^
question exchange
exam
M. Pilar Tarazona and Enrique Saiz Departamento de Qui'mica Ffsica Universidad de Alcala de Henares 28871 Alcala de Henares, Spain
Helmholtz free energy, A, or Gibbs free energy, G) depend on the composition, or in its role in the study of chemical equilibria (1-3). However, for the students, it is a difficult and subtle concept that parts from a not easy mathematical
definition (partial derivative), not absolute mensurable magnitude and a difficult to grasp concept of partial molar magnitude. a
Because a clear understanding of the concept of chemical potential is necessary prior to its use in the study of equilibrium, we present a two-part question that can be used in exams or in class discussions immediately after introducing the concept. The first part is the definition of chemical potential. The second part is a collection of false statements, most of them in different exams, gathered from students answers and the students are required to explain, from the definition of chemical potential, the reasons for their being erroneous. Question A. Define Chemical Potential B. The following statements are erroneous because they contain several mistakes and misconceptions. From the definition of chemical potential, explain the reasons why they are incorrect.
2. 3. 4. 5.
6.
7.
8. 9.
882
a
system is the
partial molar internal energy for the component. The chemical potential of a component in a system formed
by several components is the molar Gibbs free energy. The chemical potential of a system is the sum of the chemical potential of the components of the system. The chemical potential of 2 mol of A is twice the chemical potential of 1 mol of A. If a system is increased in size without varying the pressure, temperature, and composition, the chemical potentials of the components increase proportionally. In a system formed by 1 mol of each of two components, A and B, the addition of one extra mole of A do not alter the value of the chemical potential of B. Because the chemical potential is the partial derivative of Gibbs free energy, G, at P and T constant, chemical potential is independent of the values of P and T. The chemical potentials of pure substances can be measured directly in the laboratory using a potentiometer. The reason that there are not tables of chemical potential of pure substances is the difficulties encountered in purifying the substances.
Journal of Chemical Education
Cincinnati, OH 45221
Acceptable Solutions Part A
Chemical potential for a component in a system of several components is defined as the partial molar Gibbs free energy. Thus, the chemical potential for the component i,
The concept of chemical potential is prominent in physical chemistry courses, and most textbooks of physical chemistry and chemical thermodynamics explain its crucial importance focusing in the chemical potential either as a way to know how the thermodynamic properties (internal energy, U, enthalpy, H,
potential of a component in
oy
^
10
Understanding Chemical Potential
1. The chemical
eaneo
h
This is not the only possible definition for the chemical potential because, as most textbooks explain, definitions can be obtained from the other state functions such as internal energy, U, enthalpy 11, and Helmholtz free energy, A:
However, the first one relating chemical potential with Gibbs free energy is the most convenient in classical chemical thermodynamics, because the conditions of the derivative are constant temperature and pressure that are not only the most habitual conditions in chemistry but also they are the required ones for a partial molar property. Part B 1. The partial molar internal energy of component i is defined as:
Ut =
and measures how the internal energy of component i varies with the amount of i holding constants P, T, and the amounts of the other components. On the contrary, the definition of chemical potential as the partial derivative of internal energy holds constants S and V instead P and T (eq 2). Thus, p, and (7, are different magnitudes. Chemical potential is only the partial molar Gibbs free energy because the conditions of the derivative are P and T (see eq 1). 2. The molar Gibbs free energy Gm and the partial molar Gibbs free energy are the same only if the system has one component as can be seen substituting G=nGm in eq 1 for one component 'dnGm^ dn
'3G™
dn
+
G_
=
0 +
G„
G„
3. As stated in the definition, chemical potential is not a magnitude of the whole system but of each component of the system. Thus, it makes no sense to speak of “chemical potential of the system”. Besides chemical potential is an intensive property, and intensive properties are not additive for a system. Moreover, because the chemical potential is the partial molar Gibbs free energy, the sum of the products of chemical potential of each component by the mole amount of the component renders the value of Gibbs free energy, G, for the system G
4. Chemical
sions
are
=
2>ni
potential is an intensive property, its dimen-
energy per mole, thus the chemical potential of A
