Ksp Math: Quicker way?

[SaintJude]

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Since it looks like April MCAT has been math-heavy, I'd like to review my math techniques for common problems. Does anyone have a quicker / more efficient way to do the following problem?

Q: The solubility of ZnF2 is 2.03g/100mL at 25 degrees. What is the Ksp value for ZnF2?

A: ZnF2 ----> Zn2+ 2F- So Ksp = [Zn2+][F-]^2

[Zn2+] = (2.03 g/ 103 g ) /L ≈ (2/ 100) moles /L = (.02 / .1) = 0.2 M

[F] = 0.4 --> [F-]^2 = 16 x 10^-2

So Ksp = [Zn2+][F-]^2 = 0.2 M ( 16 x 10^-2 ) = 3.2 x 10^-2

This took me like 3 minutes. I mean I'm not a fan of Kaplan's triage, but if these math heavy questions take me that long, I feel like I have no choice but to triage.

 

[MedPR]

Yes, Ksp=[Zn][F]^2.

Ksp = 4x^3 = 4(0.2^3) = 0.032.

Took about 15 seconds.

 

[folktale]

Yes, Ksp=[Zn][F]^2.

Ksp = 4x^3 = 4(0.2^3) = 0.032.

Took about 15 seconds.

Well, you still have to find out what x is. So probably about 30 seconds to even a minute.

 

[MedPR]

Well, you still have to find out what x is. So probably about 30 seconds to even a minute.

I guess so, but if you've done a lot of stoichiometry problems you might have the molar mass of Zn and F memorized just like C, O, N, and H. In that case, it's just a matter of addition.

 

[SaintJude]

Yes, Ksp=[Zn][F]^2.

Ksp = 4x^3 = 4(0.2^3) = 0.032.

Took about 15 seconds.

VERY good point. If I had the Ksp OR the "x" value, I can use that "shortcut"

Ksp = x (2x)^2 = x(4x^2) = 4x^3.

Actually, I need to memorize the following formulas...I could probably derive them, but I need all the time I can get

MX3 -> Ksp = 27x^4

MX2--> Ksp = 4x^3

MX---> Ksp = x^2