Which of the following compounds has the greatest molar solubility?
A) AgBr, Ksp= 5.4 x 10^13
B) Ba3(PO4)2, Ksp = 3.0 x 10^-23
C) Al(OH)3, Ksp = 1.9 x 10^-33
D) MgF2, Ksp = 7.4 x 10^-11
E) Pb(OH)2, Ksp = 1.2 x 10^-15
I know the answer for this problem is D. Would it be safe to assume that the greatest molar solubility, is associated with the compound with the highest Ksp value? In this case D?
No, that is not a safe assumption. You must go through with EACH comound and determine the solbility from the Ksp
So, for this problem would I need to take the square root of all of the Ksp values in order to find the greatest solubility?
No, that won't work either. That is the way to do A and here is why.
..............AgBr ==> Ag^+ + Br^-
I............solid...........0..........0
C..........solid............x..........x
E..........solid............x..........x
Ksp = (Ag^+)(Br^-)
5.4E-13 = (x)(x) and
x = sqrt Ksp. Now do the B part.
.............Ba3(PO4)2 ==> 3Ba^2+ + 2(PO4)^3-
I............solid......................0...............0
C..........solid.....................3x..............2x
E...........solid....................3x..............2x
Ksp = (Ba^2+)(PO4^3-)
3E-23 = (3x)^3(2x)^2 = 108x^5
x=(3E-23/108)^1/5 = (3E-23/108)^0.2 = ?
That looks like a lot of work to go through; however, you make mental mistakes if you don't follow the long route to the solution. You need to do C, D, and E the same way. You will see that C involves the 4th root(that's 0.25) while D and E involve the cube root.
Yes, in general, the molar solubility of a compound can be related to its solubility product constant (Ksp). The higher the Ksp value, the greater the molar solubility of the compound.
In this case, you are correct that compound D, MgF2, has the highest Ksp value compared to the other options. Therefore, compound D, MgF2, has the greatest molar solubility among the given compounds.
It is important to note that molar solubility refers to the amount of a solute (in moles) that can dissolve in a given amount of solvent to form a saturated solution. Ksp, on the other hand, represents the equilibrium constant for the solubility equilibrium of a sparingly soluble salt.