on the amount of A (provided that the composition of the system does not change). 5. The above answer is valid. Chemical potential is an intensive property and does not depend on the size of the system. 6. Chemical potential of the component i depends on the composition of the system; i.e., on the amounts of the rest of components and adding one mol of A modifies the molar A:B composition from 1:1 to 2:1. Thus, the chemical potential of both A and B are changed. Because these questions are prepared to be formulated immediately after the definition of chemical potential, the above reasoning can be enough, although the use of the Gibbs-Duhem relationship (that will be studier later on), allows a mathematical verification (1). 7. This statement is a frequent mathematical misconception about partial derivatives. Because the chemical potential is the partial molar Gibbs free energy and this magnitude depends on the pressure and temperature of the system, chemical potential depends also on P and T. Moreover because the same relationships hold for the partial molar magnitudes than for the corresponding magnitudes, the dependence of p; with P and Tcan be easily deduced (2)
does not depend
dp,
=
-S;dT + VtdP
8. The chemical potential of a pure substance is the molar Gibbs free energy, thus, an energy per mole and there is no device that can measure energies directly. (Apotentiometer measures voltages with a net current flow equal to
zero). 9. Because we cannot have absolute values of Gibbs free energy for a system in chemical thermodynamics, we can only calculate values of variation of this magnitude and could not have absolute values of chemical potential
Literature Cited 1.
Atkins,
P. W.
Physical Chemistry, Oxford University Press: Oxford, 1990.
2. Noggle, J. H. Physical Chemistry, Little, Brown and Company: Boston, 1985. 3. Hock, P. A. Chemical Thermodynamics; Oxford University Press: Oxford, 1983.
Make-up Exams: What’s a Professor to Do? Stephen W. Carper
University of Nevada-Las Vegas Las Vegas, NV 89154
Make-up exams are one of the most difficult issues to face a professor. When a student cannot take an exam at the same time and place as the other students, it places a burden on the professor. It may not be practical to have students take the exam earlier or later than the rest of the class. Exams in survey courses of biochemistry contain both quantitative, as well as qualitative, problems. As such, a new exam cannot be generated simply by changing
variables in the quantitative problems. Many students that take biochemistry are preprofessional (pre-med) majors. Treating the students in a fair manner (no early or late exams) is a major concern. With a large class it is inevitable that a few students will miss any specific test. It is an unreasonable, but common, expectation that a separate exam will be written for each student who needs to take a make-up. Students are not given an exam from an earlier year because these exams are placed on reserve in the library for the students to use as study guides. So, the dilemma is how to evaluate the students’ understanding of biochemistry without spending several hours on each student. The solution to this problem of make-up exams is to let the student write and then take their own exam. The students are given a one-page handout, outlining expectations for their exam. They are told that they will be graded subjectively on the quality of both their questions and answers. The students will receive: 10 points for a good question, five points for an average question, and zero points if it is not the correct type of question. The catch is that only thought type are allowed on the exam. This prevents the student from asking simple questions such as “What is the structure of alanine?” The students are given one week in which to complete the assignment. This allows a student who cannot attend the course for several weeks still to make up any missed exams. The exam is “open book,” and the students are encouraged to read other textbooks to gather ideas for questions. However, the students are cautioned that if they plagiarize a question out of a textbook they will receive a failing grade in the class. The students also are encouraged to seek guidance in crafting their questions during office hours. Students are warned to plan at least one hour’s time for each question/answer and not to wait until the night before the exam is due to start the project. This type of make-up exam is beneficial to both the student and professor. The student benefits by having time to think deeply about the subject material and not just to repeat lots of memorized facts. The professor benefits by not having to spend several hours writing an exam; as well as receiving ideas for potential thought questions for future exams.
Most students that have taken this type of make-up have expressed the opinion that initially they thought it would be very easy to do; but they were surprised at how much time it eventually took to complete the exam. Several students have commented that they enjoyed this type of evaluation. Although their questions/answers have proven to be very entertaining at times, overall the students have done very well in constructing thought-provoking questions. exam
Volume 72
Number 10
October 1995
883
