###### Learning Outcomes:

By the end of this module, you should be able to:

Employ statistical thermodynamics to understand the distribution of molecular states by considering configurations and weights; derive the Boltzmann distribution and use it to predict the populations of states in systems at thermal equilibrium; define what is meant by the molecular partition function, interpret it, and, in certain simple cases, calculate it; describe how thermodynamic information, such as the internal energy or the statistical entropy of a system, may be extracted from the partition function; employ the partition function to obtain any thermodynamic function, for example, the Helmholtz energy, the pressure, the enthalpy, the Gibbs energy, for a system; factorize the molecular partition function into a product of translational, rotational, vibrational and electronic contributions.

Understand the dispersal of energy and the origin of the spontaneity of physical and chemical change; define the property of entropy in thermodynamic terms and describe it from a statistical viewpoint; understand that entropy is a state function; Describe the entropy changes that accompany specific processes such as expansion, phase transition, and heating.

Understand the criteria for spontaneity in terms of the properties of the Helmholtz energy and the Gibbs energy; use the Gibbs energy to express the spontaneity of a process in terms of the properties of a system; use the Gibbs energy to predict the maximum non-expansion work that a system can do; use the fact that the Gibbs energy is a state function to find relations between system properties in terms of Maxwell relations.

Describe mixtures of substances in thermodynamic terms using the class of properties known as partial molar quantities; describe the thermodynamics of mixing; apply the concept of the chemical potential of a substance to describe the physical properties of liquid mixtures; understand how Raoult’s and Henry’s laws may be used to express the chemical potential of a substance in terms of its mole fraction in a mixture; understand the effect of a solute on the thermodynamic properties of a solution, e.g. the lowering of vapour pressure of the solvent.

Describe the use of phase diagrams as a means to discuss the thermodynamic description of the stabilities and transformations of one or more phases; describe the characteristic properties of phase transitions; apply the phase rule to explain phase stability and equilibria between phases for systems involving more than one component; describe the thermodynamic aspects of phase transitions with reference to the dependence of stability on conditions such as temperature and pressure and to the location of phase boundaries.

Execute laboratory experiments involving the construction of simple electrochemical cells and the measurement of equilibrium processes; Calculate relevant physical properties from laboratory experiments, including appropriate propagation of measurement uncertainty; explain the relationship between Gibbs Free Energy and equilibrium; describe the relevance of equilibrium to simple electrochemical systems; use the Nernst equation to predict the energy generated by simple Galvanic cells to extract parameters such as electromotive force and solubility constant.

###### Indicative Module Content:

Lectures 1 & 2 - The Energy Levels of Atoms and Molecules

Quantization of energy; electronic, translational, rotational and vibrational energies.

Workshop 1: Calculating the Energies of Atoms and Molecules

Calculating electronic, translational, rotational and vibrational energies of systems; expressing energies as wavelengths and wavenumbers, unit conversion in mathematics.

Lectures 3 & 4 - The Boltzmann Factor and Partition Functions Probability; ensemble energy; electronic, translational, vibrational, rotational, molecular partition functions.

Workshop 2 – The Distribution of Energy

Calculating the energies and degeneracies of simple systems; deriving expressions for partition functions. The laws of logs in mathematics.

Lecture 5 & 6 - Statistical Energy & Entropy

System partition functions for solid and fluid systems; statistical (ensemble) molecular energy and the link to internal energy. The third law of thermodynamics, micro- and macro-states, the relationship between absolute entropy and the partition function.

Workshop 3 – Elementary Statistical Mechanics

Using the partition function to determine the internal energy and absolute entropy of a particle or collection of particles; differentiation in mathematics.

Lectures 7 & 8 - The First Law

Heat, work and pressure (classical and statistical); state and path functions; reversible processes; enthalpy; heat capacity.

Workshop 4 – Elementary Classical Thermodynamics

The directionality of heat and work; reversible and irreversible gas expansion, interpreting calorimetry data.

Lectures 9 & 10 - The Second Law

Entropy, and spontaneity, reversible and irreversible heat exchange, entropy temperature dependence, heat flow and heat engines.

Workshop 5 – Entropy Changes in Ideal Gas Systems

The relationship between entropy, enthalpy and internal energy. The relationship between constant volume and constant pressure heat capacity. Integration and partial derivatives in mathematics.

Lectures 11 and 12 – The Helmholtz and Gibbs Energy

Derivation of Gibbs and Helmholtz energies; natural variables; the Maxwell relations; statistical Gibbs and Helmholtz energies. Inequalities in mathematics.

Workshop 6 – Thermodynamic Functions

Manipulating thermodynamic functions under system constraints (isochoric, isothermal etc.), deriving and using the Maxwell relations to determine thermodynamic system changes; second order derivatives in mathematics.

Lectures 13 and 14 - Physical Transformation

Open thermodynamic systems, chemical potential as applied to phase change, chemical potential in mixtures; partial molar quantities; phase diagrams and phase boundaries; Clausius-Clapeyron equation.

Workshop 7 – Phase Diagrams

Interpreting phase diagrams and calculating thermodynamic properties from them; the relationship between the chemical potential of two phases.

Lectures 15 and 16 – Mixtures and Composition

Vapor pressure; Ideal and non-ideal solutions; Raoult and Henry's laws; liquid-liquid solution activity; composition diagrams; mixing energy; liquid-solid solutions; colligative properties.

Workshop 8 – Properties of Solutions

Calculating vapour pressure for liquid-liquid and liquid-solid mixtures; using colligative properties to determine molecular mass.