Writing Ksp expression

Question

While doing Ksp problems, I found that in some problems you have write out the expression with a coefficient multiplied by x while others you only have to put the exponent outside the bracket.

example with coefficient:

the Ksp of CaF2 is 3.9 x 10^-11. What is the molar solubility?

ksp= (x)(2x)^2

example without coefficient:

Write the Ksp expression for CaF2

ksp= (Ca^2+)(F-)^2

My question is that when do you know to times the 2 by x inside the bracket and when to simply put the coefficient as an exponent outside the bracket instead? Thanks!

Answer 1

I would disagree with the way you wrote the first Ksp expression, unless you have additional information. You should always write it as Ksp = [Ca²⁺][F^-]²

Then, if you don't know the concentration of either ion, you would write

let x = [Ca²⁺] and then [F^-] = 2x and then you would have Ksp = (x)(2x)²

So, in summary, the way you have written the first expression indicates that you do not know the concentration of either of the ions (so you call them x and 2x) and you probably have a Ksp value and are solving for x. In the second expression, you know the concentrations of each ion and so you don't use "x" as a value and you are probably solving for a value of Ksp.

Hint: It's probably never a good idea to write the coefficient inside the bracket unless you first qualify what x is equal to, as above when x = [Ca²⁺]. Hope this makes sense.