Effect of Sodium Chloride on the Freezing Point of Water: A Thorough Analysis

Understanding how the addition of sodium chloride (NaCl) affects the freezing point of water is fundamental to several scientific and practical applications, including cryopreservation, agriculture, and food preservation. In this detailed analysis, we will explore how the concentration of NaCl in water impacts the freezing point, specifically focusing on the example where 31.65 grams of NaCl is added to 220.0 mL of water at 34 degrees Celsius.

Introduction to Freezing Point Depression

Freezing point depression is the phenomenon where the freezing point of a solution is lower than that of the pure solvent. This effect is observed when a non-volatile solute, such as NaCl, is dissolved in a solvent, such as water. The degree to which the freezing point is depressed is proportional to the concentration of the solute.

Experiment Details

For this experiment, we are adding 31.65 grams of NaCl to 220.0 mL of water at 34 degrees Celsius. The molar mass of NaCl is 58.5 g/mol, indicating that 31.65 grams of NaCl corresponds to approximately 0.5416 moles. This concentration is 12.57% by weight (wt/wt).

Calculating Molality and Freezing Point Depression

Molality is a measure of concentration that is calculated by the moles of solute per kilogram of solvent, whereas molality accounts for the mass of the solution rather than the solvent alone.

Molality Calculation:

First, calculate the moles of NaCl:

Moles NaCl 31.65 g / 58.44 g/mol 0.5416 mol

Next, determine the mass of water. Since 1 mL of water equals approximately 0.994 g/mL at room temperature and we are at 34 degrees Celsius:

mass water 220.0 mL X 0.994 g/mL 221 g H2O ≈ 0.221 kg H2O

Now, calculate the molality:

Molality 0.5416 mol / 0.221 kg H2O 2.47 molal

Freezing Point Depression Calculation:

The freezing point depression constant (Kf) for water is 1.86°C/m. For NaCl, which completely ionizes in solution, the van't Hoff factor (i) is 2.

Using the formula for freezing point depression:

ΔTf i Kf m

ΔTf 2 × 1.86°C/m × 2.47 m 9.15°C

Therefore, the solution will freeze at:

Freezing point of the solution 0 - 9.15°C -9.15°C

Conclusion and Practical Applications

The significant reduction in the freezing point of water due to the addition of NaCl makes it a valuable tool in various practical applications. For instance, in cold regions, salt is commonly used to de-ice roads by lowering the freezing point of water. Understanding the exact freezing point depression allows for precise control over these processes.

It is essential to note that the effect of NaCl on water includes the formation of two equivalents of ions (Na and Cl-) when dissolved in water:

NaCl(s) H2O → Na (aq) Cl-(aq)

Therefore, the accurate determination of the molal fusion point depression constant (kf) is crucial for precise calculations.

Understanding these principles can aid in the development of solutions for various industries and applications where control over the freezing point of solutions is critical.