Is it possible to calculate the value of the solubility product constant without being given any concentrations?

3 answers

no.
Well if you use: (delta)G=-RT*ln(k), you can get a k value if you're given the values for (delta)G and the temperature.
Not quite.

the equation you give ignores entropy

deltaG= -RT lnk + S/T

You have to know T, S, and deltaG

http://en.wikipedia.org/wiki/Van_%27t_Hoff_equation