© September, 2010, Cerro, Higgins & Whitaker ( Last Update: October 21, 2010)


Material Balances For Chemical Engineers

A text for the first course in chemical engineering

Historical Perspective: More than half a century ago, the typical chemical engineering program began with a course devoted to material and energy balances. The dominant text was Chemical Process Principles (1943) by Hougen and Watson. Stoichiometry was covered in four pages and restricted mostly to single independent reactions. More than sixty years later the typical chemical engineering program still begins with a course on material and energy balances. But much has changed in those intervening years. For example, students now have access to powerful computational software (Matlab, Mathematica) and simulators (Aspen) at their disposal. Yet the discussion of stoichiometry in standard undergraduate textbooks is still restricted to mostly single independent reactions, with little if any methodology for handling real world stoichiometry involving multiple independent reactions.

Paradigm Shift: Motivated by the "sketches" of Aris in Introduction to the Analysis of Chemical Reactors (1965), the "foundation" provided by Amundson in Mathematical Methods in Chemical Engineering (1966), and the "perspective" of Reklaitis in Introduction to Material and Energy Balances (1983), we have focused on providing a rigorous treatment of material balances for reacting systems. It is a treatment that will not require revision and upgrading in a subsequent course. Our presentation is based on the two axioms for the mass of multicomponent systems, and it is not limited to single independent reactions. The latter are dominant in the academic world and almost non-existent in the real world where our students must practice their profession. The philosophy behind this text is that the axioms and the associated proved theorems are the tools that we use to solve material balance problems, and are also the basis for the use of computational software to solve more demanding problems. We have purposely avoided any extensive use of software in this text because we believe that having a firm grasp of the theory is what is needed most. There is ample opportunity for students in subsequent courses to focus on numerical solutions of specific problems. In this text we make a clear the distinction between global stoichiometry, local stoichiometry, and the stoichiometry related to elementary reaction steps. It is of no value to the students to shield them from the underlying theory, thus we propose a paradigm shift from the approach initiated by Hougen and Watson to a new and rigorous analysis of chemical engineering fundamentals.


Material Balances For Chemical Engineers

Ramon L. Cerro
Department of Chemical Engineering
University of Alabama at Huntsville

Brian G. Higgins and Stephen Whitaker
Department of Chemical Engineering and Material Science
University of California at Davis

This text has been written for use in the first course in a typical chemical engineering program. That first course is generally taken after students have completed their studies of calculus and vector analysis, and these subjects are employed throughout this text. Since courses on ordinary differential equations and linear algebra are often taken simultaneously with the first chemical engineering course, these subjects are introduced as needed.

Macroscopic balance analysis represents a central issue for professional chemical engineers. This text provides both the foundation for that analysis and the transition from the prerequisite courses in mathematics, chemistry, and physics. Any text that represents a key element of an educational program should build upon the previously required courses in the program, and we have written a text which does that. In addition, any text that represents a key element of an educational program should provide a framework for future study. This text provides that framework for future courses in fluid mechanics, heat transfer, mass transfer, reactor design, and process design.

The first four chapters of this text deal with fundamental concepts, and the problems associated with these beginning chapters are meant to enhance the students' understanding of these concepts. The remaining chapters deal with applications of macroscopic balances, except for Chapters 6 which treats the subject of stoichiometry. Throughout the text, one will find a variety of problems beginning with those that can be solved by hand and ending with those that must be solved using computer software.

The problems in the text have been chosen to illustrate concepts and to help develop skills, and a detailed solutions manual has been prepared as an aid to instructors. Students are encouraged to use the problems to teach themselves the fundamental concepts associated with macroscopic balance analysis of multicomponent, reacting systems for this type of analysis will be a recurring theme throughout their professional lives.

Many students and faculty have contributed to the completion of this text, and there are too many for us to identify individually. However, we would be remise if we did not point out that Professor Ruben Carbonell first introduced this approach to teaching material balances at UC Davis in the late 1970's

Ramon, L. Cerro
Brian G Higgins
Stephen Whitaker