Question

At 25 ?C, the osmotic pressure of a solution of the salt XY is 60.8torr . What is the solubility product of XY at 25 ?C?

Answer 1

XY(s) ----------> X⁺(aq) + Y^-(aq)

Now, Osmotic pressure, P (in atm) = i*Molar concentration of XY*R*T ;

where R = universal gas constant = 0.0821 ; T = temperature in kelvin = 298 K ; i = Van't Hoff's factor =2 as XY completely dissociates into its respective ions

760 torr = 1atm

Now, (60.8/760) = 2*molar concentration*0.0821*298

or, molar concentration = 1.635*10^-3 M

now, Molar concentration of X^-, [X^-] = Molar concentration of Y^-, [Y^-] = Molar concenmtration of XY = 1.635*10^-3 M

Thus, K_sp = [X^-][Y^-] = 2.673*10^-6