Chemical and Physical Foundations

Assuming complete solute dissociation and ideal solution behavior, which of the following aqueous solutions has the greatest osmotic pressure at the same temperature?

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Answer: D (0.08 M Al2(SO4)30.08\ \mathrm{M}\ Al_{2}(SO_{4})_{3})

Osmotic pressure is given by Π=iMRT\Pi=iMRT, where ii is the van't Hoff factor. Because the solutions are at the same temperature, their values of iMiM can be compared. The values are (1)(1)(0.28 M){}(0.28\ \mathrm{M})=0.28 M{}=0.28\ \mathrm{M} for C6H12O6C_{6}H_{12}O_{6}, (2)(2)(0.16 M){}(0.16\ \mathrm{M})=0.32 M{}=0.32\ \mathrm{M} for NaClNaCl, and (3)(3)(0.12 M){}(0.12\ \mathrm{M})=0.36 M{}=0.36\ \mathrm{M} for CaCl2CaCl_{2}. Each formula unit of Al2(SO4)3Al_{2}(SO_{4})_{3} produces five ions, so its value is (5)(5)(0.08 M){}(0.08\ \mathrm{M})=0.40 M{}=0.40\ \mathrm{M}. Therefore, the Al2(SO4)3Al_{2}(SO_{4})_{3} solution has the greatest osmotic pressure.

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