Comparing the Ksp values, which of the following is the LEAST soluble in water?

A. MnCO3..........8.8x10^-11
B. FeCO3...........2.1x10^-11
C. Ag2CO3.........8.1x10^-12
D. BaCrO4..........8.5x10^-11

This is from EK 1001 gen chem (#534)...They say the answer is B: I think the answer is A....First of all, that question is somewhat wrong because Ksp can only tells you about solubity when the solubility expressions are the same... A, B and D have the same expresion(X^2), but the expression for C is (4X^3)...Ksp of A is less than B...Why is B the answer? Am I wrong in my reasonning?

The setup: You found x which is the molar solubility. The question is asking for what is LEAST soluble.

So by knowing Ag2CO3 is something along the lines of __x10^4 power, you can rule it out immediately as the MOST soluable (or pick that if that was what the question was asking). Knowing that the other choices follow the pattern of x^2 = ___x10^11 (all the same power), you can pick what the LEAST soluble is by picking the lowest number which is B.

the long way is to carry out the math but square root of 2.1 will always be less than square root of 8.8

NEVER compare Ksp values when examining relative solubilities without first checking the Ksp expressions. You want to compare molar solubilities to determine relative solubilities, and molar solubility is (x) in the Ksp expression. For this problem, A, B, and D had Ksp expressions of x^2, while C has 4x^3.

Therefore the Ksp of C cannot be compared with any of the others because the units are different.

As Nutty said, C can be ruled out with a quick math approximation. Among the remaining three, units are all the same because Ksp expressions are the same, meaning we can compare Ksp's directly and just look for the lowest, being B.

Calculation of molar solubility (x) for each choice also proves B is correct.

NEVER compare Ksp values when examining relative solubilities without first checking the Ksp expressions. You want to compare molar solubilities to determine relative solubilities, and molar solubility is (x) in the Ksp expression. For this problem, A, B, and D had Ksp expressions of x^2, while C has 4x^3.

Therefore the Ksp of C cannot be compared with any of the others because the units are different.

As Nutty said, C can be ruled out with a quick math approximation. Among the remaining three, units are all the same because Ksp expressions are the same, meaning we can compare Ksp's directly and just look for the lowest, being B.

Calculation of molar solubility (x) for each choice also proves B is correct.