Physical Chemistry

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Gases and the Four Laws of Thermodynamics

The laws of thermodynamics form the foundation for all systems involving the exchange of energy. Explore these processes and identify the fundamental physical quantities that define the world around us.

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Ideal Gases

Learn about ideal gases, the theoretical gases that adhere to the ideal gas law, which is the theoretically flawless mathematical relationship among pressure, volume, and temperature.
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Non-ideal Gases

Study the non-ideal gases, whose molecules are bound by attractive forces that make them behave more realistically.
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Zeroth Law of Thermodynamics

Dig into applications of the zeroth law of thermodynamics, which states that if two thermodynamic systems are in equilibrium with a third system, they are in equilibrium with each other.
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First Law of Thermodynamics

Apply your knowledge of the first law of thermodynamics, an application of the law of conservation of energy, to solve for heat, entropy, and other variables.
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Second Law of Thermodynamics

The second law of thermodynamics states that the entropy in an isolated system increases over time. Use this knowledge to identify characteristics in systems, and calculate changes in entropy and efficiency.
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Third Law of Thermodynamics

The third law of thermodynamics, developed by Walther Nernst, states that as a system approaches absolute zero, the entropy change of a system undergoing a reversible isothermal process reaches zero as well.
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Gibbs Energy and Chemical Potential

What drives a physical or a chemical process to occur? Dig deep into the concepts of free energy and chemical potential to determine spontaneity conditions and characterize the state of equilibrium.

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Spontaneity Conditions

How do changes in free energy make a process spontaneous or non-spontaneous?
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Gibbs Energy and Helmholtz Energy

Compare and contrast Gibbs and Helmholtz free energies and how they are used to derive many thermodynamic mathematical relationships.
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Natural Variable Equations, Partial Derivatives, and Differential Equations

Employ different techniques of partial differentiation and integration to derive the relations between thermodynamic properties.
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Maxwell Relationships

Gain a better appreciation of the application of the laws of thermodynamics as you employ Maxwell relations to evaluate properties for real and ideal systems.
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Fugacity

Fugacity is a measure of how likely a gas is to expand or escape; apply this property to model real gas behavior.
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Chemical Equilibria

The laws of thermodynamics ultimately point to the state of equilibrium. Understand and be proficient in the quantitative treatment of equilibrium and the factors that affect equilibrium. Examine equilibria involving gaseous, aqueous, and condensed phases, as well as equilibria in single- and multiple-component systems.

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Chemical Equilibrium

Review chemical equilibria, where reactants and products are both present in constant ratios.
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Solutions in Condensed Phases

Analyze how chemical equilibria occur and are stabilized in solutions in the condensed phase.
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Changes in Equilibrium Constants

Equilibrium constants, unlike their names, have the ability to change depending on system conditions, such as a change in temperature.
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Pre-Quantum Mechanics

Move from the classical world to one in which quanta dictate the interactions of matter and energy. Uncover the origins of the quantized nature of electronic transitions, and conceptualize the behavior of atoms governed by the laws of quantum mechanics.

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Laws of Motion

Review Isaac Newton's fundamental laws of motion that encapsulate the motion of bodies of matter.
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Unexplainable Phenomena

Analyze the "unexplainable phenomena" that confounded classical scientists: atomic line spectra, atomic structure, light, and the photoelectric effect.
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Atomic Spectra and Structure

Use the Rydberg equation to calculate wavelengths and wavenumbers of light.
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The Photoelectric Effect

Learn about Heinrich Hertz's and Philipp Eduard Anton von Lenard's earliest discoveries regarding the photoelectric effect.
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The Nature of Light

Scientists have studied and debated light for centuries. Analyze historical light experimentation, including Thomas Young's double-slit experiment.
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Quantum Theory

Apply Max Planck's and Albert Einstein's laws to determine the energy of light.
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Bohr’s Theory of the Hydrogen Atom

Evaluate how Niels Bohr repurposed the Rydberg equation to develop the nuclear atomic theory and the quantization of a measurable quantity.
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The de Broglie Equation

Louis de Broglie hypothesized that particles like electrons could have wave properties. Using the de Broglie equation, predict the relationship between wavelength and momentum.
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Quantum Mechanics

Quantum mechanics forced scientists at the turn of the century to consider a new version of reality. Explore the foundational principles of quantum mechanics, from the mysterious nature of wave-particle duality to the probabilistic wavefunction and how it governs the behavior of our microscopic world. You will find the truth of the quantum mechanics to be stranger than science fiction.

