Which of the following ideal solutions exhibits the greatest osmotic pressure at the same temperature and volume?

• A. 1.0 M NaCl
• B. 1.0 M glucose
• C. 0.5 M NaCl
• D. 0.5 M glucose

Answer: (A)

Verified step by step guidance

1. Recall that osmotic pressure (\( \Pi \)) for an ideal solution is given by the formula: \[\Pi = i M R T\] where \( i \) is the van't Hoff factor (number of particles the solute dissociates into), \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
2. Identify the van't Hoff factor (\( i \)) for each solute: - For glucose, which does not dissociate, \( i = 1 \). - For NaCl, which dissociates into Na\( ^+ \) and Cl\( ^- \), \( i = 2 \).
3. Calculate the effective concentration of particles (\( i \times M \)) for each solution: - 1.0 M NaCl: \( 2 \times 1.0 = 2.0 \) - 1.0 M glucose: \( 1 \times 1.0 = 1.0 \) - 0.5 M NaCl: \( 2 \times 0.5 = 1.0 \) - 0.5 M glucose: \( 1 \times 0.5 = 0.5 \)
4. Since \( R \) and \( T \) are constant and the volume is the same, the solution with the highest \( iM \) value will have the greatest osmotic pressure.
5. Compare the \( iM \) values and conclude that the 1.0 M NaCl solution, with the highest effective particle concentration, exhibits the greatest osmotic pressure.