Chapter 13 and Chapter 14

Chemistry Chapter Summaries - Restructured

Chapter 13: Solutions

13.1: The Solution Process

  • Solute-Solvent Interactions: The formation of a solution involves interactions between solute and solvent molecules. Hydration is a specific type of solvation where the solvent is water.

  • Energy Changes and Solution Formation: The overall enthalpy change (ΔHsoln) is the sum of the enthalpy changes for separating solute molecules (ΔH1), separating solvent molecules (ΔH2), and forming solute-solvent interactions (ΔH3). ΔH1 and ΔH2 are endothermic (positive), while ΔH3 is exothermic (negative). Solution formation can be exothermic or endothermic overall. Exothermic processes tend to be spontaneous. A solution will not form if the overall enthalpy change is too endothermic. ΔH3 must be comparable in magnitude to ΔH1 + ΔH2. "Like dissolves like" – polar solvents dissolve polar solutes, and nonpolar solvents dissolve nonpolar solutes. Ionic substances generally do not dissolve in nonpolar liquids.

  • Solution Formation, Spontaneity, and Disorder: Spontaneous processes are favored by a decrease in energy (exothermic) and an increase in disorder (entropy). Solutions form unless solute-solute or solvent-solvent interactions are too strong relative to solute-solvent interactions.

  • Solution Formation and Chemical Reactions: Distinguish between the physical process of solution formation and a chemical reaction that leads to a solution.

13.2: Saturated Solutions and Solubility

  • Equilibrium: Crystallization is the reverse of solution formation. A dynamic equilibrium exists in a saturated solution between the processes of dissolution and crystallization.

  • Saturation: A saturated solution contains the maximum amount of dissolved solute. Solubility is the amount of solute required to saturate a solution. An unsaturated solution contains less solute than needed for saturation, while a supersaturated solution contains more. Crystallization of excess solute from a supersaturated solution is usually exothermic.

13.3: Factors Affecting Solubility

  • Solute-Solvent Interactions: "Like dissolves like." Miscible liquids mix in all proportions, while immiscible liquids do not. Hydrogen bonding leads to high solubility. Solubility often increases with increasing molar mass (due to increased London dispersion forces).

  • Pressure Effects: Henry's Law (Cg = kPg) describes the relationship between gas pressure and solubility. The solubility of a gas in a liquid increases with increasing pressure. Cg is the gas solubility, Pg is the partial pressure of the gas, and k is Henry's Law constant.

  • Temperature Effects: The solubility of most solid solutes in water increases with increasing temperature. The solubility of gases in water decreases with increasing temperature.

13.4: Ways of Expressing Concentration

  • Qualitative: Solutions can be described qualitatively as dilute or concentrated.

  • Quantitative:

    • Mass percentage: (mass of component / total mass of solution) * 100

    • Parts per million (ppm): (mass of component / total mass of solution) * 10^6 (1 ppm = 1 mg solute/L solution)

    • Parts per billion (ppb): (mass of component / total mass of solution) * 10^9

13.4.1: Mole Fraction, Molarity, and Molality

  • Mole fraction: (moles of component / total moles of all components)

  • Molarity (M): (moles of solute / liters of solution)

  • Molality (m): (moles of solute / kilograms of solvent)

  • Molality is independent of temperature, unlike molarity.

13.5: Colligative Properties

Colligative properties depend on the number of solute particles, not their identity.

  • Vapor Pressure Lowering: Raoult's Law (PA = XAPA°): The vapor pressure of a solution is lower than that of the pure solvent. PA is the solution's vapor pressure, XA is the mole fraction of the solvent, and PA° is the vapor pressure of the pure solvent.

  • Boiling-Point Elevation: ΔTb = Kbm. The boiling point of a solution is higher than that of the pure solvent. Kb is the molal boiling-point-elevation constant.

  • Freezing-Point Depression: ΔTf = Kfm. The freezing point of a solution is lower than that of the pure solvent. Kf is the molal freezing-point-depression constant.

  • Osmosis: The movement of solvent from a less concentrated to a more concentrated solution across a semipermeable membrane. Osmotic pressure (π) is the pressure needed to prevent osmosis: π = (n/V)RT = MRT. Isotonic solutions have the same osmotic pressure. Hypotonic solutions have lower osmotic pressure, and hypertonic solutions have higher osmotic pressure.

  • Molar Mass Determination: Colligative properties can be used to determine the molar mass of a solute.

13.6: Colloids

  • Colloids are intermediate between solutions and heterogeneous mixtures. Colloid particle size ranges from 10 to 2000 Å.

  • Tyndall Effect: Colloids scatter light.

