GUEST AUTHOR Lewis Katz University of Connecticut Storrs, 06268
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Textbook Errors, 75
Notes for Introductory Chemistry
The Laftice Type of CsCl
One of the most persistent errors in chemistry texts is the statement that CsCl is body-centered cubic.' I n fact it is simple cubic, as is brought out in the following discussion. Associated with every crystal structure is a lattice. Based on the structure one may describe the lattice as the collection of points with identical atomic environments (including orientation). There are fourteen lattice types-the so-called Bravais lattices; for a given structure the lattice type is unique. Although a unit cell in the lattice could be chosen in an infinite variety of ways, one ordinarily follows the conventions of the crystal system in choosing the unit cell. CsCl is cubic, so one follows the cubic convention, which is to choose the smallest unit cell shaped like a cube. For CsC1, this unit cell has lattice points only at the corners. The lattice type is therefore primitive (simple), not body-centered. The reason the error is so common is easy to understand. The structure may be described by starting with a body-centered cubic lattice and placing cesiums a t the corners of each cubic cell and chlorines at the body centers. However, the body-centered lattice is not the lattice of the resulting structure, since the points of the body-centered array do not have identical environments. The X-ray evidence for the CsCl lattice type is unambiguous. Non-primitive lattice types are recognized by systematic absences among the general X-ray reflections. In particular, a body-centered lattice would be recognized by the systematic absence of all reflections for which the sum of the Miller indices was odd. No such systematic absences are observed for CsCI. The Number of Components for the CaCOa System
Applying the phase rule would he a much simpler task if it were not for the problem of counting components. No attempt will be made here to consider the question in general terms, however. The system CaC03(s), CaO(s), and C02(g) is widely chosen as an example of a two component system. However, the statement is sometimes made that if one begins with pure CaC03 which then partly dissociates, the system is a one component system. It is clear from substitution into the phase rule that this cannot he true. With three phases and one component the system would he invariant; it could only exist in equilibrium a t a single temperature and pressure, a triple point. I n fact the system can exist in equilibrium over a range of temperatures under diierent pressures of Con. Thus, CaCOa partly dissociated into CaO and C02is still a two component system. 282
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Journal of Chemicol Education
To emphasize the problem one should point out that commonly a pure substance which partly dissociates i s a one component system. For example pure PCls dissociating partly into PC13 and Clz would be a one component system. The diierence between the CaC03 and PC4 cases lies in the fact that for CaC03 the dissociation products are in different phases, whereas for PC& the dissociation products are in the same phase. For CaC03 the dissociation of pure CaC03 does not result in any new restrictions on the concentrations of the dissociation products as compared with the general case, so the number of components remains two; for PCls the dissociation of pure PC15 does result in a new restriction on the concentrations of the dissociation products as compared with the general case, so the number of components is reduced to one. CaC03 is not unique. Other components whose dissociation products are in two different phases, such as hydrates (for example N E ~ S O I . ~ O H Z are ~ )two , component systems when dissociation equilibrium is reached, even when prepared from the pure compound. Freezing Point Depression and Solute Volatility
I n most undergraduate chemistry texts, colligative properties are discussed together, and, for simplicity, it is assumed that the solute is non-volatile. I t is then reasonable and instructive t o show the origin of the boiling point elevation and the freezing point depression on the same vapor pressure versus temperature diagram, or on two similar diagrams. Although this practice is not wrong in itself, it often misleads. What is not brought out is the following: although t,he nonvolatility of the solute is a requirement for the boiling point elevation treatment (volatile solutes would affect the boiling points and might even bring about a substantial lowering), it is not a requirement for the freezing point depression problem. I n the latter case it is only the depression of the solvent vapor pressure which is important, and this will be brought about by the addition of solute whether or not the solute is volatile. It is not hard to convince students that the nonvolatility of the solute is not a requirement for freezing point depressions, since the least expensive widely used automotive antifreeze is certainly more volatile than the water solvent. The requirement that the solvent freeze out pure Suggestions of material sidt,able for this column and guest columns suitable for publication directly should be sent with a s many details s s possible, and particularly wit,h references to modern textbooks to W. H. Eberhxrdt, School of Chemistry, Georgia Institute of Technology, Atlanta, Georgia 30332. ' Since the purpose of this column is to prevent the spread and continuation of errors and not the evaluation of individual text,s, the sources of error discussed will not be cited. In order to be presented, an error must occur in at least two indepsndent recent standard books.
for the simple treatment to be valid is properly stated in these discussions. The point is usually made somewhere in most texts that if the solvent does not freeze
out pure the freezing point depression will be smaller and, with sufficient solid solubility, could even become a freezing point elevation.
Volume 44, Number 5, May 1967
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