RALPHK. BIRDWHISTELL
textbook Forum
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 college chemistry courses for science majors. The first chapters on chemical equilibrium in current textbooks' for these courses make a n "error" in the solution of certain types of equilibrium problems. This diminishes the student's understanding of chemical equilibria and may add to their difficulties with subsequent equilibrium topics, for example, acid-base equilibria. These textbooks carefully e x ~ l a i nthat mass action exoressions can be written for m y chemical equation tequil~bnumchapter! even lfthv actual 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 equilibrium some of each intermediate is in the equilibrium mixture, and the amounts depend on the values of the equilibrium constants for the elementary steps. All currently available first-year chemistry textbooks that we examined' ignore this situation in their dismssions of equilibrium calculations. A simple illustration is the example in which the initial concentration, CA,of a reactant, A, is given along with a n equation and the equilibrium constant, K. The equilibrium concentrations of the reactant [A] and product [B] are to be calculated:
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 a t equilibrium means that [Bl # x. Many problems in which the initial conditions (concentrations or partial pressures) are given and equilibrium 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 e the unsolved bv i m o r i n ~Dossible intermediates. in s ~ i t of derstan&ng that most reactions are multi&ep.it may be that eauilibrium concentrations of the intermediates are nedigible. 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 prollIems is the calculation of'the solubilitv ol' ionic comoounds from solubility product constants (~,b). Even tboigh this
-
The problem is completed by stating that a t equilibrium [A] = CA- x and [Bl = x and then solving for x:
'We base Ins Jpon exam nat on of approx mately 15 n1rodJctory cnem slry textooods for sclence majors.
Volume 71
Number 9 Se~tember1994
769
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:
500
600
700
900
800
1000
Temperature, K
Relative atomic iodine concentration,
c,
x
100% versus temperature
at various total concentrations. problem has been thoroughly discussed in this Journal ( I , 2 and 3), firsbyear textbooks consistently neglect the equilibrium concentration of the undissociated compound (ion pair) which could be considerable. The "error" we describe here appears in the first chapters 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:
The relative differences2between 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 beginning 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 reactions are multistep and another chapter, often a subsequent one, ignores that fundamental understanding of reactions and oerforms calculations incorrectlv in ~rinciple, 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 students should be told the whole stow. .. that is. what a~oroximations 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 calculations 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. "
A
L
Hz + 1, 72ZHI
(3)
It bas been shown (4,5) that the actual mechanism of this reaction is probably
Many textbooks describe this mechanism in their kinetics chapters. Our complaint is a general conceptual one; however, this specific reaction is an example appearing almost 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 reaction 3, K = 29.0 (this is the value at 1OOOK).The "textbook" solution yields: [I2]= [H21=1.35x lo4 M and [HI] = 7.29 x 104 M. Relative difference = 770
exact solution -textbooksolution x 100% exactsolution
Journal of Chemical Education
A
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 Herbert 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 (reprintedfmm JANAFThermachemicallhbles by M. Chase et a]., 3-rd ed.), 0 854.
