Standard Enthalpies of Formation of Ions In Solution Theodros Solomon Addis Ababa University. P.O. Box 1176, Addis Ababa, Ethiopia
An examination of several p o ~ u l a rundergraduate ohvsical chemistry textbooks sh&& that the ihermody&aic properties of ions in solution is introduced a t different stages in the course, and, as a result, the definition of the standard enthalpyof formation of Hr inaqueous solution is worded in such different ways as to lead toward considerable confusion. Thus, for example, some texthooks (1-6)discuss AHfo of ions in an earlv the - chanter . on thermochemistn,. (before . thermodynamic treatment of solutions in general), whereas others 17) introduce this later on in a c h a ~ t e on r electrolvte solutio& Of those who introduce AH? ofions in solution in the chaoter on thermochemistrv, most (1-4) define the standard ekhalpy of formation of H + in an infinitely dilute aqueous solution as being equal to zero. All the others (5-7), define AHfo (the standard enthalpy of formation) of Hf a t unit activity as being equal to zero. Since a solution of unit activitv is not the same as an infinitelv dilute solution. students are confused on referring to diffeient texts and believe that there are different conventions for the definition of AHf of H+ in aqueous solution. Furthermore, they fail tosee how values of the standard Gibbs free enerev. euthalov. and entropy of formation of ions in solution coildall be tabulated toeether, with AHto values based ononeset ofdefinitions. (H+at infinite dilutibn), and the rest (AGE' and ASP) based on another convention (H+a t unit activity). Those definitions introduced during discussions on the thermodynamics of solutions invariably refer to the standard e n t h a l ~ vof formation of Hf at unit activitv. since the (by then) airlady introduced concept of standard states of solutions also refer to solutions of unit activitv. Consistencv is thus preserved. Furthermore, in a later treatment of electrochemical cells. the standard electrode potential for the following: 1 - H2(g,1bar) = Ht(o = 1) 2
+e
is defined as being equal to zero, by convention. This, of course. leads to settine the standard Gihhs free enerev. enthalpy; and entropy orformation of H - (at unit activyi).) as also being equal tnzero. A consistent set ofdefinitions there-
fore prevails only if one always refers to the formation of H+ at unit activity. This, however, does not imply that those definitions referring to the formation of H+ a t infinite dilution are wrong; only that they are introduced somewhat prematurely, and are, in fact, a result of the definition of the standard state of solutions. That both definitions are equivalent can only come after a study of the thermodynamics of solutions and after noting the following: 11) .-,
The -~~~ standard state of an electrolvte solution. as defined bv Albeny r61,is "the hypothetically ideal solutron at unit activity in which ions haw the pnqrrtrcs they du at infinite dilutiun". The ideal adution is thus an extrapolation uf the behavior at infinite dilution. (2) In ideal solutions, enthalpies are independent of composition; thus, provided one is dealing with ideal solutions,the standard enthalpy change for the formation of Ht of any composition, whether of unit activitv or of infinite dilution, is the same, since there is no enthalpy ihange on mixing the &nponents'of an ideal solution. ~~~~
~~~
Therefore, the definition of AH? of Hf in aqueous solution. as beine-eoual . to zero. is the same. whether one refers to an infinitely dilute solution or one of unit activity, but only because of the thermodvnamic properties of ideal solutions. and the definition of the stand&dstate of electrolyte solu: tions. A consistent treatment of the thermodynamic propertiesof ions insolutions is thus best left to later chapters until the thermodynamics of electrolyte solutions can be discussed fully. 1f one has to introduce them in the early chapter on thermochemistry, then reference should he made to the formation of Hf a t unit activity, since this is the convention that students will encounter in later chapters. Literature Clted 1. Adamso", A. W . A
Textbook 0iPhyaicol Chemistry, 2nd rd.; Academic: New York,
1979: p 154.
W.
271.
2. Afkins, P. Phyaicoi Chemistry, 3rd ed.: Oxford University: Oxford, 1987; p 90, 3. Banow, G. M . Physical Chemislry.4fh ad.; MeCraw-Hill: Kogskusha, Tokyo, 1979, p > ",A.. 4. Berry. R.S.: Rice. S. A ; R0s.J.Physical Chemistry; Wiley: New York, 1980:p 5. Maron, S. H.; Lando, J. 8. Fundomenlok a/ Physicol Chemistry; MacMillan: New
.
557.
York, 1974: p281. 6. Alberfy, R. A. Physical Chemislry, 7th ed.: Wiley:New York, 1987;p 60-1.253. 7. Levine. I. N. Physical Ch~miafry. 3rd ed.: McGraw-Hill: New York, 1988: p 288.
Volume 68 Number 1 January 1991
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