Chapter 14 & 15 Study Guide: Solutions and Chemical Kinetics

Chapter 14: Solutions

Definitions and Identification of Solution Components

Understanding the basic terminology of solutions is essential for analyzing chemical mixtures.

• Solute: The substance dissolved in a solution; usually present in a smaller amount.

• Solvent: The substance in which the solute is dissolved; usually present in a larger amount.

• Solution: A homogeneous mixture of solute and solvent.

• Example: In salt water, salt is the solute and water is the solvent.

Intermolecular Forces and Solubility

The type and strength of intermolecular forces determine solubility and miscibility in solvents.

• Types of Intermolecular Forces:

  • Dispersion (London) forces

  • Dipole-dipole interactions

  • Hydrogen bonding

  • Ion-dipole forces

• Solubility Prediction: Polar solutes dissolve in polar solvents (e.g., water); nonpolar solutes dissolve in nonpolar solvents (e.g., hexane).

• Example: Ethanol (polar) dissolves in water; oil (nonpolar) dissolves in hexane.

Saturated, Unsaturated, and Supersaturated Solutions

Solutions can be classified based on the amount of solute dissolved relative to the solvent's capacity.

• Saturated Solution: Contains the maximum amount of solute that can dissolve at a given temperature.

• Unsaturated Solution: Contains less solute than the maximum possible; more solute can dissolve.

• Supersaturated Solution: Contains more solute than is normally possible at a given temperature; unstable and may precipitate.

• Example: Adding sugar to tea until no more dissolves creates a saturated solution.

Dissociation of Solutes

When ionic compounds dissolve, they break into ions; the number of particles affects solution properties.

• Example: NaCl dissociates into Na+ and Cl- (2 particles per formula unit).

• Formula: For ionic compounds, count the total number of ions produced per formula unit.

Concentration Units and Conversions

Concentration quantifies the amount of solute in a given amount of solution or solvent.

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Molality (m): $m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}$

• Percent by mass: $\%\text{ by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100$

• Percent by volume: $\%\text{ by volume} = \frac{\text{volume of solute}}{\text{volume of solution}} \times 100$

• ppm: $\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$

• ppb: $\text{ppb} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^9$

• Conversion: Use dimensional analysis to convert between units.

Effects of Temperature and Pressure on Solubility

Solubility of substances depends on temperature and pressure, especially for gases.

• Solids: Solubility generally increases with temperature.

• Gases: Solubility decreases with increasing temperature; increases with increasing pressure.

• Liquids: Effects vary; often less pronounced than for solids or gases.

• Example: Carbonated beverages lose CO2 (gas) when warmed.

Raoult’s Law: Vapor Pressure of Solutions

Raoult’s Law relates the vapor pressure of a solution to the vapor pressure of the pure solvent.

• Formula: $P_{\text{solution}} = X_{\text{solvent}} \cdot P^0_{\text{solvent}}$

• Where: $X_{\text{solvent}}$ is the mole fraction of the solvent; $P^0_{\text{solvent}}$ is the vapor pressure of the pure solvent.

• Application: Used to predict lowering of vapor pressure in solutions.

Henry’s Law: Solubility of Gases

Henry’s Law quantifies the solubility of a gas in a liquid as a function of pressure.

• Formula: $C = k_P \cdot P$

• Where: $C$ is the concentration of the gas, $k_P$ is the Henry’s Law constant, $P$ is the partial pressure of the gas.

• Example: Oxygen solubility in water increases with higher atmospheric pressure.

Colligative Properties

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

• Types:

  • Vapor pressure lowering

  • Boiling point elevation

  • Freezing point depression

  • Osmotic pressure

• Effect: More particles (from dissociation) increase the magnitude of colligative effects.

• Example: Adding salt to water lowers its freezing point.

Chapter 15: Chemical Kinetics

Main Factors Affecting Reaction Rates

Several factors influence how quickly a chemical reaction proceeds.

• Concentration: Higher concentration increases rate.

• Temperature: Higher temperature increases rate.

• Catalysts: Catalysts increase rate without being consumed.

