Derive the direct relationship between Osmotic Pressure ( $$\pi$$ ) and Depression in Freezing Point ( $$\Delta T_f$$ ) for a dilute solution at temperature $$T$$ .

Question

Derive the direct relationship between Osmotic Pressure ( $$\pi$$  ) and Depression in Freezing Point ( $$\Delta T_f$$  ) for a dilute solution at temperature  $$T$$  .

Canvas Classes · Accepted Answer

$$\pi = \Delta T_f 	imes \frac{d \cdot R \cdot T}{1000 \cdot K_f}$$    Logic: $$\pi = CRT$$  and $$\Delta T_f = K_f \cdot m$$. For dilute solutions, Molarity ( $$C$$  )  $$\approx$$  Molality ( $$m$$  ) $$	imes$$  density ( $$d$$  ). Substituting $$m$$   gives the relation.

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