is destroyer wrong?

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Gen Chem # 50

the question is Ksp Fe(OH)2 @ STP = 1.6x10^-14 what is the solubility of Fe(OH)2 in 0.025 M FeCl2....

answer was given as 4x10^-7 M

I understand how they got to this answer using the common ion effects, yet how is that the solubility of Fe(OH)2, isnt their answer just the molar solubility (or concentration) of Fe in the solution? if I am right with my assumption, how would you calculate the correct answer? unless the reasoning is that because there is only one Fe in the compound this number (4x10^-7 M)is the concentration of Fe in soln. and thus the molar solubility of the compound, Is molar solubility and concentration at equilibrium the same thing in a common ion effect question?

thanks

 

[fsddsms]

Gen Chem # 50

the question is Ksp Fe(OH)2 @ STP = 1.6x10^-14 what is the solubility of Fe(OH)2 in 0.025 M FeCl2....

answer was given as 4x10^-7 M

I understand how they got to this answer using the common ion effects, yet how is that the solubility of Fe(OH)2, isnt their answer just the molar solubility (or concentration) of Fe in the solution? if I am right with my assumption, how would you calculate the correct answer? unless the reasoning is that because there is only one Fe in the compound this number (4x10^-7 M)is the concentration of Fe in soln. and thus the molar solubility of the compound, Is molar solubility and concentration at equilibrium the same thing in a common ion effect question?

thanks

It has to do with the fact that the Ksp is very small (1.6 x 10^-14). So it is estimating that the Ksp is so low that very little Fe is coming from the Fe(OH)2 and more from the FeCl2. That's why u drop the x when trying to solve the problem to make it easier.

Here's how i calc'd it out just now

Fe(OH)2 -> Fe2+ + 2OH-

1.6x 10^-14 = [x][2x]^2
1.6 x 10^-14 = [x + 0.025][4x^2] <~~~ here you drop the x because that x is coming from the Fe(OH)2 which has a very small Ksp so hardly any Fe is coming from Fe(OH)2 and the majority of it is from the 0.025

1.6 x 10^-14 = [0.025][4x^2]
square root (16 x 10^-14) = square root (x^2)
4 x 10^-7 = x = answer

Remember, we drop that x to estimate that hardly any Fe is from the original Fe(OH)2 bc of the small solubility constant. If Ksp were bigger then we cannot drop that x in our approximation and it will become some type of quadratic equation.

Hope that helps.