The True Meanlng of Isothermal To the Editor:
In a recent letter [1988, 65, 1871, D. Fain attempts to clarifv the meanina of the term isothermal to be attached to relations such as 2kT, < 0. He correctly poinb out that all that is required is that the initial and final temperatures be equal: the-path need not he known. In his proof he assumes that the pressure has to be constant throughout. The purpose of this letter is to point out that for a spontaneous reaction the relation AG < 0 is valid under more general conditions and that it is not necessarv to consider the surroundings. The discussion bv Fain assumes that (1) the oressure is the same throughoit and (2) the system is in contact with a thermostat. This is t o enahle him t o evaluate the work done during the process and to allow the use of thelaws of thermodynamics as they pertain to the universe. Even moderately violent reactions will in general lead t o inhomogeneities of both temperature and pressure. Thus, it is not realistic to assume that the pressure is constant. One can avoid details of the interactions between system and surroundings by using the laws of thermodynamics as they pertain to the system and the function-of-state property of G. The driving force of a reaction is the affinity A = -(aG/ a&,., Discussion of chemical reactions in terms of the affinitv is beine increasinelv used in the newer undermaduate tkxts. ~ h e a d v a n t a ~ e o f u s i the n g affinity is twofold~(1)only the system need be considered, (2) for a spontaneous chemi; ca1 reaction.4 is positive under any conditions whatsoever: A is the quantity of choice for a consideration of general changes. We note the following properties of A. A is directional: if A is positive in the forward direction then the affinity for the backward reaction is negative. A ?pontaneous reaction takes place in the direction of positive A; a t equilibrium A = 0. We consider a closed system described by T, p, composition I. We are eiven that the svstem undereoes a soontaneous chemical cKange till it reaches the statesdescribed by T , .D.. comoosition 11. We have to show that AG < 0. We assume forsirnblicity that the final stateisastateofequilibriumand that 11 is the equilibrium state closest to 1. We are thus excluding any metastable states. By assumption, then, A reaches 0 for the first time at composition 11. This is true when there is only one chemical reaction and for most cases of interest. We confine ourselves to a single chemical reaction described by [; the treatment can be extended to the case of many reactions without difficulty. Since the change is spontanepus, A(T, p, I) > 0, and as the reaction proceeds forward A decreases t o 0 a t composition 11.Since the process is irreversible. the chanee cannot be described bv a oath. However, since G is a f&ction of state we may callulatk AG bv considerine anv oath. Choose a reversible oath alone . . is iposir which T, p &co&tant. Then d~ = 4 d ~since tive at the beeinnine and becomes 0 only when i t reaches the equilibrium &ate, follows that A is positive all along the oath. Consequentlv AG < 0 for the spontaneous change considered. The clarification ~ v e by n D. Fain is very useful because the term isothermaiis o n e ~ t h ais t used often in chemistry courses. I t is quite correctly understood to refer to a process where the temperature of the system is constant. Unfortunately, most texts donot state results in their generality. For examole. it is often stated that. for isothermal orocesses involhng ideal gases, AU = 0 and AH = 0. While chis statement is true, i t is not general. The most general statement is that, for all processes involving ideal gases, if Tz = TI, AU = 0 and AH = 0. The path is irrelevant: U and H a r e functions of state depending on the temperature only. We have extended Fain's clarification to include any conditions whatso630
Journal of Chemical Education
ever: if a reaction takes place spontaneously AG < 0 provided only that the initial and final equilibrium states have the same temperature and pressure. The emphasis on the function-of-state property of G is important since there are quantities like q and w whose values depend not only on the initial and final states but also on the path. Sebastlan G. Canagaratna Ohio Nwlhern University Ada. OH 45810
Chernobyl, Ukraine-Not To the Editor:
Chernobyl, Russla
I would like to point out a glaring geographical error that recurs in an otherwise excellent article "Chernobvl-What Happened?" [1988, 65, 1037). The article state; that the accident a t the nuclear power plant happened in "Chernobyl, Russia," and discusses the events leading up to the accident, and the impact of the explosion on "European Russia and Western Europe." In fact, Chernobyl is not in Russia, but in Ukraine, an entirely separate country with its own people, history and culture. Ukraine, as well as White Russia, Lithuania, and Armenia, are all forcibly part of the Soviet Union, and to refer to a place in Ukraine, or Estonia, or White Russia as beine in Russia is entirelv incorrect. The conntries of the Union of Soviet Socialist Republics are as separate linguisticallv. culturallv. and ethnicallv as are the countries of West. e r n ~ u r o p e~: h t a i n~, e r m a n
