Three aqueous solutions are prepared at a constant temperature by dissolving 5 g of ethylene glycol ( C ₂ H ₆ O ₂ ), 5 g of glycerol ( C ₃ H ₈ O ₃ ), and 5 g of glucose ( C ₆ H ₁₂ O ₆ ) separately in water to make 500 mL of each solution. Let their osmotic pressures be ₁ , ₂ , and ₃ respectively. Which of the following represents the correct increasing order of their osmotic pressures?

Step-by-step solution

Osmotic pressure is given by = C R T = w M V R T Since the mass of solute w , volume of solution V , and temperature T are constant for all three solutions, the osmotic pressure is inversely proportional to the molar mass M of the solute. 1 M Molar mass of ethylene glycol ( C ₂ H ₆ O ₂ ), M₁ = 24 + 6 + 32 = 62 g mol ⁻¹ Molar mass of glycerol ( C ₃ H ₈ O ₃ ), M₂ = 36 + 8 + 48 = 92 g mol ⁻¹ Molar mass of glucose ( C ₆ H ₁₂ O ₆ ), M₃ = 72 + 12 + 96 = 180 g mol ⁻¹ The order of molar masses is M₃ > M₂ > M₁ . Therefore,