the quantitative and theoretical study of the properties of the elements in their various states of combination. Physical Chemistry Ira N.

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1 CHEM 331 Physical Chemistry Fall 2013 Systems In broad strokes, we can define Physical Chemistry as: the quantitative and theoretical study of the properties of the elements in their various states of combination. Or, in slightly different language, it is: A Textbook of Physical Chemistry Arthur W. Adamson the study of the underlying physical principles that govern the properties and behavior of chemical systems. Physical Chemistry Ira N. Levine It is the study of chemical systems such that we understand the quantitative relationships between the various properties of a system and the theoretical underpinnings of those relationships, from an atomic to a macroscopic point of view. In this study, we may apply many of the methodologies of physics to our problems of interest, but in the end we are chemists trying to understand chemical phenomena. This can include the study of the behavior of gases, the rates of chemical reactions, the powering of a battery or how the electronic behavior of atoms influences chemical bonding. Physical chemistry includes a study of the macroscopic behavior of matter; large scale systems like a glass of water, a superconducting magnet or a lead storage battery. This study is the province of the Physical Chemistry I (CHEM 331) course. Thermodynamics, as employed by Gibbs, will provide the framework for understanding this behavior. The goal of this course is to develop a thorough understanding of the Gibbs Free Energy and then to unleash its power in explaining the macroscopic chemical phenomena of equilibrium systems. Physical chemistry also includes a study of the microscopic behavior of matter; small scale systems like atoms and molecules. The Physical Chemistry II (CHEM 332) course makes this study its task. Quantum mechanics is used to explain the electronic structure of atoms and molecules and the spectroscopy needed to understand their behavior. Statistical mechanics is the theory by which we connect these two realms. For example, a simple molecular model of a gas (microscopic view) can explain, with the help of the Kinetic Molecular Theory (statistical mechanics), Boyle's Law (macroscopic view). The development of this theory is taken up in the Statistical Thermodynamics (CHEM 524) course.

2 Finally, the study of chemical reaction rates, both macroscopically and microscopically, rounds out our consideration of physical chemistry. How molecules come together in time and form new molecules, that which we view primarily from the perspective of the cauldron, is the focus of the Molecular Reactions Dynamics (CHEM 427) class. And even with this, much is left untouched. When we talk about macroscopic systems, we mean those systems with which we are usually familiar. (Bulb of Chlorine Gas) (Chemical Equil. btwn Dinitrogen Tetroxide & Nitrogen Dioxide) (Glass of Liquid Water) (Glass of Ice Water) (Electrochemical Cell)

3 H.B Callen describes with considerable clarity the nature of thermodynamic systems and why we can restrict our considerations to such drastically simple systems. Thermodynamics is a subject of great generality, applicable to systems of elaborate structure with all manner of complex mechanical, electrical, and thermal properties. It is the thermal properties on which we wish to focus our chief attention. Therefore it is convenient to idealize and simplify the mechanical and electrical properties of the systems that we shall study initially. Similarly, in mechanics we consider uncharged and unpolarized systems, whereas in electricity we consider systems with no elastic compressibility or other mechanical attributes. The generality of either subject is not essentially reduced by this idealization, and after the separate content of each subject has been studied it is a simple matter to combine the theories to treat systems of simultaneously complicated electrical and mechanical properties. Similarly, in our study of thermodynamics we idealize our systems so that their mechanical and electrical properties are almost trivially simple. When the essential content of thermodynamics has thus been developed, it again is a simple matter to extend the analysis to systems with relatively complex mechanical and electrical structure. The essential point we wish to stress is that the restrictions on the types of systems considered are not basic limitations on the generality of thermodynamic theory but are adopted merely for simplicity of exposition. Thermodynamic systems are separated from the surrounding Universe by an appropriate Wall. This wall can be rigid and diathermal, perhaps constructed of metal plates, or adiabatic, constructed of styrofoam. It could be a movable piston, semipermeable membrane, or some other such structure. Universe System Wall The system is expected to be in Equilibrium. This means the system: exhibits no Turbulence. contains no Thermal Gradients. is Independent of its History. Systems that are not in equilibrium, by this definition, are: Steel Depends on the nature of the cold-working, heat treatment, quenching and annealing.

