Pharmaceutics I: Physical Pharmacy - Week 5 Study Notes

Understand colligative properties.
Be able to calculate colligative properties of non-electrolyte and electrolyte solutions.
Be able to calculate osmolality of electrolyte solutions.
Be able to calculate one colligative property from another.
Be able to determine the molecular weight of non-electrolytes and electrolytes using colligative properties.

Additive Properties
- These depend on the total contribution of the atoms in the molecule or on the sum of the properties of the constituents in a solution. Examples include molecular weight and the weight of the solution.
Constitutive Properties
- These depend on the arrangement and kind of atoms in the molecule, and to a lesser degree, on the number of molecules. Examples include conductivity, refractive index, and solubility.
Colligative Properties
- These depend on the number of particles in a solution and are independent of the type of particles. Key colligative properties include:
- Vapor pressure lowering
- Boiling point elevation
- Freezing point depression
- Osmotic pressure

Colligative properties can be observed in both non-electrolyte solutions and electrolyte solutions, beginning with non-electrolytes.

Colligative properties are characteristics based on the ratio of the number of solute particles to solvent particles.

Vapor Pressure Lowering
- Occurs when a non-volatile solute is added to a volatile solvent.
- The vapor pressure ( $pA$ ) of a solution is less than the vapor pressure of the pure solvent ( $p^oA$ ):
 $pA < p^oA$
- The decrease in vapor pressure ($ riangle pA$) is proportional to the mole fraction of the solute ( $XB$ ) in the solution:
 $riangle p = p^oXB = p^o \frac{nB}{nA + nB}$
- The percentage decrease in vapor pressure is expressed as:
 riangle p rac{p^o - pA}{p^o} imes 100 ext{} = XB imes 100 ext{}
Boiling Point Elevation
- The boiling point of a solution is higher than that of the pure solvent.
- The increase in boiling point ($ riangle Tb$) is proportional to the molal concentration ( $m$ ) of the solute: $riangle Tb = K_b m$
Freezing Point Depression
- The melting point (freezing point) of a solution is lower than that of the pure solvent.
- The decrease in freezing point ($ riangle Tf$) is proportional to the molal concentration of the solute: $riangle Tf = K_f m$
Osmotic Pressure ($ heta$)
- Defined as the pressure required to prevent the inward flow of water across a semipermeable membrane.
- Osmotic pressure is directly related to vapor pressure lowering:
  $p^o > p ext{ or } p^o = p + heta$
- Using Morse's equation, the osmotic pressure is proportional to the molal concentration of the solute:
  $heta = RTm$

Example 1: Vapor Pressure Lowering
- If 171.2 g of sucrose (MW = 342.3 g/mol) is dissolved in 1000 g of water (MW = 18 g/mol), calculate the percentage decrease in water vapor pressure at room temperature.
Example 2: Boiling Point Elevation Calculation
- Consider a solution with 10.0 g of sucrose in 100 g of water. Determine the new boiling point of the sucrose solution (MW = 342.3 g/mol).
Example 3: Freezing Point Depression
- Given the same sucrose solution, calculate the freezing point of the sucrose solution (MW = 342.3 g/mol).
Example 4: Osmotic Pressure Calculation
- Calculate the osmotic pressure of the sucrose solution with 10.0 g sucrose in 100 g of water (MW = 342.3 g/mol).
Example 5: Van't Hoff Factor Calculation
- For a solution of 0.10 m acetic acid with a freezing point of -0.188 °C (Kf = 1.86), determine the van't Hoff factor and the measured osmolality:
  0.188 = i rac{K_f m}
Example 6: Average Osmolality of Blood
- The freezing point of blood from normal subjects averages -0.5712 °C. What is the average milliosmolality?
Example 7: Osmotic Pressure of Blood
- Calculate the osmotic pressure at 25 °C if the freezing point of blood is -0.52 °C.
Example 8: Milliosmolarity Calculation of Sodium Bicarbonate Solution
- Given a sodium bicarbonate solution, calculate its milliosmolarity using anhydrous Sodium bicarbonate concentration (0.030 g/mL), density (1.0192 g/mL), and measured osmolality (614.9 mOsm/kg).

Electrolyte solutions exhibit similar colligative properties as non-electrolyte solutions.
Unlike non-electrolytes, electrolytes dissociate into cations and anions, increasing the number of free ions.
Van't Hoff Factor (i)
- The number of effective particles in solution is more significant than the theoretical number of free ions ( $v$ ):
- Relationships:
 $heta = iRTm$
 $riangle Tf = iKf m$
 $riangle Tb = iKb m$
Osmolality (Osm)
- In electrolyte solutions, osmolality is calculated as molality ( $m$ ) multiplied by the van't Hoff factor ( $i$ ):
  $Osm/kg = i imes m$
- For non-electrolyte solutions, osmolality = molality as $i = 1$ .

Osmolarity:
- Expressed in units Osmol/L or mOsm/L, defined as molarity multiplied by the van't Hoff factor:
  $Osm/L = iM$
Osmolality:
- Concentration expressed in Osmol/Kg or mOsm/Kg, crucial for biological and medical applications.

Tonicity refers to the effective osmotic pressure of a solution, indicating cellular response:
- Hypertonic: Higher osmotic pressure leading to cellular shrinkage.
- Isotonic: No change in cellular constituents; equal osmotic pressure (e.g., 0.9% NaCl, 5% dextrose solutions).
- Hypotonic: Lower osmotic pressure, which may lead to cell swelling.
Isosmotic (Iso-osmotic): Equal osmotic pressure based on freezing point depression.
- Example: A 2% boric acid solution is isosmotic but not isotonic as blood cells may diffuse through its solute.

To determine if a solution is hypertonic, isotonic, or hypotonic:
- Compare the freezing point of the solution with the blood freezing point (-0.52 °C).
- Also assess the osmolality in reference to the blood osmolality (~280 mOsm/kg).
 - Hypertonic Solution: Lower than -0.52 °C; osmolality > 280 mOsm/kg.
 - Hypotonic Solution: Higher than -0.52 °C; osmolality < 280 mOsm/kg.