Exam 3 General Chemistry Study Guide: Gases, Thermochemistry, and Quantum-Mechanical Model of the Atom

Chapter 6. Gases

6.5 Applications of the Ideal Gas Law: Molar Volume, Density, and Molar Mass of a Gas

The ideal gas law is a fundamental equation describing the behavior of gases under various conditions. It allows calculation of properties such as molar volume, density, and molar mass.

• Ideal Gas Law: $PV = nRT$

• Molar Volume: The volume occupied by one mole of an ideal gas at standard temperature and pressure (STP).

• Density of a Gas: $d = \frac{PM}{RT}$, where M is molar mass.

• Molar Mass: $M = \frac{dRT}{P}$

• Relationship: Understand how pressure, volume, temperature, and amount of gas are interrelated.

• Example: Calculate the molar mass of a gas given its density at a known temperature and pressure.

6.6 Mixtures of Gases and Partial Pressures

Mixtures of gases exhibit properties that can be described using Dalton's Law of Partial Pressures.

• Partial Pressure: The pressure exerted by a single component in a mixture of gases.

• Dalton's Law: $P_{total} = P_1 + P_2 + P_3 + ...$

• Mole Fraction: $X_i = \frac{n_i}{n_{total}}$

• Relationship: $P_i = X_i P_{total}$

• Example: Calculate the partial pressure of oxygen in air.

6.7 Gases in Chemical Reactions: Stoichiometry Revisited

Stoichiometry involving gases uses the ideal gas law to relate volumes to moles and other quantities.

• Gas Stoichiometry: Use $PV = nRT$ to convert between volume and moles in reactions.

• Application: Calculate the volume of gas produced in a reaction at given conditions.

6.8 Kinetic Molecular Theory: A Model for Gases

The kinetic molecular theory explains the behavior of gases based on the motion of their particles.

• Postulates: Gases consist of tiny particles in constant, random motion; collisions are elastic.

• Boyle's, Charles's, Avogadro's Laws: Explained by kinetic theory.

• Average Kinetic Energy: $KE_{avg} = \frac{3}{2}RT$

• Root Mean Square Velocity: $u_{rms} = \sqrt{3RT/M}$

• Distribution of Molecular Speeds: Graphical representation shows most molecules have speeds near the average.

6.9 Effusion and Diffusion of Gases

Effusion and diffusion describe the movement of gas molecules through small openings and across spaces.

• Effusion: Movement of gas through a tiny hole.

• Diffusion: Mixing of gases.

• Graham's Law of Effusion: $\text{Rate}_1/\text{Rate}_2 = \sqrt{M_2/M_1}$

• Mean Free Path: Average distance a molecule travels between collisions.

6.10 Real Gases: The Effects of Size and Intermolecular Forces

Real gases deviate from ideal behavior due to molecular size and intermolecular forces.

• Van der Waals Equation: $[P + a(n/V)^2][V - nb] = nRT$

• Correction Factors: 'a' corrects for intermolecular forces, 'b' for molecular volume.

• Application: Recognize when to use the Van der Waals equation for non-ideal gases.

Equations and Relationships in Chapter 6

• $PV = nRT$

• $P_{total} = P_1 + P_2 + ...$

• $P_i = X_i P_{total}$

• $X_i = n_i / n_{total}$

• $KE_{avg} = \frac{3}{2}RT$

• $u_{rms} = \sqrt{3RT/M}$

• Graham's Law: $\text{Rate}_1/\text{Rate}_2 = \sqrt{M_2/M_1}$

• Van der Waals: $[P + a(n/V)^2][V - nb] = nRT$

Chapter 7. Thermochemistry

7.2 The Nature of Energy: Key Definitions

Thermochemistry studies energy changes in chemical reactions, focusing on heat and work.

• Energy: The capacity to do work or produce heat.

• Types of Energy: Kinetic, potential, thermal, chemical.

• System and Surroundings: The part of the universe under study and everything else.

• Units: Joule (J), calorie (cal), kilowatt-hour (kWh).

7.3 The First Law of Thermodynamics: There Is No Free Lunch

The first law states that energy cannot be created or destroyed, only transferred.

• First Law: $\Delta E = q + w$

• Internal Energy: The total energy of a system.

• Heat (q): Energy transferred due to temperature difference.

• Work (w): Energy transferred when an object is moved by a force.

7.4 Quantifying Heat and Work

Heat capacity and work are key concepts for measuring energy changes.

• Heat Capacity (C): Amount of heat required to raise temperature by 1°C.

