If each of the following is an ideal solution at 37 °C, the lowest osmotic pressure, equaling 20 atm, is produced by:

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11ecba2d_11f3_127d_a3bf_cd07c1799398_MD0008_00 When two solutions with different solute concentrations are separated by a semi-permeable membrane, the solvent from the solution of lower solute concentration will diffuse across the membrane into the solution of higher solute concentration until the solution concentrations equalize. This behavior is called osmosis. The diffusion of the solvent during osmosis produces an osmotic pressure against the membrane, which is calculated for an ideal solution by the relationship: 11ecba2d_11f3_127e_a3bf_e9f69df757fa_MD0008_00 where Π is the osmotic pressure, i is the van 't Hoff factor (the number of species a molecule will form when dissolved in solution), M is the solute molar concentration (mol/L), R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the solution temperature (Kelvin). When the ionic MgSO₄ is dissolved in water, it dissociates into two ions (Mg⁺² and SO₄⁻²), making the van 't Hoff factor equal to 2. A solution that has 0.40 M MgSO₄, therefore, produces a solution that has 0.40 M Mg⁺² and 0.40 M SO₄⁻² and gives a solution with an osmotic pressure expressed generally by: 11ecba2d_11f3_398f_a3bf_6d64cf167cec_MD0008_00 At 37 °C (310 K), RT = 25 L·atm/mol, yielding a pressure of 20 atm. 11ecba2d_11f3_3990_a3bf_f53e30557ac5_MD0008_00 The other solutions involve compounds for which the product of the van 't Hoff factor and the molar solute concentration produce a higher osmotic pressure; therefore, 0.40 M MgSO₄ exhibits the lowest osmotic pressure. (Choice A) Aqueous Na₂SO₄ dissociates into 2 Na⁺ and SO₄⁻² (i = 3). Therefore, Π = 3(0.32)RT = 0.96RT atm. (Choice C) Aqueous (NH₄)₂SO₄ dissociates into 2 NH₄⁺ and SO₄⁻² (i = 3). As such, Π = 3(0.40)RT = 1.2RT atm. (Choice D) Fructose dissolved in water does not dissociate (i = 1). Consequently, Π = 1(0.90)RT = 0.90RT atm. Educational objective: Osmosis is the diffusion of solvent across semi-permeable membrane from a solution of lower solute concentration into a solution of higher solute concentration until the solution concentrations equalize. During osmosis, solvent diffusion imparts an osmotic pressure that is calculated by Π = iMRT, which is the product of the van 't Hoff factor, the solute molar concentration, the ideal gas constant, and the absolute temperature.

If Each of the Following Is an Ideal Solution at 37