Comprehensive Study Notes on Solutions and Liquid Solutions

Introduction to Solutions and Their Importance

• Definition of Solution: A solution is a homogeneous mixture consisting of two or more components.
• Homogeneity: Homogeneity implies that the composition and properties of the mixture are uniform throughout the entire volume.
• Components of a Solution:
  • Solvent: The component present in the largest quantity, which determines the physical state (solid, liquid, or gas) of the resulting solution.
  • Solute: One or more components present in the solution other than the solvent.
• Binary Solutions: Solutions consisting of exactly two components. This unit focuses primarily on binary solutions.
• Real-World Importance of Composition:
  • Brass: A mixture of copper and zinc.
  • German Silver: A mixture of copper, zinc, and nickel.
  • Bronze: A mixture of copper and tin.
  • Fluoride Ions in Water:
    • $1.0\,ppm$ prevents tooth decay.
    • $1.5\,ppm$ causes mottled teeth.
    • High concentrations are poisonous (e.g., sodium fluoride used in rat poison).
  • Intravenous Injections: Must contain salt concentrations that match the ionic concentrations of blood plasma.

Types of Solutions

Solutions are classified based on the physical state of the solute and solvent (Table 1.1):

• Gaseous Solutions:
  • Gas-Gas: Mixture of oxygen and nitrogen gases.
  • Liquid-Gas: Chloroform mixed with nitrogen gas.
  • Solid-Gas: Camphor in nitrogen gas.
• Liquid Solutions:
  • Gas-Liquid: Oxygen dissolved in water.
  • Liquid-Liquid: Ethanol dissolved in water.
  • Solid-Liquid: Glucose dissolved in water.
• Solid Solutions:
  • Gas-Solid: Solution of hydrogen in palladium.
  • Liquid-Solid: Amalgam of mercury with sodium.
  • Solid-Solid: Copper dissolved in gold.

Expressing Concentration of Solutions

Concentration can be described qualitatively (dilute vs. concentrated) or quantitatively. Quantitative methods include:

• Mass Percentage ($w/w$):
  • Definition: \text{Mass % of a component} = \frac{\text{Mass of component in solution}}{\text{Total mass of solution}} \times 100
  • Example: 10% glucose in water means $10\,g$ glucose in $90\,g$ water.
• Volume Percentage ($V/V$):
  • Definition: \text{Volume % of a component} = \frac{\text{Volume of component}}{\text{Total volume of solution}} \times 100
  • Example: 35% ($v/v$) ethylene glycol is used as car antifreeze, lowering the freezing point of water to $255.4\,K$ ($-17.6^{\circ}C$).
• Mass by Volume Percentage ($w/V$):
  • Definition: The mass of solute dissolved in $100\,mL$ of the solution. Commonly used in medicine.
• Parts Per Million (ppm):
  • Used for trace quantities.
  • $\text{ppm} = \frac{\text{Number of parts of the component}}{\text{Total number of parts of all components}} \times 10^6$
  • Example: Sea water contains $6 \times 10^{-3}\,g$ of dissolved $O_2$ per litre ($1030\,g$), which is $5.8\,ppm$.
• Mole Fraction ($x$):
  • Definition: $\text{Mole fraction of a component} = \frac{\text{Number of moles of the component}}{\text{Total number of moles of all components}}$
  • Formula for component A in a binary mixture: $x_A = \frac{n_A}{n_A + n_B}$
  • Sum of mole fractions: $x_1 + x_2 + ... + x_i = 1$
• Molarity ($M$):
  • Definition: Number of moles of solute dissolved in one litre (or one cubic decimetre) of solution.
  • $\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in litre}}$
  • Temperature Dependency: Molarity changes with temperature because volume depends on temperature.
• Molality ($m$):
  • Definition: Number of moles of solute per kilogram ($kg$) of solvent.
  • $\text{Molality} = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$
  • Independence from Temperature: Mass %, ppm, mole fraction, and molality are temperature-independent.

