In-Depth Notes on Electrolytes and Freezing Point Depression

Electrolyte Dissolution: When an electrolyte, such as sodium phosphate ($\text{Na}3\text{PO}4$), is dissolved in a solvent (like water), it dissociates into its constituent ions. This dissolution process not only alters the chemical composition but also significantly affects colligative properties, such as boiling and freezing points. The electrolytic dissociation increases the number of solute particles in the solution, which is a critical factor in determining how these properties change.

Van 't Hoff Factor (i): This factor represents the number of particles that the solute contributes to the solution. For sodium phosphate, it dissociates into three sodium ions ($\text{Na}^+$) and one phosphate ion ($\text{PO}_4^{3-}$), leading to a total of four particles in solution. Thus, the Van 't Hoff Factor, $i$, for sodium phosphate is 4, indicating that each formula unit produces four ions in solution. This factor is essential to correctly applying freezing point depression calculations, as it directly influences the extent of freezing point depression observed.

Understanding Freezing Point Depression Formula: The freezing point depression can be quantified using the formula: \Delta Tf = Kf \times m \times i where:

• \Delta T_f = change in freezing point

• Kf = freezing point depression constant of the solvent (for water, Kf = 1.858 \text{ °C/m})

• m = molality of the solution, which is defined as the number of moles of solute per kilogram of solvent

• i = Van 't Hoff factor, indicating the number of particles the solute contributes to the solution

Example Calculation: Suppose we have a 0.010 molal solution of sodium phosphate ($m = 0.010$). To calculate the freezing point depression: \Delta Tf = 1.858 \times 0.010 \times 4 gives: \Delta Tf = 0.0743 \text{ °C}. The actual freezing point of the solution would then be: 0 - 0.0743 \text{ °C} = -0.0743 \text{ °C}, thus effectively lowering the freezing point of water from its normal 0 °C.

Estimating Freezing Point Values: While theoretical calculations provide a reasonable estimate of freezing point depression, several approximation issues may arise. Real-world applications can show that the change in freezing point may be slightly less than calculated due to factors such as ionic recombination where some ions may not fully dissociate in solution, resulting in a less than expected increase in particle count. Such anomalies can lead to an actual freezing point that is somewhat higher than the calculated value, for example, closer to -0.05 °C instead of the computed -0.0743 °C.

Determining Molecular Weight from Freezing Point Depression: The molecular weight of a solute can be determined using freezing point depression through a systematic approach:

1. Find Molality: Use the freezing point depression method to calculate molality.

2. Calculate Moles: Obtain moles of solute from the calculated molality and the mass of solvent.

3. Calculate Molar Mass: Finally, divide the grams of solute by the moles obtained to calculate the molar mass of the solute.

Example Problem: If we have 37.0 g of a non-electrolyte covalent compound added to 200 g of water, and the resulting freezing point is -5.58 °C (noting that pure water freezes at 0 °C):

• Step 1: Find Molality: Using the freezing point depression formula, we know that \Delta Tf = Kf \times m, where \Delta Tf = 5.58 \text{ °C} (the depression). Inverting the equation gives: m = \frac{\Delta Tf}{K_f} = \frac{5.58}{1.858} \approx 3.00 \text{ molal}.

• Step 2: Calculate Moles: Convert 200 g of water to kilograms (200 g = 0.200 kg). Now, calculate the moles of solute using the relation of molality: \text{molality} = \frac{\text{moles of solute}}{\text{kg of solvent}}, leading us to: \text{moles of solute} = 3.00 \times 0.200 \approx 0.600 \text{ moles}.

• Step 3: Calculate Molar Mass: Given that we have 37.0 g of solute, the calculation for molar mass yields: \text{Molar Mass} = \frac{37.0 \text{ g}}{0.600 \text{ moles}} \approx 61.7 \text{ g/mol}.

Conclusion: The concepts of freezing point depression enable laboratory experiments to determine the molecular weights of unknown compounds effectively. This method is particularly valuable when dealing with non-electrolytes, as the Van 't Hoff factors can be disregarded. Additionally, while topics like osmotic pressure and colloids were introduced, they were not heavily assessed in the exam context; however, understanding the definitions and principles behind these concepts remains crucial for comprehensive knowledge in physical chemistry.