH)2 in water is 1.2 × 10–11 mol3/L3. If the Mg2+ concentration in an acid solution is 1.2 × 10–5, what is the pH at which Mg(OH)2 just begins to precipitate?

A . 3
B . 4
C . 5
D . 11

I know this seems simple, but I guessed to get it right, not knowing the exact route to take, but the explanation is not helpful for me! Can you explain it in a step by step process please?🙂

Which option is the answer?

 

[shishicd]

this seems deceptively simple, but....
from the solubility constant we know
[Mg][OH]^2=1.2 e-11
the problem gives us the concentration of Mg, which we can plug into the equation to find the concentration of OH- at equilibrium, which would be the 'tipping point' before MgOH2 starts to precipitate.
1.2 e-6 * [OH]^2 = 1.2 e-11
[OH] = 10 e-3
pOH = 3
pH = 14 - pOH = 11

does this look right?

 

[TheBoondocks]

this seems deceptively simple, but....
from the solubility constant we know
[Mg][OH]^2=1.2 e-11
the problem gives us the concentration of Mg, which we can plug into the equation to find the concentration of OH- at equilibrium, which would be the 'tipping point' before MgOH2 starts to precipitate.
1.2 e-6 * [OH]^2 = 1.2 e-11
[OH] = 10 e-3
pOH = 3
pH = 14 - pOH = 11

does this look right?

Yes.

 

[cathyrn]

I am also confused but i thought
[mg][oh]=4x^3

 

[TheBoondocks]

I am also confused but i thought
[mg][oh]=4x^3

correct, however, you should still get the same answer.

1.2e-11/1.2e-6= e-5=4x^2 x= 1.5e-3= oh poh= approximate to 3, actually slightly above 3 for pOH
14-3= 11

 

[Corvette]

I get why the answer is 11, but quick question: If the Mg2+ concentration is 1.2e-5, why isn't the OH- concentration 2(1.2e-5) = 2.4e-5? For every Mg2+ ion, won't there be 2 OH- ions?

 

[VanBrown]

that should be automatic points without doing any math whatsoever...

if you have any hydroxide salt in solution the solution will be basic when it is saturated.. the only answer choice possible is D.

 

[rocketbooster]

that should be automatic points without doing any math whatsoever...

if you have any hydroxide salt in solution the solution will be basic when it is saturated.. the only answer choice possible is D.

yeah, that's a super simple question. as long as you read that the Mg(OH2) was put in water, then it's guaranteed to be basic and there's only 1 basic answer.

 

[rocketbooster]

I get why the answer is 11, but quick question: If the Mg2+ concentration is 1.2e-5, why isn't the OH- concentration 2(1.2e-5) = 2.4e-5? For every Mg2+ ion, won't there be 2 OH- ions?

that should be correct...solving it either way should get the same [OH-] but for some reason it doesn't.

ummm...

Ksp = x(2x)^2 = 4x^3
1.2*10-11 =4x^3
x = 1.44 * 10-4

That x should equal the [Mg2+] given in the question, but it doesn't. So, yes, their #s are wrong. The [Mg2+] given in the question is mathematically wrong. It does not match up to solving for the [Mg2+] on your own. They didn't want you to check for that, though. They only wanted you to recognize that the answer had to be basic, so no math is needed. In the case you did math anyway, they gave you an easy [Mg2+] to work with so you don't spend too much more time on the question.

 

[shishicd]

that should be correct...solving it either way should get the same [OH-] but for some reason it doesn't.

ummm...

Ksp = x(2x)^2 = 4x^3
1.2*10-11 =4x^3
x = 1.44 * 10-4

That x should equal the [Mg2+] given in the question, but it doesn't. So, yes, their #s are wrong. The [Mg2+] given in the question is mathematically wrong. It does not match up to solving for the [Mg2+] on your own. They didn't want you to check for that, though. They only wanted you to recognize that the answer had to be basic, so no math is needed. In the case you did math anyway, they gave you an easy [Mg2+] to work with so you don't spend too much more time on the question.

actually, Ksp = x(x)^2. i don't know why the coefficients work differently for Ksp, but they do!

 

[FIREitUP]

i think this is supposed to be a common ion effect problem. either way it's a pretty bad problem.