Chapter 14 & 15 Study Guide: Solutions and Chemical Kinetics

Chapter 14: Solutions

Definitions: Solute, Solvent, and Solution

Understanding the basic components of a solution is essential in chemistry. A solution is a homogeneous mixture composed of two or more substances.

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

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

• Solution: The resulting homogeneous mixture of solute and solvent.

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

Types of Intermolecular Forces and Solubility

Intermolecular forces determine the solubility of substances in various solvents.

• Types: Dispersion (London) forces, dipole-dipole interactions, hydrogen bonding, ion-dipole forces.

• Solubility Prediction: "Like dissolves like"—polar solutes dissolve in polar solvents (e.g., water), nonpolar solutes dissolve in nonpolar solvents (e.g., hexane).

• Example: Ethanol (polar) dissolves in water (polar) due to hydrogen bonding.

Saturated, Unsaturated, and Supersaturated Solutions

Solutions can be classified based on the amount of solute dissolved.

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

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

• Supersaturated: 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.

• Key Point: The number of particles produced depends on the formula. For example, NaCl produces 2 ions (Na+ and Cl-).

• Example: CaCl2 produces 3 ions (Ca2+ and 2 Cl-).

Concentration Units and Conversions

Concentration expresses the amount of solute in a given amount of solution.

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

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

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

• 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 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 drinks 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.

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

• 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 how adding solute lowers vapor pressure.

Henry’s Law: Solubility of Gases

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

• Equation: $C = k_P \times P$

• 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 of Reaction Rate

The reaction rate measures how quickly reactants are converted to products.

• Average Rate: Change in concentration over a time interval.

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

• Expression: $\text{Rate} = -\frac{1}{a} \frac{d[\text{A}]}{dt} = \frac{1}{b} \frac{d[\text{B}]}{dt}$ for $a \text{A} \rightarrow b \text{B}$

Rate Laws and Reaction Order

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

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

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

• Units for k: Depend on overall reaction order.

• Example: For a first-order reaction, $k$ has units of $s^{-1}$.

Rate Constant vs. Rate of Reaction

• Rate Constant (k): A proportionality constant specific to a reaction at a given temperature.

• Rate: The speed at which reactants are converted to products; depends on concentrations and $k$.

Method of Initial Rates

This method determines the rate law by comparing initial rates with varying reactant concentrations.

• Procedure: Measure initial rates for different concentrations; deduce exponents in rate law.

• Example: Doubling [A] while keeping [B] constant and observing rate change.

Determining Reaction Order from Concentration vs. Time Data

Reaction order can be deduced by analyzing how concentration changes over time.

• Zero Order: $[A]$ vs. time is linear.

• First Order: $\ln[A]$ vs. time is linear.

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

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

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

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 to react.

Arrhenius Equation

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

• Equation: $k = A e^{-E_a/(RT)}$

• 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 $E_a$ or predict $k$ at different temperatures.

Reaction Energy Diagrams

Energy diagrams illustrate the energy changes during a reaction.

• Activation Energy: Difference between reactants and transition state.

• Enthalpy Change (ΔH): Difference between reactants and products.

• Transition State: Highest energy point; unstable.

• Intermediates: Species formed and consumed during the reaction.

Reaction Mechanisms

A reaction mechanism describes the sequence of elementary steps leading to the overall reaction.

• Overall Reaction: Sum of elementary steps.

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

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

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 an elementary step, rate law is based on molecularity.

Catalysts

Catalysts increase reaction rates by lowering activation energy.

• Key Point: Catalysts are not consumed in the reaction.

• Example: Enzymes act as biological catalysts.