The correct relation for determining the molar mass of solute ($M_2$) using osmotic pressure measurement, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $M_2=\frac{w_2RT}{ПV}$
Osmotic pressure is a colligative property that depends on the number of solute particles present in the solution. The fundamental relation for osmotic pressure is Π = CRT
where Π = osmotic pressure
C = molar concentration of solution
R = universal gas constant
T = absolute temperature
Molar concentration can be written as C = n / V
where n is the number of moles of solute and V is the volume of the solution.
Number of moles of solute is n = w₂ / M₂
where w₂ = mass of solute M₂ = molar mass of solute
Substituting in the osmotic pressure equation:
Π = (w₂ / M₂V) RT
Rearranging to obtain molar mass: M₂ = (w₂RT) / (ΠV)
Thus the correct relation for determining molar mass using osmotic pressure is M₂ = (w₂RT) / (ΠV)