To determine the relationship between the osmotic pressures of solutions
X and
Y, we first need to understand that osmotic pressure
(Ï€) for a solution is given by the formula:
Ï€=iCRTwhere:
−i is the van't Hoff factor, which represents the number of particles the solute dissociates into in the solution.
C is the molar concentration of the solution. -
R is the gas constant. -
T is the temperature (in Kelvin).
For the electrolyte
X2A, it dissociates into three ions (two
X ions and one
A ion), thus
i=3 for this electrolyte. The concentration
(C) of
X2A is
0.04M.
The osmotic pressure for
X2A can be calculated as:
π1=3×0.04×R×Tπ1=0.12×(R×T)In contrast,
Y being a non-electrolyte does not dissociate, therefore
i=1 for
Y, and its concentration
(C) is
0.2M. The osmotic pressure of
Y(P2) is thus:
P2=1×0.2×R×TP2=0.2×(R×T) To find the relationship between
Ï€1 (osmotic pressure of
X ) and
P2 :
‌=‌‌=‌=0.6Thus,
Ï€=0.6P2, which corresponds to Option
A.