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The Wavefunction

Explain how the behavior of a wave can be expressed mathematically to determine expressions that are acceptable wavefunctions.
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Observables and Operators

Determine the values of observables, and use various operators to study eigenvalues and eigenfunctions.
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The Uncertainty Principle

Use Heisenberg's uncertainty principle to determine the measurement of uncertainties in various contexts.
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Born Interpretation of the Wavefunction

Building upon Heisenberg's uncertainty principle, use the Born interpretation of the wavefunction to calculate probabilities of where electrons are located.
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Normalization

Normalize wavefunctions in accordance with Born's interpretation of the wavefunction.
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Schrödinger Equation

Erwin Schrödinger's equation is used to determine a significant observable in quantum mechanics: energy.
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Average Values and Tunneling

Calculate average values (or expectation values) of various observables, and predict where and when tunneling can occur in a system.
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Degeneracy

Apply the concept of degeneracy, where distinct linearly independent wavefunctions have the same energies with different sets of quantum numbers.
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Orthogonality

If two wavefunctions are multiplied together, and their integral is zero, they are considered orthogonal. Demonstrate via proofs how wavefunctions can be orthogonal to one another.
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Model Systems and the Hydrogen Atom

Explore various model systems in quantum mechanics, including the classical harmonic oscillator, two- and three-dimensional rotations, and the hydrogen atom wavefunctions.
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Symmetry in Quantum Mechanics

Evaluate how symmetry is viewed in various wavefunctions.
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Atoms and Molecules

What are the foundations of chemistry? Chemistry explains everything based on atoms and molecules. Atoms and molecules are explained through the application of quantum mechanics.

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Spin

Explain the importance of the innate angular momentum all electrons have known as spin.
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The Helium Atom

Apply the basic principles of quantum mechanics to develop models for atomic helium as well as some simple diatomic molecules.
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Spin Orbitals and the Pauli Principle

According to the Pauli principle, each electron in a given system has a unique set of four quantum numbers. Use this principle to determine the spin orbitals for electrons.
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Other Atoms and the Aufbau Principle

Assign electrons to spin orbitals in more complex, larger atoms.
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Symmetry

Begin your study of symmetry with group theory: symmetry operations and groups, character tables, the great orthogonality theorem, symmetry-adapted linear combinations, and valence bond theory.
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Rotational and Vibrational Spectroscopy

What are the practical applications of quantum mechanics? Spectroscopy. From quantum mechanical models, we develop basic principles of rotational (microwave) and vibrational (infrared) spectroscopy. Spectroscopy is a takeaway tool of this physical chemistry course.

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Vibrations in Molecules

Determine the number of vibrational degrees of freedom for various molecules.
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Kinetics

Explore the realm of kinetics, or how, and how fast, a reaction happens. Master the derivation and utility of the rate equations for reactions at different orders. Get acquainted with the different reaction mechanisms, including enzyme-catalyzed, parallel, consecutive, chain, and oscillating reactions, as well as the theories governing reaction rate.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

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Re-answering questions correctly will improve your weighted average status.

Rates and Rate Laws

Review the speed at which chemical reactions occur with rates and rate laws.
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Enzyme Kinetics

Investigate how enzymes catalyze chemical reactions, how reaction rates are measured experimentally, and how varying reaction conditions affect the rates.
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Equilibrium for a Simple Reaction

When a reaction approaches equilibrium, concentrations of reactants and products start to equalize.
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Temperature Dependence

Learn how temperature affects chemical reaction rates and how activation energy is derived from temperature and enthalpy changes.
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The Steady-State Approximation

The steady-state approximation takes into account the fact that intermediates often occur in reactions but are neither the reactant nor product. Evaluate how the approximation is used to derive rate laws.
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Chain and Oscillating Reactions

Compare and contrast chain and oscillating reactions and how they are graphed with respect to temperature and pressure.
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