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Problems and Solutions to Accompany Chang’s Physical Chemistry for the Biosciences

Mark D. Marshall Amherst College
Helen O. Leung Amherst College


In an old joke, a New Yorker’s response to a tourist’s question, “How do you get to Carnegie Hall?” is “Practice, practice, practice.”  The same could be said for achieving success in science.  The only way to really learn chemistry is to do chemistry.  Our intention for this solutions manual is to encourage students of physical chemistry to work many problems – even more than they are assigned!  We know that our own mastery of the subject improved by solving all of the problems posed by Raymond Chang in his textbook and that new, previously undiscovered connections were revealed to us as we discussed how to approach each one.  We hope that students, too, will discuss these solutions because explaining how a question is answered is the best way of being certain that you understand the material yourself. 

 Indeed, we may further extend the opening metaphor.  Just as there is more to music than playing or singing the right notes at right time, there is more to science than simply getting the right answer.  Science is a process for recognizing important questions and how to set about seeking answers to those questions.  Conversation is an important part of that process, and with our own students we would be certain to discuss the assumptions involved in arriving at a solution and to explain the intermediate steps used to determine an answer.  We have tried to approximate that experience in this solutions manual by adopting a similar style; only for the simplest problems are the answers merely quoted.  

We have made every effort to ensure consistency in the values of the physical constants used, both internally and with those given in the textbook.  Similarly, we strived for a careful and consistent choice of units and symbols.  Of course, every measurement has an associated uncertainty that must be considered when comparing results from different experiments or those of experiment with predictions from theory.  It is good to practice this aspect of science, too, and we have done so by paying attention to the number of significant figures used in answering each problem.  The appropriate number of significant figures is determined by the data given.  So, for example, if a pressure is given as 0.729 atm, then the answer to the problem should contain three significant figures.  Quantities given as “1 mole” or “5 L” are taken to be exact.  Intermediate calculations are done retaining one extra digit, and the final answer is rounded to the correct number of significant figures as a last step.  (This is important; rounding too early will cause a loss of significance in your calculations.)  If a numerical result from a previous part of a problem is used in a subsequent part, the value with the extra digit is used.  In such cases, the answer to the earlier part would look similar to “98.7654 kJ mol-1 = 98.765 kJ mol-1,” where the first value, 98.7654 kJ mol-1, is used later in the problem and the “correct” answer is the second.  Of course, every rule has its exceptions, and we did choose to be more flexible in problems involving exponentiation and logarithms. 

 Throughout the preparation of this manual, Raymond Chang provided us with extremely valuable guidance; we are grateful for the opportunity to once again work with him.  Jane Ellis of University Science Books kept us calm and on task when we would begin to drift towards frenzy, and we thank her for overseeing the transformation of our default-settings LaTeX manuscript into a well-designed publication.  Paul C. Anagnostopoulos of Windfall Software provided timely advice regarding the discipline of EPS files from misbehaving graphics programs and handled the most incorrigible himself. 

Finally, one of us has performed at Carnegie Hall, but that is another story.. 

Mark D. Marshall 
Helen O. Leung 
Amherst, Massachusetts