Solubility of Solids and Gases in Liquids

• General Rule: "Like dissolves like." Polar solutes dissolve in polar solvents (e.g., sodium chloride in water); non-polar solutes dissolve in non-polar solvents (e.g., naphthalene in benzene).
• Dynamic Equilibrium: When the rate of dissolution equals the rate of crystallization.
  • $\text{Solute} + \text{Solvent} \rightleftharpoons \text{Solution}$
• Saturated Solution: No more solute can be dissolved at the same temperature and pressure.
• Effect of Temperature on Solid Solubility:
  • If dissolution is endothermic ($\Delta_{sol}H > 0$), solubility increases with temperature.
  • If dissolution is exothermic ($\Delta_{sol}H < 0$), solubility decreases with temperature.
• Effect of Pressure on Solid Solubility: Negligible, as solids and liquids are incompressible.
• Solubility of Gases in Liquids:
  • Solubility increases with increase of pressure.
  • Solubility decreases with increase of temperature because the dissolution of gases in liquids is typically an exothermic process (similar to condensation).

Henry's Law

• Definition: At a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the surface of the liquid or solution.
• Mathematical Expression: $p = K_H x$
  • $p$ is the partial pressure of the gas.
  • $x$ is the mole fraction of the gas in the solution.
  • $K_H$ is the Henry's law constant.
• Key Observations:
  • $K_H$ depends on the nature of the gas.
  • Higher $K_H$ at a given pressure indicates lower solubility.
  • $K_H$ increases as temperature increases, meaning gas solubility decreases at higher temperatures. This explains why aquatic species are more comfortable in cold water (higher dissolved $O_2$).
• Applications:
  • Soft Drinks: Sealed under high pressure to increase $CO_2$ solubility.
  • Scuba Diving: High pressure underwater increases nitrogen solubility in blood. Rapid ascent causes nitrogen bubbles (bends). Divers use tanks diluted with helium ($11.7\%\,He$, $56.2\%\,N_2$, $32.1\%\,O_2$) to prevent this.
  • Anoxia: At high altitudes, low partial pressure of $O_2$ leads to low blood oxygen, causing weakness and mental confusion.

Raoult's Law and Vapour Pressure

• Vapour Pressure: The pressure exerted by vapours over a liquid phase at equilibrium in a closed vessel.
• Vapour Pressure of Liquid-Liquid Solutions: For a solution of volatile liquids, the partial vapour pressure of each component ($p_i$) is directly proportional to its mole fraction ($x_i$).
  • $p_1 = p_1^0 x_1$ and $p_2 = p_2^0 x_2$
  • Total Pressure ($p_{total}$): $p_{total} = p_1 + p_2 = p_1^0 + (p_2^0 - p_1^0)x_2$
• Composition of Vapour Phase: If $y_i$ represents the mole fraction in the vapour phase:
  • $p_i = y_i p_{total}$
• Vapour Pressure of Solutions of Solids in Liquids: Adding a non-volatile solute reduces the vapour pressure of the solvent. This happens because solute particles occupy part of the surface, reducing the escaping tendency of solvent molecules.
• Raoult's Law as a Special Case of Henry's Law: For a gas in a liquid, Raoult's Law ($p_1 = p_1^0 x_1$) is identical in form to Henry's Law ($p = K_H x$), where $K_H$ equals $p_1^0$.

Ideal and Non-Ideal Solutions

• Ideal Solutions:
  • Obey Raoult's law over the entire range of concentration.
  • $\Delta_{mix}H = 0$ (No heat change on mixing).
  • $\Delta_{mix}V = 0$ (Initial volumes equal final volume).
  • Molecular basis: $A-A$ and $B-B$ interactions are nearly equal to $A-B$ interactions.
  • Examples: n-hexane and n-heptane; bromoethane and chloroethane.
• Non-Ideal Solutions: Do not obey Raoult's law.
  • Positive Deviation: $A-B$ interactions are weaker than $A-A$ or $B-B$. Vapour pressure is higher than predicted. Example: Ethanol and acetone; carbon disulphide and acetone.
  • Negative Deviation: $A-B$ interactions are stronger than $A-A$ or $B-B$. Vapour pressure is lower than predicted. Example: Phenol and aniline; chloroform and acetone.
• Azeotropes: Binary mixtures that have the same composition in liquid and vapour phase and boil at a constant temperature.
  • Minimum Boiling Azeotrope: Formed by solutions with large positive deviations (e.g., $95\%$ ethanol-water).
  • Maximum Boiling Azeotrope: Formed by solutions with large negative deviations (e.g., $68\%$ nitric acid and $32\%$ water).