  • Hydrophilic and Hydrophobic Colloids: Hydrophilic colloids are dispersed in water, while hydrophobic colloids are not. Hydrophobic colloids require stabilization (e.g., adsorption of ions).

  • Coagulation: Enlarging colloidal particles by heating or adding an electrolyte.

  • Dialysis: Separating colloidal particles using a semipermeable membrane.

Chapter 14: Chemical Kinetics

14.1: Factors that Affect Reaction Rates

  • Reactant concentration

  • Temperature

  • Presence of a catalyst

  • Surface area (for solids and liquids)

14.2: Reaction Rates

  • Reaction rate: The speed of a chemical reaction.

  • Average rate: Δmoles B / Δt (for A → B). The rate is negative with respect to reactants.

  • Instantaneous rate: The rate at a specific time (the slope of the tangent to the concentration vs. time curve).

  • Rate and Stoichiometry: For aA + bB → cC + dD, the rate is expressed as: -1/a(Δ[A]/Δt) = -1/b(Δ[B]/Δt) = 1/c(Δ[C]/Δt) = 1/d(Δ[D]/Δt)

14.2.1: Rates in Terms of Concentrations

Rates are typically expressed in units of M/s.

14.2.2: Reaction Rates and Stoichiometry

The stoichiometric coefficients are used to relate the rates of change of different reactants and products.

14.3: Concentration and Rate

  • Rate law: Expresses the relationship between rate and reactant concentrations. Rate = k[A]^m[B]^n.

  • Rate constant (k): A proportionality constant.

14.3.1: Reaction Order

  • Reaction order: The exponent of a concentration term in the rate law (m and n in the example above).

  • Overall reaction order: The sum of the individual reaction orders (m + n).

  • Reaction orders are determined experimentally.

14.3.2: Units of Rate Constants

The units of k depend on the overall reaction order.

14.3.3: Using Initial Rates to Determine Rate Laws

Initial rates can be used to determine the exponents in the rate law.

14.4: The Change of Concentration with Time

14.4.1: First-Order Reactions

  • Rate = -Δ[A]/Δt = k[A]

  • ln[A]t - ln[A]0 = -kt

  • ln([A]t/[A]0) = -kt

  • ln[A]t = -kt + ln[A]0

14.4.2: Half-Life

  • Half-life (t1/2): The time required for the reactant concentration to decrease to half its initial value.

  • For a first-order reaction: t1/2 = 0.693/k

14.4.3: Second-Order Reactions

  • Rate = k[A]^2

  • 1/[A]t = kt + 1/[A]0

  • t1/2 = 1/(k[A]0)

14.5: Temperature and Rate

14.5.1: The Collision Model

Molecules must collide with sufficient energy and proper orientation to react.

14.5.2: Activation Energy

  • Activation energy (Ea): The minimum energy required for a reaction to occur.

  • Activated complex (transition state): The unstable intermediate at the top of the energy barrier.

14.5.3: The Arrhenius Equation

  • k = Ae^(-Ea/RT)

  • ln k = -Ealn k = -Ea/RT + ln A

  • ln(k1/k2) = (Ea/R)(1/T2 - 1/T1)

14.6: Reaction Mechanisms

  • Reaction mechanism: The step-by-step pathway by which a reaction occurs.

14.6.1: Elementary Steps

  • Elementary step: A single step in a reaction mechanism.

  • Molecularity: The number of molecules involved in an elementary step (unimolecular, bimolecular, termolecular).

14.6.2: Rate Laws of Elementary Steps

The rate law of an elementary step is determined by its stoichiometry.

14.6.3: Rate Laws of Multi-step Mechanisms

The rate-determining step (the slowest step) determines the overall rate law.

14.6.4: Mechanisms with an Initial Slow Step vs. Mechanisms with an Initial Fast Step

If a fast step precedes the slow step, an intermediate is formed. The concentration of the intermediate is determined by assuming equilibrium in the fast step.

14.7: Catalysis

  • Catalyst: A substance that increases the rate of a reaction without being consumed.

14.7.1: Homogeneous Catalysis

The catalyst is in the same phase as the reactants.

14.7.2: Heterogeneous Catalysis

The catalyst is in a different phase from the reactants. Adsorption (binding to the surface) is often the first step.

14.7.3: Enzymes

  • Enzymes: Biological catalysts (proteins).

  • Substrate: The reactant in an enzyme-catalyzed reaction.

  • Active site: The region of the enzyme where the substrate binds.

  • Lock-and-key model: The substrate fits specifically into the active site.

  • Enzyme-substrate complex: The enzyme bound to the substrate.

  • Enzyme inhibitors: Molecules that bind to enzymes and decrease their activity.

  • Turnover number: The number of reactions catalyzed by one enzyme molecule per unit time.