Question

Rank the following aqueous solutions in order of increasing (a) osmotic pressure; (b) boiling point; (c) freezing point; (d) vapor pressure at \(50^{\circ} \mathrm{C}\) : (I) \(0.100 \mathrm{~m} \mathrm{NaNO}_{3}\) (II) \(0.100 \mathrm{~m}\) glucose (III) \(0.100 \mathrm{~m} \mathrm{CaCl}_{2}\)

Short answer

(a) II < I < III (b) II < I < III (c) III < I < II (d) II < I < III

Step-by-step solution

- Understanding Osmotic Pressure

Osmotic pressure depends on the number of solute particles in a solution. Use the formula for osmotic pressure \( \Pi = iMRT \)and determine the van't Hoff factor (i) for each solution: - For NaNO3: i = 2 (since it dissociates into Na+ and NO3-)- For glucose: i = 1 (it does not dissociate)- For CaCl2: i = 3 (it dissociates into Ca2+ and 2Cl-). Rank them according to the iM value.

- Ranking Osmotic Pressure

Using van't Hoff factors outlined in Step 1, rank the solutions by increasing osmotic pressure:(II) < (I) < (III).

- Understanding Boiling Point

Boiling point elevation is also dependent on the number of particles in solution. The formula is \( \Delta T_b = i K_b m \). Use van't Hoff factors to rank the boiling points. Solutions with higher 'i' values will have higher boiling points.

- Ranking Boiling Point

Using the van't Hoff factors, rank the solutions by increasing boiling point:(II) < (I) < (III).

- Understanding Freezing Point

Freezing point depression, like boiling point elevation, depends on the number of solute particles. The formula is \( \Delta T_f = i K_f m \). Solutions with higher 'i' values will have lower freezing points.

- Ranking Freezing Point

Using the van't Hoff factors, rank the solutions by decreasing freezing point (i.e., lower freezing points are ranked higher):(III) < (I) < (II).

- Understanding Vapor Pressure

Vapor pressure lowering also depends on the number of particles in solution. Higher 'i' values mean lower vapor pressure due to the greater number of solute particles causing a greater reduction in vapor pressure.

- Ranking Vapor Pressure

Using van't Hoff factors, rank the solutions by increasing vapor pressure (highest to lowest reduction):(II) < (I) < (III).

Key concepts

Osmotic Pressure

Osmotic pressure can be understood as the pressure required to stop the flow of water through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. It's a critical concept in biology and chemistry, influencing how substances distribute across cells and how nutrients are absorbed. The formula for osmotic pressure is given by \(\[ \Pi = iMRT \]\), where \(i\) is the van't Hoff factor (number of dissociated particles per formula unit), \(M\) is molarity, \(R\) is the gas constant, and \(T\) is temperature in Kelvin.

• For NaNO\textsubscript{3}, the van't Hoff factor \(i = 2\) as it dissociates into Na\textsuperscript{+} and NO\textsubscript{3}\textsuperscript{-}.
• For glucose, \(i = 1\) since it does not dissociate.
• For CaCl\textsubscript{2}, \(i = 3\) as it dissociates into Ca\textsuperscript{2+} and 2Cl\textsuperscript{-}.

Hence, the ranking of solutions from lowest to highest osmotic pressure is: glucose (II) < NaNO\textsubscript{3} (I) < CaCl\textsubscript{2} (III).

Boiling Point Elevation

Boiling point elevation is a colligative property, which means it depends on the number of particles in a solution rather than their nature. The formula used is \( \Delta T\textsubscript{b} = iK\textsubscript{b}m \) where \( \Delta T\textsubscript{b} \) is the boiling point elevation, \(i\) is the van't Hoff factor, \(K\textsubscript{b}\) is the boiling point elevation constant, and \(m\) is the molality of the solution.

• NaNO\textsubscript{3} dissociates into two particles (i = 2).
• Glucose does not dissociate, so i = 1.
• CaCl\textsubscript{2} dissociates into three particles (i = 3).

The greater the number of particles, the higher the boiling point elevation. Thus, ranking the solutions from lowest to highest boiling point is: glucose (II) < NaNO\textsubscript{3} (I) < CaCl\textsubscript{2} (III).

Freezing Point Depression

Freezing point depression, similar to boiling point elevation, is another colligative property. It is described by the formula \( \Delta T\textsubscript{f} = iK\textsubscript{f}m \), where \( \Delta T\textsubscript{f} \) is the decrease in the freezing point, \(i\) is the van't Hoff factor, \(K\textsubscript{f}\) is the freezing point depression constant, and \(m\) is the molality.

• NaNO\textsubscript{3}: \(i = 2\).
• Glucose: \(i = 1\).
• CaCl\textsubscript{2}: \(i = 3\).

The more particles dissolved, the lower the freezing point. Therefore, ranking the solutions from highest to lowest freezing point (lowest to highest depression) is: CaCl\textsubscript{2} (III) < NaNO\textsubscript{3} (I) < glucose (II).

Vapor Pressure Lowering

Vapor pressure lowering is yet another colligative property impacted by the number of solute particles in a solution. When a non-volatile solute is added to a solvent, the vapor pressure of the solvent decreases. This is mathematically represented by Raoult's Law.

• NaNO\textsubscript{3} dissociating into 2 particles means \(i = 2\).
• Glucose not dissociating means \(i = 1\).
• CaCl\textsubscript{2} dissociating into 3 particles means \(i = 3\).

The higher the number of dissolved particles, the greater the lowering of vapor pressure. Thus, the ranking from highest to lowest vapor pressure is: glucose (II) < NaNO\textsubscript{3} (I) < CaCl\textsubscript{2} (III).