Physical Properties of Solutions and Colloid Systems

Types of Solutions and Solubility

• A saturated solution is defined as a solution containing the maximum amount of a solute that will dissolve in a specific solvent at a specific temperature.

• Solubility refers to the amount of solute dissolved in a given volume of a saturated solution. It is a value specific to a particular solute, solvent, and temperature. For example, the solubility of $NaCl$ in water at $20^{\circ}C$ is $36\,g$ per $100\,mL$. If the temperature or solvent changes, the solubility value will also change.

• An unsaturated solution is one that contains less solute than the solvent has the capacity to dissolve at that specific temperature.

• A supersaturated solution contains more dissolved solute than is typically present in a saturated solution. These solutions are generally unstable.

• Solutions can exist in various states depending on the states of the solute and solvent:

  • Gas in Gas: Example is Air.
  • Gas in Liquid: Example is Carbonated water.
  • Gas in Solid: Example is $H_{2}$ gas in palladium.
  • Liquid in Liquid: Example is Ethanol in water.
  • Liquid in Solid: Example is Mercury in silver.
  • Solid in Liquid: Example is Saltwater.
  • Solid in Solid: Example is Brass (an alloy of $Cu$ and $Zn$).

The Solution Process and Intermolecular Interactions

• Intermolecular forces holding molecules together in solids and liquids are central to the solution process. When a solute dissolves, its molecules disperse and become surrounded by solvent molecules, a process called solvation.

• The ease of dissolution depends on three types of interactions:

  1. Solute-solute interactions.
  2. Solvent-solvent interactions.
  3. Solute-solvent interactions.

• The enthalpy of solution ($\Delta H_{\text{soln}}$) is the sum of three steps:

  • Step 1: Separating solute particles ($\Delta H_{1} > 0$, endothermic).
  • Step 2: Separating solvent particles ($\Delta H_{2} > 0$, endothermic).
  • Step 3: Solute and solvent particles mixing ($\Delta H_{3} < 0$, exothermic).
  • $\Delta H_{\text{soln}} = \Delta H_{1} + \Delta H_{2} + \Delta H_{3}$.

• Dissolution is generally encouraged when the process is exothermic ($\Delta H_{\text{soln}} < 0$) and discouraged when it is endothermic ($\Delta H_{\text{soln}} > 0$).

• The principle "like dissolves like" suggests that substances with similar intermolecular forces (type and magnitude) are likely to be soluble in one another because their mixing is usually not highly endothermic. For example, nonpolar $CCl_{4}$ and nonpolar $C_{6}H_{6}$ (benzene) are miscible, meaning they are completely soluble in each other in all proportions.

• Solubility Preferences:

  • Bromine ($Br_{2}$): Nonpolar; more soluble in benzene ($C_{6}H_{6}$).
  • Sodium iodide ($NaI$): Ionic; more soluble in polar water ($H_{2}O$).
  • Carbon tetrachloride ($CCl_{4}$): Nonpolar; more soluble in benzene.
  • Formaldehyde ($CH_{2}O$): Polar; more soluble in water.

• The Driving Forces for Dissolution:

  • Enthalpy: Exothermic processes favor dissolution.
  • Entropy ($S$): This factor measures the diversity of ways a system can store energy (energy dispersal). Systems tend toward higher entropy, where particles are free-ranging and mobile. Because solute particles are more mobile in solution than in a crystalline solid, dissolution increases entropy. This promotes dissolution even for endothermic processes, such as the dissolving of ammonium nitrate ($NH_{4}NO_{3}$) in water, provided the entropic gain outweighs the endothermic barrier.

Concentration Units and Measurements

• Molarity ($M$):

  • $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Mole Fraction ($X_{A}$):

  • $X_{A} = \frac{\text{moles of component A}}{\text{sum of moles of all components}}$

• Molality ($m$):

  • $m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$
  • Advantage: Molality is temperature independent, whereas Molarity changes with volume expansions or contractions caused by temperature shifts.

• Percent by Mass:

  • $\text{Percent by mass} = \frac{\text{mass of solute}}{\text{mass of solute} + \text{mass of solvent}} \times 100\%$
  • Also temperature independent and does not require knowledge of molar mass.

• Parts Per Million ($ppm$):

  • Calculated similarly to percent by mass but multiplied by $10^{6}$ instead of $100$.

Factors That Affect Solubility

• Temperature: For most solid solutes, solubility in water increases with increasing temperature. However, some substances like $Ce_{2}(SO_{4})_{3}$ show a decrease in solubility as temperature rises.

