Colligative Properties and Concentration Unit Conversions

Problem Statement: A solution contains a mole fraction of iodine at 0.00889 and methylene chloride at 0.9911, which indicates that this solution consists primarily of methylene chloride as the solvent and iodine as the solute.

Definition of Molality: Molality (m) is defined as the number of moles of solute (iodine) contained in one kilogram of solvent (methylene chloride). It is a crucial concentration term used in colligative properties calculations and is represented mathematically as:
m = \frac{n{solute} (moles~of~solute)}{mass{solvent} (kg)}

Mole Fraction Interpretation: Mole fractions are dimensionless and represent the ratio of moles of a component to the total moles of all components in the solution. Here, 0.00889 corresponds to 0.00889 moles of iodine, while the remainder, represented by the mole fraction of methylene chloride, indicates its proportion in the solution.

Finding Moles of Methylene Chloride: To ascertain the amount of methylene chloride in the solution, we observe that the mole fraction of methylene chloride is 0.9911. This implies optimal solvation, where the larger mole fraction identifies the solvent predominating over the solute, leading to 0.9911 moles of methylene chloride.

Molar Mass Conversion: By using the molar mass of methylene chloride (85 g/mol), we can convert the moles of methylene chloride to grams:

• Grams of methylene chloride:
  0.9911~moles\times 85~g/mol = 84.24~grams

To consider practical applications, we convert grams to kilograms (as required in the molality formula). The conversion yields:

• 84.24~grams \equiv 0.08424~kg

Calculating Molality: With the determined quantities, we can compute the molality of the solution:

• Molality (m):
  m = \frac{moles~of~iodine}{kg~of~methylene~chloride} = \frac{0.00889~moles}{0.08424~kg} \approx 0.106~molal

This means that the solution's molality is approximately 0.106 molal, illustrating the concentration of iodine in the methylene chloride solvent. This derivation is significant for understanding the solution behavior in contexts like chemical reactions and physical property modifications.

Introduction to Colligative Properties:

Definition: Colligative properties are features of solutions that depend on the concentration of solute particles rather than their specific identity. These properties play a crucial role in various fields, including chemistry, biology, and environmental science.

Key Colligative Properties:

1. Vapor Pressure Reduction: When a non-volatile solute is added to a solvent, the vapor pressure above the solution decreases compared to that above the pure solvent, based on Raoult’s Law. The extent of vapor pressure lowering correlates directly with the amount of solute added.

   • Example: Saltwater has a lower vapor pressure than pure water. The presence of salt reduces the number of water molecules at the surface capable of evaporating, resulting in lower vapor pressure and affecting boiling points as well.

2. Boiling Point Elevation: Adding a solute to a solvent results in an increase in the boiling point. The boiling point elevation is determined by the number of solute particles present in the solution.

   • Example: Saltwater boils at a higher temperature than pure water, which is utilized in cooking to achieve quicker meal preparation.

3. Freezing Point Depression: The freezing point of a solution is lower than that of the pure solvent. Adding solute disrupts the formation of the solid lattice structure of ice.

   • Example: Roads are salted to prevent ice formation during winter, as this lowers the freezing point of water, thereby aiding in maintaining safer transportation conditions.

4. Osmotic Pressure: This property refers to the pressure required to prevent the flow of solvent molecules through a semipermeable membrane from a dilute solution to a more concentrated solution. The greater the solute concentration, the higher the osmotic pressure required to reach equilibrium.

All of these properties are essential for predicting how solutions behave under various conditions, particularly in practical applications such as chemical reactions, culinary practices, and even biological processes.

Vapor Pressure of Solutions:

Raoult's Law: The relationship governing the vapor pressure of solutions states that the vapor pressure of a solution (P{solution}) can be calculated using the vapor pressure of the pure solvent (P^{pure solvent}) along with the mole fraction of the solvent (X{solvent}):
P{solution} = P^{pure~solvent} \times X{solvent}

Applying Raoult's Law: Example Problem:
Given a solution containing 50 grams of ethanol (C2H5OH) and 8.56 grams of eugenol (C10H12O2), we can calculate the vapor pressure of the solution step-by-step:

1. Determine Molar Masses:

   • Ethanol: 46 g/mol

   • Eugenol: 164 g/mol

2. Calculate Moles:

   • Moles of ethanol:
     \frac{50~g}{46~g/mol} \approx 1.09~moles

   • Moles of eugenol:
     \frac{8.56~g}{164~g/mol} \approx 0.0522~moles

3. Total Moles Calculation:
   Total moles = Moles of ethanol + Moles of eugenol
   1.09~moles + 0.0522~moles \approx 1.14~moles

4. Calculate Mole Fraction of Ethanol:
   Mole fraction of ethanol (X{ethanol}): X{ethanol} = \frac{1.09}{1.14} \approx 0.956

5. Calculate Vapor Pressure of the Solution:
   Using Raoult's Law:

• Vapor pressure of pure ethanol at 20°C is 44.6 mmHg.

• Calculate the vapor pressure of the solution:
  P_{solution} = 44.6~mmHg \times 0.956 \approx 42.6~mmHg

1. Determine Vapor Pressure Lowering:
   The difference between the vapor pressure of pure ethanol and the vapor pressure of the solution:

• Vapor pressure lowering = 44.6 mmHg - 42.6 mmHg = 2.0 mmHg.

Conclusion:
Understanding colligative properties is essential for grasping the behavior of solutions under various conditions. Their implications are particularly significant in practical applications such as cooking, road maintenance, and chemical processes. Furthermore, this knowledge helps in predicting and controlling the characteristics of solutions in both industrial and laboratory settings.