Chads video question Ksp calculations

[510586]

Hey everyone I have a question about one of the quiz questions on chad's videos.
Q. Sc3+ can be added to a solution of 0.0001M NaF to what maximum concentration before a precipitate forms (Ksp,ScF3 = 4.2x10-18)?

The way to do it is :
Ksp = [Sc3+][F-]3
4.2x10-18 = [Sc3+](0.0001)3

I was wondering why do we cube the F- if there is only .0001M NaF to begin with? I thought we only cube it if the solid itself is dissociating? Can someone please clarify?

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[DustFreeEraser]

You're getting confused with multiplying the concentration by 3 vs cubing
If a solid was dissociating we would write
Ksp = [x][3x]^3 where x = concentration of Sc and 3x =concentration of F
Since we're given concentration of F, we just plug that in for 3x and still keep the cubing part as that is part of the equation.

 

[510586]

Oh ok I get it so the equilibrium expression will always use the coefficient as the exponent, and only if it is the solid dissociating alone would there be that 3x. Thanks!