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 pur- pose 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 sur- roundings.

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 to enahle him to evaluate the work done during the process and to allow the use of thelaws of thermo- dynamics as they pertain to the universe. Even moderately violent reactions will in general lead to 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 affini- tv is beine increasinelv used in the newer undermaduate tkxts. ~ h e a d v a n t a ~ e o f u s i n g the 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 direc- tional: 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 equilib- rium A = 0.

We consider a closed system described by T, p, composi- tion I. We are eiven that the svstem undereoes a soontane- ous 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 reac- tion 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 which T, p &co&tant. Then d~ = 4 d ~ . since .i is posir 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. -

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The clarification ~ v e n by D. Fain is very useful because the term isothermaiis one~that is used often in chemistry courses. I t is quite correctly understood to refer to a process where the temperature of the system is constant. Unfortu- nately, 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 state- ment 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 Hare functions of state depending on the temperature only. We have ex- tended Fain's clarification to include any conditions whatso-

ever: if a reaction takes place spontaneously AG < 0 provid- ed 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 Chernobyl, Russla To the Editor:

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 "Cherno- byl, 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 linguisti- callv. culturallv. and ethnicallv as are the countries of West. e rn~urope : ~ h t a i n , ~ e r m a n < France, Italy, and Spain. The proper way to refer to a town such as Chernobyl is to say: "Chernobyl, Ukraine" or "Chernobyl, the Soviet Union," or "Chernobyl, USSR".

I hope future authors will remember this distinction.

Andrew Fessak ' 1626 10th Avenue

Brooklyn. NY 11215

Student Science Tralnlng Programs-Large and Thrlvlng To the Editor:

The editorial titled "Educatine the Next Generation of Scientists," [1988,65,469] refers to thes'old, KSF-supported Summer Science Trainine Promams" and notes that "these kinds of programs appear to be making a comeback under NSF andlor private sponsorshio".

This is somewhat misleading, as the I988 Directory of Student Science Trainin2 Promums for High Abilitv Pre- college Students listed 5 ~ 7 prngrams-that provide courses, research opportunities, or a combination of the two. I would contend that this is not a "comeback" but a demonstration that this kind of activity is large and thriving.

I invite the readers of the Journal of Chemical Education w srart their own programs. Those interested can receive free a draft conv of "Student Science Trainine Proerams: A - - Handbook fo;i)irectors", which will provide some sugges- tions on how to oreanize and administer a ~ romam. Thev may also request acopy of the 1990~irector;if t i ey so wish.

E. G. Sherburne, Jr. Science Service

1719 N Street. N.W. Washington. DC 20036

630 Journal of Chemical Education