Is it possible to calculate the value of the solubility product constant without being given any concentrations?
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
No, it is not possible to calculate the value of the solubility product constant (Ksp) without any information about the concentrations.
To calculate the Ksp, you need to know the concentration of the dissolved ions in a saturated solution. The Ksp describes the equilibrium between a solid salt and its dissolved ions in a solution and is a constant at a given temperature. It is determined through experimental measurements, typically involving the saturation of a solution and measuring the equilibrium concentrations of the dissolved ions.
Without knowing the concentrations of the dissolved ions, you cannot determine the Ksp. Therefore, you would need either experimental data or information about the concentrations of the dissolved ions to calculate the value of the solubility product constant.