General Chemistry II: Chemical Kinetics, Solutions, and Thermodynamics Study Guide

Chemical Kinetics

Rate Laws and Reaction Order

Chemical kinetics studies the speed of chemical reactions and the factors affecting them. The rate law expresses the relationship between the rate of a reaction and the concentration of reactants.

• Rate Law: For a reaction aA + bB → products, the rate law is generally $\text{Rate} = k[A]^m[B]^n$ where k is the rate constant, and m, n are reaction orders.

• Integrated Rate Laws: These equations relate reactant concentration to time for zero, first, and second order reactions.

• Half-Life: The time required for half of the reactant to be consumed. For first order: $t_{1/2} = \frac{0.693}{k}$

Order	Rate Law	Integrated Rate Law	Half-Life
0	Rate = k	$[A] = [A]_0 - kt$	$\frac{[A]_0}{2k}$
1	Rate = k[A]	$\ln[A] = \ln[A]_0 - kt$	$\frac{0.693}{k}$
2	Rate = k[A]^2	$\frac{1}{[A]} = \frac{1}{[A]_0} + kt$	$\frac{1}{k[A]_0}$

Example: If a reaction is second order in NO2, and the rate constant is $4.3 \times 10^{-4} \text{M}^{-1}\text{s}^{-1}$, use the integrated rate law to find concentration after a given time.

Reaction Mechanisms and Energy Diagrams

Reactions often proceed via multiple steps, each with its own rate law. The rate-determining step is the slowest step, controlling the overall rate.

• Intermediates: Species produced in one step and consumed in another; do not appear in the overall reaction.

• Transition States: High-energy states at the peak of the energy diagram; represent the point of maximum energy during a reaction step.

• Energy Diagrams: Show the energy changes during a reaction, including activation energy and whether the reaction is exothermic or endothermic.

Example: In a multi-step reaction, intermediates are identified as substances not present in the overall equation but formed and consumed in steps.

Solutions and Colligative Properties

Concentration Units

Solutions are homogeneous mixtures of solute and solvent. Concentration can be expressed in several ways:

• Mole Fraction (X): $X_A = \frac{n_A}{n_{total}}$

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

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

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

Colligative Properties

Colligative properties depend on the number of solute particles, not their identity. These include boiling point elevation, freezing point depression, and osmotic pressure.

• Boiling Point Elevation: $\Delta T_b = iK_b m$

• Freezing Point Depression: $\Delta T_f = iK_f m$

• Osmotic Pressure: $\Pi = MRT$

Example: Calculate the osmotic pressure of a 0.045M solution at 30°C using $\Pi = MRT$.

Solubility and Henry's Law

Solubility is the maximum amount of solute that can dissolve in a solvent at a given temperature. Henry's Law relates the solubility of a gas to its partial pressure:

• $C = k_H P$ where C is concentration, k_H is Henry's law constant, and P is partial pressure.

Example: Use Henry's law to find the concentration of O2 in water at a given partial pressure.

Thermodynamics and Reaction Energetics

Exothermic vs. Endothermic Reactions

Reactions can release or absorb energy:

• Exothermic: Release heat; products have lower energy than reactants.

• Endothermic: Absorb heat; products have higher energy than reactants.

Energy diagrams show the difference in energy between reactants and products, and the activation energy required.

Reference Data and Constants

Useful Constants and Conversions

• 1 atm = 760 torr = 101.3 kPa = 1.013 bar = 14.7 psi

• R = 0.08206 L·atm/(mol·K) or R = 8.314 J/(mol·K)

• 1 g = 1,000 mg

• 1 mL = 1 cm3

Key Formulas

• Ideal Gas Law: $PV = nRT$

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

• Osmotic Pressure: $\Pi = MRT$

• Boiling Point Elevation: $\Delta T_b = iK_b m$

• Freezing Point Depression: $\Delta T_f = iK_f m$

Periodic Table

The periodic table organizes elements by atomic number and properties. It is essential for determining molar masses, element classification, and chemical behavior.

Tables

Experimental Data Table

This table summarizes initial concentrations and initial rates for a reaction, useful for determining rate laws and rate constants.

Trial	Initial [A]	Initial [B]	Initial [C]	Initial Rate
1	0.075M	0.030M	0.020M	1.40 × 10-2 M/s
2	0.150M	0.030M	0.020M	2.80 × 10-2 M/s
3	0.075M	0.060M	0.020M	2.80 × 10-2 M/s
4	0.075M	0.030M	0.040M	2.52 × 10-2 M/s

Purpose: Used to determine reaction order with respect to each reactant and calculate the rate constant.

Additional info:

• Questions cover topics from Ch.12 (Physical Properties of Solutions) and Ch.13 (Chemical Kinetics), with supporting reference material from Ch.5 (Gases) and Ch.6 (Thermochemistry).

• Reference sheet and periodic table are standard exam aids for General Chemistry II.