Jochen Vogt - Exam Survival Guide: Physical Chemistry

Springer International Publishing AG 2017

Jochen Vogt 1

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Abstract

This introductory chapter develops and discusses a concept of mathematically oriented problem-solving in physical chemistry. Based on a definition of the scientific discipline physical chemistry, the basic skills needed for successful problem-solving are identified. The concept of problem-solving is exemplified using a sample problem text. Finally, an overview of the problems in the various chapters is given, along with comments on the level of difficulty and thematic cross-links among the various topics.

Physical chemistry is a scientific discipline that explores chemical topics using physical theory and technique. This definition also explains the rather challenging nature of the subject physical chemistry taught as part of university curricula. It combines three basic skills that we must develop in the course of our studies. First, we should have enough of a chemical background to understand the problem. Second, we must know the fundamental laws of physics and we need to develop some sense of the significance of fundamental physical quantities in chemical contexts. Finally, experience including the ability of recognition is a fourth necessary ingredient that considerably enhances our effectivity in problem-solving. This is quite a lot. For the solution of a concrete, non-trivial problem of a certain complexity, all these skills need to be combined to work out a solution.

In this introductory chapter, a short guide to dealing with physical chemistry problems is offered to cultivate your problem-solving skills. It picks up on the typical difficulties experienced by students that I have noticed over a period of teaching of about 15 years at a faculty of engineering. The scheme assumes a problem of relatively high complexity that requires both logical linking of facts from one or more contexts, along with the setup and execution of a mathematical solution. The five different stages listed do not follow a strictly sequential scheme. Instead, these stages are merely simultaneous intellectual activities that work together to find the solution.

As an example of a concrete problem text, consider Problem on page 64. The problem text is reproduced here and the quantities provided and sought, along with the key-words according to points 1.a, 1.b, and 1.c, are highlighted:

Let us look at the various stages of this problem-solving scheme. Careful reading of the text is important. We must analyze the problem with regard to the quantities given and the quantities to be calculated. In preparation for stage 4, we should assign a unique symbol to each quantity. Note that in many cases it is crucial to distinguish between the initial value of a certain quantity and its value in the final state, or the values that the quantity takes during an ongoing process. In the concrete problem, we must distinguish between the vapor pressure of pure diethyl ether (a common symbol would be p ), and its vapor pressure in the binary mixture (symbol p ). Moreover, it is crucial to define all quantities in the same system of units, usually the SI system. Sometimes you need to convert some of the quantities (see Table A.2 in the appendix).

In the second stage, the essential issues , which are inevitable for the solution of the problem, are identified. A first assignment of the problem to a general topic is made based on the recognition of lecture content, seminar work, laboratory work, etc. Quite often, we find such essential issues coded in key words appearing in the problem text. In the concrete problem, such a key-word is the ideal mixture, implying the application of Raoults law (Eq.() on page 54). Another essential issue is stoichiometry and the definition of the mole fraction and molar mass. A third ingredient is the fact that the solvent diethyl ether and the unknown compound constitute a binary mixturea point that is not explicitly stated in the problem text. Sometimes, it is quite useful to make a sketch to collect and arrange such essential issues visually, and to identify the logical links between them. This is especially true for problems involving processes with an initial state and a final state.

Depending on your experience and the complexity of the problem, you will not immediately identify the correct approach. In this case, it is important to assess the points you do not yet understand (stage 3). Sometimes, it is good advice to think pragmatically. For example, do not become intimidated by problem texts filled with impressively long names of chemical compounds. Sometimes, you just need the molecular formula to determine a molar mass; in other cases, they can be replaced altogether by shorter symbols. At the stage where you do not yet see through the solution pathway, an detail that is lacking, such as an undefined quantity may be canceled out in the calculation. However, it may also indicate that you have missed something. Be hopeful and at the same time critical with the setup of your solution.

The next step is to write down the equations resulting from the list of essential issues identified (stage 4). The more experience we have, the easier it is to transpose the solution concept into a set of mathematical equations. In fact, at a level of deeper understanding, the students conceptual view based on essential issues and the mathematical formulation tend to merge. Also at this stage, we must be critical: the appearance of undefined quantities in the equations, but also too many redundant quantities, could indicate flaws in the approach and may force a reassessment. At the last stage, where the solution has been found, you should check the plausibility of your results. It is worth comparing the results with the initial estimations. An approximate agreement within the same order of magnitude strengthens the confidence with regard to the method of solution. Large differences, in contrast, require critical reflection on the entire method of solution. In this case, it is a good idea to consider possible technical errors first, e.g., arithmetic errors, such as confusion of signs or the addition of quantities with different physical units. Unexpected deviations in spite of a correct solution, in contrast, invite us to rethink a topic from a new perspective. In fact, in this case, a problem can prove to be highly useful to the individual student.