textbook Forum RALPH K. BIRDWHISTELL

Universily of West Florida Pensacola. FL32504

Chemical Equilibrium in the General Chemistry Course Vladimir E. Fainzilberg and Stewart Karp C. W. Post Campus of Long Island University, Greenvale, NY H548

Chemical equilibrium is a major topic in first-year col- lege chemistry courses for science majors. The first chap- ters on chemical equilibrium in current textbooks' for these courses make an "error" in the solution of certain types of equilibrium problems. This diminishes the stu- dent's understanding of chemical equilibria and may add to their difficulties with subsequent equilibrium topics, for example, acid-base equilibria. These textbooks carefully ex~ l a in that mass action exoressions can be written for m y chemical equation tequil~bnum chapter! even lfthv ac- tual mechanism of the rractlon IS multlsteo. They make clear that most reactions are indeed multikep (kinetics chapter) and generally (somewhere) state, but usually with little emphasis, that a t equilibrium each elementary step in the mechanism is also a t equilibrium (the principle of microscopic reversibility). This means that a t equilib- rium some of each intermediate is in the equilibrium mix- ture, and the amounts depend on the values of the equilib- rium constants for the elementary steps.

All currently available first-year chemistry textbooks that we examined' ignore this situation in their disms- sions of equilibrium calculations. A simple illustration is the example in which the initial concentration, CA, of a re- actant, A, is given along with an equation and the equilib- rium constant, K. The equilibrium concentrations of the reactant [A] and product [B] are to be calculated:

The problem is completed by stating that a t equilibrium [A] = CA - x and [Bl = x and then solving for x:

where x is the molarity of A reacted and the molarity of B formed.

This expression is adequate unless some of the reacting A forms an intermediate whose presence at equilibrium means that [Bl # x. Many problems in which the initial conditions (concentrations or partial pressures) are given and equilib- rium conditions are desired can be devised and, when more complicated reactions are used, they are among the more challenging equilibrium calculations presented to students in their early introduction to chemical equilibria. But they are solved bv i m o r i n ~ Dossible intermediates. in s ~ i t e of the un- derstan&ng that most reactions are multi&ep.it may be that eauilibrium concentrations of the intermediates are nedi- - gible. If so, this should be pointed out.

The dissociation of polyprotic acids, albeit a special case, can be seen a s a n example of this problem. However, polyprotic acid equilibria are invariably treated correctly. For a diprotic acid HzA, HA- is the intermediate in the equilibrium

and its dissociation may be neglected in a solution of H2A ifK* (dissociation constant for HA-) is much smaller than Kal (dissociation constant for H2A). If these equilibrium constants are not sufficiently different, all textbooks make it clear to tirst-year students that a more exact solution is reouired even if this solution is not taueht. -

Another example ol' intermediates in equihbrium proll- Iems is the calculation of'the solubilitv ol' ionic comoounds from solubility product constants (~,b). Even tboigh this

'We base Ins Jpon exam nat on of approx mately 15 n1rodJctory cnem slry textooods for sclence majors.

Volume 71 Number 9 Se~tember 1994 769

500 600 700 800 900 1000 Temperature, K

Relative atomic iodine concentration, x 100% versus temperature c, at various total concentrations.

problem has been thoroughly discussed in this Journal ( I , 2 and 3), firsbyear textbooks consistently neglect the equi- librium concentration of the undissociated compound (ion pair) which could be considerable.

The "error" we describe here appears in the first chap- ters in general chemistry textbooks devoted to chemical equilibrium and is not corrected or even discussed at any other place.

A frequently used reaction for equilibrium problems in these chapters is:

Hz + 1, 72 ZHI (3)

It bas been shown (4, 5) that the actual mechanism of this reaction is probably

Many textbooks describe this mechanism in their kinet- ics chapters. Our complaint is a general conceptual one; however, this specific reaction is an example appearing al- most universally in general chemistry textbooks and is used as the focus of the discussion. Students who find these reactions in their textbooks should be aware of the possible presence in an equilibrium mixture of more than just the species appearing in the overall reaction.

A typical problem involving this reaction is to calculate the equilibrium concentrations of all participating species starting with initial concentrations of, for example, [Hz] = [Iz] =5.00 x lo4 M, and the equilibrium constant for reac- tion 3, K = 29.0 (this is the value at 1OOOK). The "textbook" solution yields: [I2] = [H21=1.35 x lo4 M and [HI] = 7.29 x 104 M.

exact solution -textbooksolution Relative difference = exactsolution x 100%

770 Journal of Chemical Education

To solve this problem with the inclusion of reactions 4 and 5 and hence with the concentration of I, this set of equations must be considered:

CI = 2U21 + I11 + [HI] (6 )

CH = ZIHzl+ [HI] (7)

where eqs 6 and 7 are mass balances on the elements iodine and hydrogen, respectively. The constants in eqs 8 and 9 for reactions 4 and 5 can be calculated from thermodynamic data (61. When t h s is done and eqs69 are solved, the results are:

The relative differences2 between these results and those of the "textbook" solution given above are about 4% for [HI], 8% for [Hz], and 17% for [Izl, but the important point is that the [I1 is of the same order of magnitude as the other species in the equilibrium mixture.

When the same problem is solved for the atomic iodine concentration using eqs 6-9 for various temperatures and various initial concentrations, the results are shown graphically in Figure 1. The presence at equilibrium of atomic iodine is significant under many conditions.

It is true that all the complexities of the topics in begin- ning chemistry courses cannot be taught and, perhaps at times, liberties with rigor must be taken. However, when one chapter of a textbook clearly explains why most reac- tions are multistep and another chapter, often a sub- sequent one, ignores that fundamental understanding of reactions and oerforms calculations incorrectlv in ~rinci-

" A

ple, if not in the student's understanding becomes a little more muddled. It may well be appropriate not to teach the exact method in introductory chemistry, but stu- dents should be told the whole stow. that is. what a~oroxi- . . L A

mations have been made. Although we are averse to advocating the increase of the

size of chemistry textbooks, albrief explanation of approximations used in solving the problems discussed above may clarify instead of confuse.

It is interesting to note that in our combined teaching experience we have never met students who, on their own, raised this question of intermediates in equilibrium calcu- lations even though these intermediates were discussed in the kinetics chapter of their textbooks. We attribute this to students compartmentalizing chemistry, as a result of our teaching, that is, this is kinetics and there are equilibria, but never the twain shall meet.

Acknowledgment The authors express their gratitude to Joan E. Shields for

her valuable comments and review of the article. The authors also appreciate helpful discussions of the subject with Her- bert Morawetz.

Literature Cited 1. Meites, L.; Po&, J. S. F. Thomas, H. C. J Cham. Educ. 1968.43.667, 2. Martin. B. R. J. C h . Educ. 1986.63.491, 3. Ruaao, S. 0.: Hanania, G. I. H. J Chem Educ 1989,66,149. 4 .Sullivan, J. H. J. Chm. Phys. 1969.51.2288, 5. Bgvd, R. K Chm. Re". 1917,77,93. 6. Alberty, R. A.; Silbbey. R. J. Physrcol Chemistq; John Wiley &Sons. Inc.: New York,

1992; Table C.2 (reprinted fmm JANAFThermachemical lhbles by M. Chase et a] . , 3-rd ed.), 0 854.