General Chemistry Study Notes: Solutions and Kinetics

Solutions

A. Molarity Calculations

Molarity (M) is a measure of concentration, defined as the number of moles of solute per liter of solution.

• Formula: $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Key Point: Always use the total volume of the solution, not just the solvent.

• Example: Dissolving 0.5 mol NaCl in enough water to make 1.0 L of solution gives $M = 0.5\ \text{mol/L}$.

B. Predicting Solubility Based on Intermolecular Forces

Solubility depends on the types and strengths of intermolecular forces between solute and solvent particles.

• "Like dissolves like": Polar solutes dissolve in polar solvents; nonpolar solutes dissolve in nonpolar solvents.

• Types of forces: Hydrogen bonding, dipole-dipole, and London dispersion forces.

• Example: Table salt (NaCl) dissolves in water due to strong ion-dipole interactions.

C. Identifying Solutes and Solvents

The solute is the substance being dissolved; the solvent is the substance doing the dissolving (present in greater amount).

• Example: In a sugar-water solution, sugar is the solute and water is the solvent.

D. Particle Drawings of Solutions

Particle diagrams visually represent the arrangement of solute and solvent particles in a solution.

• Key Point: Show solute particles evenly distributed among solvent particles.

• Example: Na+ and Cl- ions surrounded by water molecules in an aqueous NaCl solution.

E. How Solutes Reduce Vapor Pressure

Adding a nonvolatile solute to a solvent lowers the solvent's vapor pressure, a phenomenon known as Raoult's Law.

• Raoult's Law: $P_{solution} = X_{solvent} \times P^0_{solvent}$

• Explanation: Solute particles block solvent molecules from escaping into the vapor phase.

• Application: This effect is the basis for boiling point elevation and freezing point depression.

F. Calculations of Freezing Point Depression and Boiling Point Elevation

Adding a solute to a solvent changes its boiling and freezing points.

• Freezing Point Depression: $\Delta T_f = i K_f m$

• Boiling Point Elevation: $\Delta T_b = i K_b m$

• Where: $i$ = van 't Hoff factor, $K_f$/$K_b$ = constants, $m$ = molality

• Example: Adding salt to ice lowers its freezing point, causing ice to melt at lower temperatures.

Kinetics

A. Factors Affecting Reaction Rates

Several factors influence how quickly a chemical reaction occurs.

• Concentration: Higher reactant concentrations generally increase rate.

• Temperature: Higher temperatures increase kinetic energy and reaction rate.

• Catalysts: Lower activation energy, increasing rate without being consumed.

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

• Nature of Reactants: Some substances react faster due to their chemical properties.

B. Interpreting Data from Initial Rate Experiments

Initial rate experiments measure how fast a reaction proceeds at the very start, allowing determination of rate laws and reaction orders.

• Key Point: Vary concentrations of reactants and measure initial rates to deduce relationships.

• Example: Doubling [A] while keeping [B] constant and observing the rate change helps determine the order with respect to A.

C. Determining the Order of Reaction and Rate Law

The order of reaction with respect to each reactant shows how the rate depends on its concentration. The rate law expresses this relationship mathematically.

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

• Order: The exponents m and n are determined experimentally.

• Example: If doubling [A] doubles the rate, the reaction is first order in A.

D. Calculating the Rate Constant

The rate constant (k) is a proportionality constant in the rate law, specific to a reaction at a given temperature.

• Calculation: Use experimental data and the rate law to solve for k.

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

E. Identifying Order of Reaction from Graphs

Graphs of concentration vs. time or rate vs. concentration can reveal the order of a reaction.

• Zero Order: [A] vs. time is linear.

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

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

• Example: Plotting ln[A] vs. time yields a straight line for a first-order reaction.

F. Drawing and Labeling Reaction Progress Diagrams

Reaction progress diagrams show the energy changes during a reaction, including reactants, products, and intermediates.

• Key Features: Activation energy peak, intermediates (if any), and overall energy change (ΔE).

• Label: Reactants, products, transition states, and intermediates.

G. Determining Activation Energy

The activation energy (Ea) is the minimum energy required for a reaction to occur.

• Arrhenius Equation: $k = A e^{-E_a/(RT)}$

• Graphical Method: Plotting ln(k) vs. 1/T yields a straight line with slope $-E_a/R$.

H. Identifying Reactants, Products, Intermediates, and Catalysts from Elementary Steps

Elementary reaction steps reveal the detailed mechanism of a reaction.

• Reactants: Consumed in the overall reaction.

• Products: Formed in the overall reaction.

• Intermediates: Produced in one step and consumed in another; do not appear in the overall equation.

• Catalysts: Present at the start and end; facilitate the reaction but are not consumed.

• Example: In a two-step mechanism, a species that appears in the products of step 1 and reactants of step 2 is an intermediate.