• Specific Heat (c): Heat required per gram per degree.

• Equations: $q = m \times c \times \Delta T$

• Pressure-Volume Work: $w = -P \Delta V$

7.5 Measuring ΔE for Chemical Reactions: Constant-Volume Calorimetry

Calorimetry measures heat changes in reactions.

• Bomb Calorimeter: Measures heat at constant volume.

• Equation: $q_{cal} = C_{cal} \times \Delta T$

7.6 Enthalpy: The Heat Evolved in a Chemical Reaction at Constant Pressure

Enthalpy (H) is the heat content of a system at constant pressure.

• Enthalpy Change: $\Delta H = q_p$

• Endothermic vs. Exothermic: Endothermic absorbs heat; exothermic releases heat.

7.7 Constant-Pressure Calorimetry: Measuring ΔHrxn

Coffee-cup calorimeter measures enthalpy changes at constant pressure.

• Equation: $q = m \times c \times \Delta T$

7.8 Relationships Involving ΔHrxn

Enthalpy changes can be calculated using reaction equations and Hess's Law.

• Hess's Law: $\Delta H_{rxn} = \sum n \Delta H_f^\circ(\text{products}) - \sum n \Delta H_f^\circ(\text{reactants})$

7.9 Determining Enthalpies of Reaction from Standard Enthalpies of Formation

Standard enthalpy of formation is used to calculate reaction enthalpies.

• Standard State: Most stable form of a substance at 1 atm and 25°C.

• Thermochemical Equations: Show enthalpy changes for reactions.

Equations and Relationships in Chapter 7

• Kinetic Energy: $KE = \frac{1}{2}mv^2$

• $\Delta E = q + w$

• $q = m \times c \times \Delta T$

• $w = -P \Delta V$

• $q_{cal} = C_{cal} \times \Delta T$

• $\Delta H = q_p$

• $\Delta H_{rxn} = \sum n \Delta H_f^\circ(\text{products}) - \sum n \Delta H_f^\circ(\text{reactants})$

Chapter 8. The Quantum-Mechanical Model of the Atom

8.2 The Nature of Light

Light exhibits both wave-like and particle-like properties, which are fundamental to understanding atomic structure.

• Electromagnetic Radiation: Energy transmitted through space as waves.

• Amplitude, Wavelength, Frequency: Key properties of waves.

• Speed of Light: $c = \lambda \nu$

• Photoelectric Effect: Demonstrates particle nature of light.

8.3 Atomic Spectroscopy and the Bohr Model

Atomic spectroscopy studies the emission and absorption of light by atoms.

• Bohr Model: Explains hydrogen atom emission spectrum.

• Energy Levels: Electrons occupy quantized energy levels.

8.4 The Wave Nature of Matter: The De Broglie Wavelength, the Uncertainty Principle, and Indeterminacy

Particles such as electrons exhibit wave-like properties, described by the de Broglie wavelength and Heisenberg's uncertainty principle.

• De Broglie Wavelength: $\lambda = \frac{h}{mv}$

• Heisenberg Uncertainty Principle: $\Delta x \times \Delta p \geq \frac{h}{4\pi}$

8.5 Quantum Mechanics and the Atom

Quantum mechanics describes the behavior of electrons in atoms using wave functions and quantum numbers.

• Schrödinger Equation: Fundamental equation for atomic orbitals.

• Quantum Numbers: Principal (n), angular momentum (l), magnetic (ml), spin (ms).

• Atomic Spectroscopy: Defines energy levels of electrons.

• Energy of a Photon: $E = h\nu$

• Energy Change in Hydrogen: $\Delta E = -2.18 \times 10^{-18} J \left[ \frac{1}{n_f^2} - \frac{1}{n_i^2} \right]$

8.6 The Shapes of Atomic Orbitals

Atomic orbitals have distinct shapes and are described by probability density functions.

• Orbital Shapes: s (spherical), p (dumbbell), d, f (complex).

• Nodes: Points where probability density is zero.

• Phase: Sign of the wave function in different regions.

Equations and Relationships in Chapter 8

• Speed of Light: $c = \lambda \nu$

• Energy of a Photon: $E = h\nu$

• De Broglie Wavelength: $\lambda = \frac{h}{mv}$

• Heisenberg Uncertainty Principle: $\Delta x \times \Delta p \geq \frac{h}{4\pi}$

• Energy Change in Hydrogen: $\Delta E = -2.18 \times 10^{-18} J \left[ \frac{1}{n_f^2} - \frac{1}{n_i^2} \right]$

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