• Pressure: Pressure primarily affects the solubility of gases in liquids. Henry's Law describes this quantitatively:

  • $c = kP$
  • $c$ is the molar concentration ($mol/L$) of the dissolved gas.
  • $P$ is the partial pressure ($atm$) of the gas over the solution.
  • $k$ is the Henry’s law constant (e.g., for $CO_{2}$ in water at $25^{\circ}C$, $k = 3.1 \times 10^{-2}\,mol/L \cdot atm$).

Colligative Properties

• Colligative properties depend only on the number of solute particles in a solution, not on their nature (identity).

• Vapor-Pressure Lowering: Adding a nonvolatile solute to a liquid decreases the vapor pressure. Raoult's Law states:

  • $P_{1} = X_{1} P_{1}^{0}$
  • $P_{1}$ is the vapor pressure of the solution, $X_{1}$ is the mole fraction of the solvent, and $P_{1}^{0}$ is the vapor pressure of the pure solvent.
  • The lowering of vapor pressure is $\Delta P = X_{2} P_{1}^{0}$, where $X_{2}$ is the mole fraction of the solute.
  • For solutions where both components are volatile: $P_{T} = X_{A} P_{A}^{0} + X_{B} P_{B}^{0}$.

• Boiling-Point Elevation ($\Delta T_{b}$): The boiling point of a solution is higher than that of the pure solvent.

  • $\Delta T_{b} = T_{b} - T_{b}^{0}$
  • $\Delta T_{b} = K_{b} m$, where $K_{b}$ is the molal boiling-point elevation constant.

• Freezing-Point Depression ($\Delta T_{f}$): The freezing point of a solution is lower than that of the pure solvent.

  • $\Delta T_{f} = T_{f}^{0} - T_{f}$
  • $\Delta T_{f} = K_{f} m$, where $K_{f}$ is the molal freezing-point depression constant.

• Osmotic Pressure ($\pi$): The pressure required to stop osmosis (the flow of solvent through a semipermeable membrane into a more concentrated solution).

  • $\pi = MRT$
  • $R = 0.08206\,L \cdot atm/K \cdot mol$. $T$ is absolute temperature in Kelvin.
  • Solutions with the same osmotic pressure are called isotonic.

• Electrolyte Solutions and the van’t Hoff Factor ($i$):

  • Electrolytes dissociate into ions, increasing the number of particles.
  • $i = \frac{\text{actual number of particles in solution after dissociation}}{\text{number of formula units initially dissolved}}$
  • Modified equations: $\Delta T_{b} = i K_{b} m$; $\Delta T_{f} = i K_{f} m$; $\pi = i MRT$.
  • In reality, measured $i$ values are often lower than calculated values due to the formation of ion pairs, especially at higher concentrations.

Calculations Using Colligative Properties

• Determining Molar Mass:

  • Freezing-point depression and osmotic pressure are most commonly used to find molar mass because they produce large, measurable changes.
  • Process: Measure $\Delta T_{f}$ or $\pi$; calculate molality ($m$) or molarity ($M$); use the mass of the solute to find the molar mass (grams per mole).

• Percent Dissociation/Ionization:

  • For strong electrolytes like $NaCl$, dissociation should be $100\%$, though it is more complete in dilute solutions.
  • For weak electrolytes, the percent ionization depends on concentration. For a 0.100 M solution of hydrofluoric acid ($HF$) with $\pi = 2.64\,atm$ at $25^{\circ}C$, the percent ionization is found to be $8\%$.

Colloids

• A colloid is a dispersion of particles ($1 \times 10^{3}\,pm$ to $1 \times 10^{6}\,pm$) of one substance throughout another. It is an intermediate state between a homogeneous solution and a heterogeneous mixture.

• Types of Colloids:

  • Aerosol: Liquid/Solid in Gas (Fog, Smoke).
  • Foam: Gas in Liquid/Solid (Whipped cream, Styrofoam).
  • Emulsion: Liquid in Liquid (Mayonnaise).
  • Sol: Solid in Liquid/Solid (Milk of magnesia, Alloys).
  • Gel: Liquid in Solid (Jelly, Butter).

• The Tyndall Effect: This is the scattering of visible light by colloidal particles, which allows one to distinguish a colloid from a true solution.

• Stability of Colloids:

  • Hydrophilic (water-loving): Stable in water; example is hemoglobin, where hydrophilic groups face outward.
  • Hydrophobic (water-fearing): Normally unstable but can be stabilized by the adsorption of ions on the surface. Adsorption refers to material collecting on the surface. Charged surfaces create electrostatic repulsion, preventing clumping.
  • Soap (e.g., sodium stearate $C_{17}H_{35}COO^{-}Na^{+}$) works via a hydrophobic tail that interacts with grease and a hydrophilic head that interacts with water to form micelles.