Colligative Properties

These properties depend solely on the number of solute particles relative to the total number of particles, regardless of identity.

1. Relative Lowering of Vapour Pressure:

   • $\frac{p_1^0 - p_1}{p_1^0} = x_2$
   • For dilute solutions: $M_2 = \frac{w_2 \times M_1}{w_1 \times \frac{p_1^0 - p_1}{p_1^0}}$

2. Elevation of Boiling Point (Ebullioscopy):

   • Boiling point increases when a non-volatile solute is added.
   • $\Delta T_b = K_b m$
   • $K_b$ is the Molal Elevation Constant (Ebullioscopic Constant).
   • $M_2 = \frac{1000 \times K_b \times w_2}{\Delta T_b \times w_1}$

3. Depression of Freezing Point (Cryoscopy):

   • Freezing point decreases when a non-volatile solute is added.
   • $\Delta T_f = K_f m$
   • $K_f$ is the Molal Depression Constant (Cryoscopic Constant).
   • $M_2 = \frac{1000 \times K_f \times w_2}{\Delta T_f \times w_1}$

4. Osmotic Pressure:

   • Osmosis: The net flow of solvent molecules from a pure solvent (or dilute solution) through a semipermeable membrane (SPM) into a solution (or concentrated solution).
   • Osmotic Pressure ((\Pi)): The excess pressure that must be applied to the solution side to stop osmosis.
   • $\Pi = C R T = \frac{n_2}{V} R T$
   • $M_2 = \frac{w_2 R T}{\Pi V}$
   • Advantage: Used for macromolecules (proteins/polymers) as it is measurable at room temperature and uses molarity.

Osmosis Applications and Reverse Osmosis

• Isotonic Solutions: Two solutions with the same osmotic pressure (e.g., $0.9\%$ mass/volume NaCl is isotonic with blood plasma).
• Hypertonic Solutions: Concentration $> 0.9\%. Blood cells shrink (plasmolysis).\n* **Hypotonic Solutions**: Concentration $< 0.9\%. Blood cells swell and may burst.
• Natural/Biological Examples:
  • Raw mangoes shrivel in brine.
  • Wilted flowers revive in fresh water.
  • Edema: Swelling of tissues in people eating lots of salt due to water retention via osmosis.
  • Preservation: Salting meat or sugaring fruits kills bacteria via dehydration.
• Reverse Osmosis: Occurs when pressure exceeding osmotic pressure is applied to the solution side, forcing pure solvent out of the solution.
  • Application: Desalination of sea water. Uses porous membranes like cellulose acetate (permeable to water, impermeable to ions).

Abnormal Molar Masses and the van’t Hoff Factor

• Abnormal Molar Mass: Experimentally determined molar mass that differs from calculated values due to association or dissociation of the solute.
  • Dissociation: Molecules split into ions (e.g., $KCl$). Observed molar mass is lower than theoretical.
  • Association: Molecules join together (e.g., ethanoic acid dimerises in benzene via hydrogen bonding). Observed molar mass is higher than theoretical.
• van’t Hoff Factor ($i$):
  • $i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}$
  • $i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}$
  • $i = \frac{\text{Total number of moles of particles after association/dissociation}}{\text{Number of moles of particles before association/dissociation}}$
• Modified Equations:
  • Relative Lowering of Vapour Pressure: $\frac{p_1^0 - p_1}{p_1^0} = i \frac{n_2}{n_1}$
  • $\Delta T_b = i K_b m$
  • $\Delta T_f = i K_f m$
  • $\Pi = i C R T$
• Example values of $i$:
  • $KCl, NaCl$: $i \approx 2$
  • $K_2SO_4$: $i \approx 3$
  • Ethanoic acid/Benzoic acid in benzene (dimerisation): $i \approx 0.5$