Question

Which of the following aqueous solutions will show maximum vapour pressure at 300 K?

• A. $0.1$ M Glucose
• B. $0.1$ M $NaCl$
• C. $0.1$ M $CaCl_2$
• D. $0.1$ M $AlCl_3$

Hint:

For colligative properties, always consider the \textbf{effective number of solute particles} \((i \times M)\).

• Larger \(i \times M\) \( \Rightarrow \) greater lowering of vapour pressure
• Larger \(i \times M\) \( \Rightarrow \) higher boiling point
• Larger \(i \times M\) \( \Rightarrow \) lower freezing point
• Larger \(i \times M\) \( \Rightarrow \) higher osmotic pressure

Answer 1

The Correct Option is A

Concept:
Vapour pressure is a colligative property. The presence of a solute lowers the vapour pressure of a solvent, and the extent of this lowering depends only on the number of solute particles present in the solution. The relative lowering of vapour pressure is proportional to the effective concentration of solute particles: \[ \text{Lowering of V.P.} \propto i \times M \] where \(i\) = van't Hoff factor (number of particles produced after dissociation) \(M\) = molarity of the solution. Thus, more particles \( \Rightarrow \) greater lowering of vapour pressure \( \Rightarrow \) smaller vapour pressure.
Step 1: {Identify the number of particles produced by each solute.} For all options, \(M = 0.1\).

• Glucose: Non–electrolyte, does not dissociate. \(i = 1\)
• \(NaCl \rightarrow Na^+ + Cl^-\), \(i = 2\)
• \(CaCl_2 \rightarrow Ca^{2+} + 2Cl^-\), \(i = 3\)
• \(AlCl_3 \rightarrow Al^{3+} + 3Cl^-\), \(i = 4\)

Step 2: {Calculate effective particle concentration \(i \times M\).} \[ \text{Glucose: } 0.1 \times 1 = 0.1 \] \[ NaCl: 0.1 \times 2 = 0.2 \] \[ CaCl_2: 0.1 \times 3 = 0.3 \] \[ AlCl_3: 0.1 \times 4 = 0.4 \]
Step 3: {Compare vapour pressures.} Since vapour pressure decreases with increasing number of solute particles, the solution with the smallest value of \(i \times M\) will have the maximum vapour pressure. Among the given options, glucose has the lowest effective particle concentration.
Step 4: {Conclusion.} Therefore, the solution with the maximum vapour pressure is: \[ 0.1 \text{ M Glucose} \]