1.0 mole of NaCl, a strong electrolyte, is added to 1.0 kg of water. The freezing point of the solution will be the freezing point of the pure water.
A) higher than.
B) lower than.
C) the same as.
The correct answer and explanation is :
The correct answer is B) lower than.
When NaCl (sodium chloride) dissolves in water, it dissociates into its ions, Na⁺ and Cl⁻. Sodium chloride is a strong electrolyte, which means it completely dissociates in solution. Therefore, adding 1.0 mole of NaCl to 1.0 kg of water will result in the formation of 1.0 mole of Na⁺ ions and 1.0 mole of Cl⁻ ions, giving a total of 2.0 moles of particles in solution (1.0 mole of Na⁺ + 1.0 mole of Cl⁻).
The freezing point of a solution depends on the number of particles in it, and this phenomenon is known as freezing point depression. Freezing point depression occurs because the dissolved particles interfere with the formation of the solid structure of the solvent (water in this case), which prevents the liquid from freezing at the normal freezing point.
The formula for freezing point depression is:
[
\Delta T_f = i \cdot K_f \cdot m
]
Where:
- (\Delta T_f) is the decrease in freezing point.
- (i) is the van ‘t Hoff factor, which represents the number of particles the solute dissociates into. For NaCl, (i = 2) (since NaCl dissociates into Na⁺ and Cl⁻).
- (K_f) is the cryoscopic constant (a constant specific to the solvent, which for water is 1.86 °C·kg/mol).
- (m) is the molality of the solution (moles of solute per kg of solvent).
Since 1.0 mole of NaCl dissociates into 2 moles of ions, the solution contains more particles than pure water. The presence of these extra particles lowers the freezing point of the solution compared to pure water, which has a freezing point of 0°C. Therefore, the freezing point of the solution will be lower than the freezing point of pure water, making the correct answer B) lower than.