4 Steel Ingots Glass Depends on its cooling rate during production. Glasses Further, initially, we will restrict ourselves to Simple Systems, defined by Callen as: Macroscopically homogeneous, isotropic, uncharged, and chemically inert, that are sufficiently large that surface effects can be neglected, and that are not acted upon by electric, magnetic or gravitational fields. This will restrict our State Variables, variables required to describe the State of the system, to: Volume (V) Pressure (P) Temperature (T) Amount (N) and rules out the following types of cases: System Droplets Rubber Band Atmosphere Pizoelectric Superconductor Extensive State Variable Surface Area Length Gravitational Field Electric Field Magnetic Field

5 Measurement of each state variable is according to the following instrumentation: Volume Ruler, Graduated Cylinder, Pycnometer, etc. Temperature Mercury in Glass Stem Thermometer, Thermistor, etc. Daniel Gabriel Fahrenheit (Fahrenheit's Temp Scale) Three Fixed Points: Brine Solution (0 o F) Ice-Point (32 o F) Body Temp (96 o F) Anders Celsius (Celsius' Temp Scale) Two Fixed Points: Ice-Point (100 o C) Steam-Point (0 o C) Amount Mass is measured using a Pan Balance. The mass measurement is then converted to an amount using the Molar Mass. # moles =

6 Pressure Large gaseous systems, like the atmosphere, can have their pressures measured using a Torricellian barometer. P atm = g h Barometer Smaller gaseous systems require a monomer for the measurement of their pressure. For an "open" manometer, the pressure is determined according to: P gas = P atm ± g h' Closed Manometer The fact that we need only a limited number of variables to describe the State of a complex molecular system can be illustrated in the following example. First consider a system containing a single molecule. Every time the molecule strikes the wall, we will have a spike in the system's pressure.

7 If we add another molecule to the system, the spikes in pressure will become more numerous and occasionally will compound. Very many molecules will give rise to a pressure that is more smooth but which still fluctuates with time. However, if we consider a system with Avogadro's Number of molecules in it, the fluctuations dampen out and the pressure is effectively constant. A view of the individual molecules and the time dependence of their coordinates is no longer needed. A single "average" pressure reading is sufficient to describe the macroscopic state of the system. Yes, occasional fluctuations from the purely random configuration of molecules which gives rise to this "average" pressure occur, but these fluctuations, given the extremely large number of molecules, are of an extremely small magnitude. The distribution of pressures around this "average" value is very sharp; very sharp indeed. The pressure is effectively a constant quantity. And, we can view the gas a being a single macroscopic fluid and the molecular picture can be ignored. We will find further that our state variables are not independent of each other and that we can restrict the necessary measurement of these parameters. An Equation of State will relate P, V, T and N.

8 Arthur W. Adamson It is customarily assumed that an Equation of State can always be written in a form involving only intensive quantities For our familiar Ideal Gas, we have: PV = NRT Defining the Molar Volume ( ) as = V/N, we have a new intensive state variable. Then, the equation of state can be written as: P = RT Walter J. Moore The state of a substance in thermal equilibrium can be fixed by specifying any two of the three variables, pressure, molar volume and temperature. g(p,, T) = 0 Using this specification, an Ideal Gas' equation of state is written as: P - RT = 0 H.B. Callen Such relationships, expressing intensive parameters in terms of the independent extensive parameters, are called equations of state. Knowledge of a single equation of state does not constitute complete knowledge of the thermodynamic properties of a system. We shall see, subsequently, that knowledge of all the equations of state of a system is [now] thermodynamically complete. It is the development of an equation of state for gaseous, liquid and solid systems that we now consider.