Solutions and Concentration in Chemistry

• Chemistry is the study of matter and its properties as well as how matter changes.
• Inorganic chemistry deals with the synthesis and behavior of inorganic and organometallic compounds.

Solutions

• A solution is a homogeneous mixture of two or more substances.
• The components of a solution are the solute and the solvent.
• The solute is the substance that is dissolved, and the solvent is the substance in which the solute is dissolved.

Types of Solutions

• Solutions can be classified based on the physical state of the solute and solvent:
  • Gas in gas (e.g., air)
  • Liquid in gas (e.g., humidity)
  • Solid in gas (e.g., smoke)
  • Gas in liquid (e.g., carbonated drinks)
  • Liquid in liquid (e.g., ethanol in water)
  • Solid in liquid (e.g., sugar in water)
  • Gas in solid (e.g., hydrogen in palladium)
  • Liquid in solid (e.g., mercury in silver amalgam)
  • Solid in solid (e.g., alloys)

Concentration Terms

• Concentration is the amount of solute present in a given quantity of solvent or solution.
• Various methods express concentration:
  • Molarity (M): Moles of solute per liter of solution (mol/L).
  • Molality (m): Moles of solute per kilogram of solvent (mol/kg).
  • Mole fraction (x): Ratio of moles of a component to the total moles of all components.
  • Mass percentage (% w/w): (Mass of solute / Mass of solution) x 100.
  • Volume percentage (% v/v): (Volume of solute / Volume of solution) x 100.
  • Parts per million (ppm): (Mass of solute / Mass of solution) x 10^6.

Solubility

• Solubility is the maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature.
• Factors affecting solubility:
  • Nature of solute and solvent: "Like dissolves like" (polar solutes dissolve in polar solvents, non-polar solutes dissolve in non-polar solvents).
  • Temperature: Solubility of most solids in liquids increases with increasing temperature, while gases in liquids usually decrease with increasing temperature.
  • Pressure: Primarily affects the solubility of gases in liquids (Henry's Law).

Henry's Law

• Henry's Law states that the partial pressure of a gas in the vapor phase is proportional to the mole fraction of the gas in the solution.
• The law is expressed as: p = K_H x, where:
  • p is the partial pressure of the gas above the solution.
  • K_H is Henry's Law constant (specific to each gas-solvent pair and temperature).
  • x is the mole fraction of the gas in the solution.
• Applications of Henry's Law:
  • Carbonated beverages: Increased pressure enhances CO2 solubility.
  • Deep-sea divers: High pressure increases nitrogen solubility in blood, leading to decompression sickness (the bends) upon rapid ascent.
  • Respiration: Oxygen and carbon dioxide exchange in the lungs and tissues.

Vapor Pressure of Solutions

• Vapor pressure is the pressure exerted by the vapor when it is in equilibrium with its liquid or solid phase.
• Raoult's Law describes the vapor pressure of solutions.

Raoult's Law

• Raoult's Law states that for a solution of volatile liquids, the partial vapor pressure of each component is directly proportional to its mole fraction in the solution.
• For a solution with two components A and B:
  • p_A = p_A^0 x_A
  • p_B = p_B^0 x_B
  • Where p_A and p_B are the partial pressures of A and B in the solution.
  • p_A^0 and p_B^0 are the vapor pressures of pure A and B.
  • x_A and x_B are the mole fractions of A and B in the solution.
• The total vapor pressure of the solution is: P_total = p_A + p_B

Ideal and Non-Ideal Solutions

• Ideal solutions obey Raoult's Law at all concentrations and temperatures.
• Non-ideal solutions do not obey Raoult's Law.
• Characteristics of ideal solutions:
  • ΔH_mix = 0 (no enthalpy change upon mixing).
  • ΔV_mix = 0 (no volume change upon mixing).
  • A-A, B-B, and A-B interactions are similar.
• Non-ideal solutions show deviations from Raoult's Law:
  • Positive deviation: Vapor pressure is higher than predicted by Raoult's Law (A-B interactions weaker than A-A and B-B).
  • Negative deviation: Vapor pressure is lower than predicted by Raoult's Law (A-B interactions stronger than A-A and B-B).

Azeotropes

• Azeotropes are binary mixtures that have the same composition in the liquid and vapor phases and boil at a constant temperature.
• Minimum-boiling azeotropes: Show large positive deviations from Raoult's Law (e.g., ethanol-water mixture).
• Maximum-boiling azeotropes: Show large negative deviations from Raoult's Law (e.g., nitric acid-water mixture).

Colligative Properties

• Colligative properties are properties of solutions that depend on the number of solute particles but not on the nature of the solute.
• The four main colligative properties are:
  • Relative lowering of vapor pressure.
  • Elevation of boiling point.
  • Depression of freezing point.
  • Osmotic pressure.

Relative Lowering of Vapor Pressure

• The relative lowering of vapor pressure is proportional to the mole fraction of the solute in the solution.
• (p_0 - p_s) / p_0 = x_2, where:
  • p_0 is the vapor pressure of the pure solvent.
  • p_s is the vapor pressure of the solution.
  • x_2 is the mole fraction of the solute.

Elevation of Boiling Point

• The boiling point of a solution is higher than that of the pure solvent.
• ΔT_b = K_b m, where:
  • ΔT_b is the elevation of the boiling point.
  • K_b is the ebullioscopic constant (boiling point elevation constant), specific to the solvent.
  • m is the molality of the solution.

Depression of Freezing Point

• The freezing point of a solution is lower than that of the pure solvent.
• ΔT_f = K_f m, where:
  • ΔT_f is the depression of the freezing point.
  • K_f is the cryoscopic constant (freezing point depression constant), specific to the solvent.
  • m is the molality of the solution.

Osmotic Pressure

• Osmosis is the spontaneous flow of solvent molecules from a region of low solute concentration to a region of high solute concentration through a semipermeable membrane.
• Osmotic pressure (π) is the excess pressure that must be applied to the solution to prevent osmosis.
• π = CRT, where:
  • π is the osmotic pressure.
  • C is the molar concentration of the solution.
  • R is the ideal gas constant.
  • T is the absolute temperature.

Van't Hoff Factor (i)

• The van't Hoff factor (i) is the ratio of the actual number of particles in solution after dissociation or association to the number of formula units initially dissolved in solution.
• i = (Total number of moles of particles after dissociation/association) / (Number of moles of solute before dissociation/association)
• For solutes that do not dissociate or associate, i = 1.
• For solutes that dissociate (e.g., NaCl → Na+ + Cl-), i > 1.
• For solutes that associate (e.g., carboxylic acids in benzene), i < 1.
• Modified colligative property equations using the van't Hoff factor:
  • ΔT_b = i K_b m
  • ΔT_f = i K_f m
  • π = i CRT