Colligative Properties II: Everything Else

Definition: Freezing point depression is the phenomenon where the freezing point of a liquid (solvent) is lowered when a solute is added to it.
Entropy Consideration:
- When a solute is added to a solvent, the disorder or entropy of the solution increases.
- Higher entropy makes it thermodynamically favorable for the liquid to remain in the liquid phase rather than transitioning into a solid state.
Conclusion: Therefore, the addition of a solute decreases the freezing point of the resulting liquid/solution.

ΔTf: Change in freezing point
- It is the difference in temperature between the freezing point of the pure solvent and the solution.
- Measured in degrees Celsius (°C) or Kelvin (K), which are equivalent in this context.
Kf: Freezing point depression constant
- This constant is unique for each type of solvent.
omsoulute:
- Refers to the molality of the solute dissolved in the solvent.
i (van't Hoff factor):
- This factor relates to the number of particles the solute forms in solution.

Problem Statement: Calculate the freezing point of a solution containing 22.0 g of octane (C8H18, molar mass 114.23 g/mol) dissolved in 148.0 g of benzene (C6H6, molar mass 78.11 g/mol).
Solution Reference: Freezing point (Tf) = 5.50 °C; Freezing constant (Kf) = 5.12 °C/m.

Problem Statement: For an aqueous 0.050 m CaCl2 solution with a freezing point of -0.27 °C, determine the actual van't Hoff factor.
Kf Used: Kf = 1.86 °C/m.

Definition: Boiling point elevation occurs when a solute is added to a solvent, causing the boiling point of the solution to be higher than that of the pure solvent.
Vapor Pressure Consideration:
- The vapor pressure of a solution is lower at all temperatures due to the presence of solute particles.
- The boiling point is defined as the temperature at which the vapor pressure of the liquid equals the atmospheric pressure.
Conclusion: Thus, adding a solute raises the boiling point since the vapor pressure is depressed.

ΔTb: Change in boiling point
- It is the temperature difference between the boiling point of the pure solvent and that of the solution.
- Measured in degrees Celsius (°C) or Kelvin (K).
Kb: Boiling point elevation constant
- Unique for each solvent.
omsoulute:
- Represents the molality of the solute in the solution.
i (van't Hoff factor):
- Refers to the number of particles formed from the solute in the solution.

Instructions: Rank the boiling points of the following aqueous solutions from lowest to highest boiling point:
A. 0.35 m Ethylene Glycol (C2H6O2)
B. 0.20 m KBr
C. 0.50 m Glucose (C6H12O6)
D. 0.20 m Na2SO4

Problem Statement: A 2.0 molal aqueous solution of glucose is found to boil at 101 °C. Predict the boiling point of a 2.0 molal solution of sucrose (C12O11H22).
Options:
A. 102 °C
B. 100.5 °C
C. 101 °C
D. Slightly higher than 100.5 °C
E. Cannot determine without Kb

Problem Statement: Determine the boiling point of a solution that contains 78.8 g of naphthalene (C10H8, molar mass 128.16 g/mol) dissolved in 722 mL of benzene (density = 0.877 g/mL).
Pure Benzene Boiling Point: 80.1 °C
Boiling Point Elevation Constant of Benzene: Kb = 2.53 °C/m.

Definition: Osmosis is the process of solvent passage through a semi-permeable membrane from an area of lower solute concentration (less concentrated) to an area of higher solute concentration (more concentrated).
- Semi-permeable membranes allow small molecules or ions, such as solvents, to pass through while restricting solutes.

Volume Changes: As the solvent moves to the more concentrated side, the volume of the concentrated side increases.
Pressure Implication:
- The greater volume of molecules on the concentrated side exerts greater pressure against the flow of solvent.

Definition: The osmotic pressure (Π) is the extra pressure exerted by the column of solvent depending on the concentration difference.
- Osmosis stops when the osmotic pressure is sufficient to balance.
Osmotic Pressure Calculation:
- ( ext{Osmotic Pressure}, \, Π = i imes M imes R imes T)
- Where:
- M: Molarity of the solution (mol/L)
- R: Ideal gas constant (0.08206 L⋅atm/mol⋅K)
- T: Temperature in Kelvin
- i: van't Hoff factor of the solute

Problem Statement: A non-electrolytic compound with a molar mass of 598 g/mol is dissolved in enough water to make 175 mL of solution at 25 °C. Given that 35.8 mg of the compound are used, determine the osmotic pressure of the resulting solution.

Instructions: Rank the following solutions in order of increasing osmotic pressure:
- I: 0.35 M C2H6O2
- II: 0.15 M BaCl2
- III: 0.15 M NaI
- Options:
  A. II < III < I
  B. III < I < II
  C. II < I < III
  D. I < III < II

Comparing Solutions:
- Two solutions can be described in terms of osmotic pressure relative to one another.
- If solutions have identical osmotic pressures, they are isotonic.
- If they differ in osmotic pressures:
- The solution with lower osmotic pressure (more dilute) is hypotonic.
- The solution with higher osmotic pressure (more concentrated) is hypertonic.

Effects on Cells:
- Isotonic solution: normal red blood cell (homeostasis).
- Hypotonic solution: water enters the cell; it swells (can burst).
- Hypertonic solution: water leaves the cell; it shrinks or crenates.

Definition: Reverse osmosis occurs when a solution is subjected to external pressure greater than its osmotic pressure, forcing the solvent through a semi-permeable membrane into pure solvent.
Application: Commonly used for purifying water, found in various bottled water brands (e.g., Aquafina, LifeWTR, Fiji, etc.).