• Surface Area: Greater surface area increases rate for heterogeneous reactions.

• Nature of Reactants: Some substances react faster than others.

Definition and Expression of Reaction Rate

Reaction rate measures the change in concentration of reactants or products over time.

• Average Rate: $\text{Average rate} = \frac{\Delta [A]}{\Delta t}$

• Instantaneous Rate: The rate at a specific moment; determined by the slope of the concentration vs. time curve.

• Example: Rate of disappearance of H2 in the reaction H2 + I2 → 2HI.

Rate Laws and Reaction Order

The rate law expresses the relationship between reaction rate and reactant concentrations.

• General Rate Law: $\text{Rate} = k [A]^m [B]^n$

• Order of Reaction: The exponents m and n indicate the order with respect to each reactant.

• Units for Rate Constant: Depend on overall reaction order (e.g., s-1 for first order).

• Example: For a first-order reaction, $\text{Rate} = k [A]$.

Rate Constant vs. Rate of Reaction

The rate constant (k) is a proportionality factor in the rate law; the rate is the actual speed of the reaction.

• Rate Constant: Characteristic of the reaction at a given temperature.

• Rate: Depends on concentrations and the rate constant.

Method of Initial Rates

This method uses initial concentration and rate data to determine the rate law experimentally.

• Procedure: Compare rates with varying initial concentrations to deduce reaction order.

• Example: Doubling [A] and observing rate change helps determine order with respect to A.

Determining Reaction Order from Concentration vs. Time Data

Analyzing how concentration changes over time can reveal the reaction order.

• Zero Order: Linear decrease in concentration over time.

• First Order: Exponential decrease; plot of ln[A] vs. time is linear.

• Second Order: Plot of 1/[A] vs. time is linear.

Integrated Rate Laws

Integrated rate laws relate concentration to time for different reaction orders.

• Zero Order: $[A]_t = [A]_0 - k t$

• First Order: $[A]_t = [A]_0 e^{-k t}$ or $\ln [A]_t = \ln [A]_0 - k t$

• Second Order: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + k t$

• Half-life: For first order, $t_{1/2} = \frac{0.693}{k}$

• Application: Use these equations to find concentration at a given time or time to reach a certain concentration.

Molecular Requirements for Reaction

For a reaction to occur, molecules must collide with proper orientation and sufficient energy.

• Activation Energy (Ea): Minimum energy required for reaction.

• Temperature: Higher temperature increases collision energy and frequency.

• Orientation: Molecules must be aligned correctly during collision.

Arrhenius Equation

The Arrhenius equation relates the rate constant to temperature and activation energy.

• Formula: $k = A e^{-E_a/(R T)}$

• Where: $A$ is the frequency factor, $E_a$ is activation energy, $R$ is the gas constant, $T$ is temperature in Kelvin.

• Application: Used to calculate activation energy or predict rate constant at different temperatures.

Reaction Energy Diagrams

Energy diagrams illustrate the energy changes during a reaction, including activation energy and enthalpy change.

• Transition State: Highest energy point; unstable arrangement.

• Intermediates: Species formed and consumed during the reaction.

• Activation Energy: Difference between reactant energy and transition state.

• Enthalpy Change (ΔH): Difference between reactant and product energies.

Reaction Mechanisms

A reaction mechanism is a sequence of elementary steps describing how a reaction occurs at the molecular level.

• Overall Reaction: Sum of elementary steps.

• Intermediates: Produced in one step, consumed in another.

• Catalysts: Added to speed up reaction, not consumed overall.

Elementary Steps and Molecularity

Elementary steps are individual reaction events; molecularity refers to the number of molecules involved.

• Unimolecular: One molecule involved.

• Bimolecular: Two molecules involved.

• Termolecular: Three molecules involved (rare).

• Rate Law: For elementary steps, rate law is based directly on reactant concentrations.

Catalysts

Catalysts increase reaction rates by providing an alternative pathway with lower activation energy.

• Effect: Lower activation energy, increase rate.

• Not Consumed: Catalysts are regenerated at the end of the reaction.

• Example: Enzymes act as biological catalysts.