Approved by Faculty Senate.

University Studies Course Approval

Department or Program: Chemistry

Course Number: 412

Semester Hours: 3

Frequency of Offering: Once per academic year, ~15 students per section, one section.

Course Title: Physical Chemistry I

Catalog Description: States of Matter and Equation of States. Thermodynamics of single component and multi-component systems. Equilibria. Computer applications. An introduction to quantum mechanics and spectroscopy. Meets University Studies Mathematics/Statistics Flag requirement. Prerequisites: one year each of college chemistry, physics, and calculus. Offered yearly.

This is an existing course previously approved by A2C2: Yes

This is a new course proposal: No

Proposal Category: Mathematics/Statistics Flag

Departmental Contact: Bill Ng, chairperson.

Email Address: __cbwng@winona.edu__

Department Approval and Date:

Dean’s Recommendation and Date: __________________________

USS Recommendation and Date: __________________________

A2C2 Recommendation and Date: __________________________

Faculty Senate Recommendation and Date: __________________________

VPAA Recommendation and Date: __________________________

Dean’s Recommendation and Date: __________________________

President’s Decision and Date: __________________________

MATHEMATICS/STATISTICS FLAG COURSE PROPOSAL

Chemistry 412: Physical Chemistry II (3 s.h.)

Chemistry is the science of matter and the changes matter can undergo. Physical chemistry deals with the physical principles underlying chemistry and seeks to account for the properties of matter (such as atoms, electrons, and energy) in terms of fundamental concepts. It provides the basic framework for branches of chemistry such as inorganic chemistry, organic chemistry, biochemistry, geochemistry, and chemical engineering. It also provides the basis for modern methods of analysis, the determination of structure, and the elucidation of the manner in which chemical reactions occur. Physical chemistry is divided into four majors areas: thermodynamics, quantum chemistry, kinetics, and statistical mechanics. This course provides an in-depth study of thermodynamics, which is the study of heat, work, energy, and the changes they produce in the states of systems. In a broad sense, thermodynamics studies the relationships between the macroscopic properties of a system (which include such properties as temperature, pressure, volume, and amount of substance) and the correlation of these macroscopic observables to the microscopic nature of the chemical universe. Mathematics is one the most important tools of physical chemistry. Much of physical chemistry involves casting physical problems into mathematical language. This involves development of mathematical models starting with microscopic predictions and correlating derived equations with macroscopic observations. Mathematical approaches include applications such as multi-variable functions, differential and integral calculus, differential equations, power series, and operator algebra. Computational data analysis via graphical and statistical treatments involves the use of software packages such as Mathcad, Excel, and HyperChem. The latter software also enables molecular visualization and enhances students’ abilities to correlate molecular structure to macroscopic behavior. As such, this course emphasizes a significant practice in the application of mathematical/statistical approaches to physical chemistry principles, thereby empowering the intellectual/critical thinking development of students in physical chemistry and enhancing their understanding of the chemical universe.

**Catalog Description**:

States of Matter and Equation of States. Thermodynamics of single component and multi-component systems. Equilibria. Computer applications. An introduction to quantum mechanics and spectroscopy. Meets University Studies Mathematics/Statistics Flag requirement. Prerequisites: one year each of college chemistry, physics, and calculus. Offered yearly.

This course includes requirements and learning activities that promote students' abilities to...

a. practice the correct application of mathematical or statistical models that are appropriate to their prerequisite knowledge of those areas; and

Requirements: Students are expected to apply various mathematical approaches in derivations of relevant macroscopic equations starting with fundamental concepts and principles in physical chemistry.

Activities: Students are provided with many opportunities (such as in-class discussions/exercises, problem sets, and quizzes/tests/examinations) to practice the correct applications of various mathematical approaches (such as multi-variable functions, differential and integral calculus, differential equations, power series, and operator algebra) in derivations and the manipulations of equations for systems under different constraints. The derivations begin with microscopic predictions/expectations and end with macroscopic results; results that can be compared to real world experimental observations.

Sample Activity: Starting with microscopic motions of gaseous molecules, students apply the techniques of multi-variable calculus in the derivations of macroscopic equations such as the Ideal Gas law ( PV = nRT ) and the kinetic molecular energy of gases ( T = 3/2RT ). Data will be provided to test the validity of model equations.

b. make proper use of modern mathematical or statistical methods appropriate to their level of prerequisite knowledge, to include, if statistics is used in a substantive way, the use of a statistical package with graphics capability when appropriate;

Requirements: Students are expected to make proper use of modern mathematical and/or statistical methods in the derivation and analysis of various physical chemistry principles. The applications of these methods will include both mathematical techniques and computational software.

Activities: Students will use mathematical approaches such as differential equations in the derivations of fundamental equations. Data analysis of real world problems will involve graphical and statistical software packages, such as Mathcad, Excel, and HyperChem. Mathcad and HyperChem will enable visualization of system properties (such as graphical interpretations of energy distributions and predications of molecular properties). Excel will provide both tabular and graphical calculations, in addition to statistical treatments of application problems. Students will choose appropriate mathematical/statistical techniques and applications in solving different problems in order to understand the relationships between microscopic and macroscopic properties. Laptops will be used in and outside the classroom for various applications.

Sample Activity: Students were asked to address the phenomena of "Boiling Eggs at 10,000 ft."

Given information:

If the barometric pressure falls 3% for each 1,000-ft increase in elevation, what is the boiling point of water at 10,000 ft? If the activation energy for cooking an egg is 125 kJ/mol, how long will it take to boil an egg at 10,000 ft to the same degree of hardness as a 3-min egg at sea level? (Assume that cooking an egg is a first-order rate process.)

Students work in groups to address the problem (using several mathematical approaches):

(A) First, the barometric pressure at 10,000 ft is calculated using either sequential iterations every 1,000 ft, or a derived model equation/graph ( P

_{1}= P_{o}(0.97)^{10}) with Excel or Mathcad.

Answer: 560 torr at 10,000 ft.

(B) Second, the boiling point of water at this pressure can be done several ways. One way is to use the Clausius-Clapeyron Equation (derived from equilibrium thermodynamics):

By assuming )V

_{vap}= RT/P and using dx/x = d(ln(x)) , one gets