If the van’t Hoff factor for NaCl is 1.88, what is the freezing point of a 0.50 molal NaCl solution in water?Kf = 1.86°C/m for water.
The correct answer and explanation is :
To calculate the freezing point depression of a solution, we can use the formula:
[
\Delta T_f = i \cdot K_f \cdot m
]
Where:
- (\Delta T_f) is the freezing point depression (how much the freezing point of the solution decreases),
- (i) is the van’t Hoff factor (the number of particles the solute dissociates into),
- (K_f) is the cryoscopic constant (freezing point depression constant) for the solvent,
- (m) is the molality of the solution (mol of solute per kg of solvent).
Step-by-Step Solution
- Given Values:
- van’t Hoff factor ((i)) = 1.88 for NaCl (which dissociates into Na(^+) and Cl(^-)),
- (K_f) for water = 1.86°C/m (this constant tells us the amount by which the freezing point of water decreases for each molal concentration of solute),
- Molality of the solution (m) = 0.50 mol/kg (0.50 mol of NaCl per kg of water).
- Step 1: Calculate Freezing Point Depression ((\Delta T_f))
Using the formula (\Delta T_f = i \cdot K_f \cdot m):
[
\Delta T_f = 1.88 \cdot 1.86 \, \text{°C/m} \cdot 0.50 \, \text{mol/kg}
]
[
\Delta T_f = 1.88 \cdot 0.93 = 1.7504 \, \text{°C}
]
Thus, the freezing point depression is 1.7504°C.
- Step 2: Calculate the New Freezing Point
The freezing point of pure water is 0°C. Since the solution’s freezing point will be lowered by (\Delta T_f), the new freezing point of the solution is:
[
\text{Freezing Point of Solution} = 0°C – 1.7504°C = -1.7504°C
]
Conclusion
The freezing point of the 0.50 molal NaCl solution in water is approximately -1.75°C.
Explanation
In the context of freezing point depression, when NaCl dissolves in water, it dissociates into Na(^+) and Cl(^-) ions, contributing to the van’t Hoff factor. The van’t Hoff factor of 1.88 suggests that NaCl dissociates slightly more than fully into two ions, which could happen due to ion pairing or other solution dynamics. The cryoscopic constant (K_f) determines how much the freezing point is depressed per molal concentration of solute. This relationship shows how adding solute to a solvent lowers its freezing point, a colligative property that depends on the number of solute particles rather than their specific chemical nature.