d t a d by WALTER A. WOLF Eisenhower College Seneca Falls. New Yark 13148
Dissociation
of a W e a k Acid
An Applied
Daniel C. Pantaleo Bloomsburg State College Bloomsburg, PA 17815
MFC Ladd Sub-Department of Chemical Physics University of Surrey Guildford, U.K. The treatment by Levy and Byersl of the equilibrium of a weak acid in water gives, for certain ranges of concentration, significantly incorrect results for [A-1. Important aspects of acid-base theory can he shown by treating this problem fully, and then introducing approximations and noting their applicability. For simplicity, consider a weak, monobasic acid, HA, a t a concentration c in water. Then by solving the equations K.
-
KY = [H+][OH-]
[H+][A-]/[HA]
[Ht] = [OH-]
+ [A-I
c = [HA]
+ [A-]
for [Hf] and for [A-1, we obtain [H+]3 + K,(H+I2 - (K.e
+ K,)[H+]
-KaK, = 0 (1)
[A-]3+(K,-e-Kw/Ka)[A-]2-2K,c[A-]+K.c2=0
(2)
Solving eqns. (1) and (2) allows one to introduce Bairstow's numerical technique2 for determining the roots of polynomials: it can be done on a pocket calculator. It may he noted that if K , in eqn. (2) is neglected, the resultingequation factorizes as ([A-12+ K.[A
'I
-c) = 0
-K.e)([A-]
(3)
The first term of eqn. (3) gives Levy and Byers' equation; the second term approximates to a root of eqn. (2) only where K, L negligible, i.e., a t high concentrations. In any given problem, the physically significant root can he selected by inspection. Cublc and QuadraticSolutions* for [I\-]' c (moi dm-=)
lo@ lo-' 10P 0
Root 1 4.154 X (4.154 x 3.430 X (3.437 X 4.192 X (9.499 X 0.000
in no01
lo-' 10-9 10V 10-I)
lo-' 10')
Root 2 -4.331 (-4.334 -5.235 (-5.237 -2.279 (-1.895 -1.800 1-1.800
Exam in Coordination C h e m i s t r y
X
x
lo-'
io-'1 X 10P X lo@) X 10P X lo-? X lo-'
x
Root 3 1.000 X lo-' .. . 9.913 X lo-'
...
1.905 X lo-' ... 0.000 ...
In psrenthesea. [ ] implies concentration in mol dm-3 K. = 1.800 X 10W mol dm-"
For several years I have given an applied exam in coordination chemistry to smaller sections of general chemistry courses. The same format was used recently in an upper level inorganic chemistry course. T o begin the exam each student randomly draws or is assigned a bottle of a stock chemical. The pool of reagents consists of such comnounds as ferric chloride. cobalt chloride and nickel chloride i n thcir original lx,ttles. '['he Iahd provides the formulas for these cmrdination comoounds as FeCI&H?O. - . CoClr6H20, NiClz.6Hz0. Other compounds such as [Cu(en)n]SO4, [Ni(en)a]S04 and [Ni(NH3)4]C12, which are easily prepared and kept for this purpose, can also he used. From the formula on the label and by observing his or her particular compound the student is to write the electronic configuration of the central metal ion, provide a systematic name for and draw a possible structure for this compound, identify which species satisfy the charge and coordination valences of the central metal ion and (based on class discussions of d orbital energy splitting diagrams) account in a qualitative manner for the color and possibilities for the compound's paramagnetic or diamagnetic properties. For more advanced classes the auestions become more rieomus. For example the student is asked to draw the d orbit2 splittine diarrram for the central metal ion. calculate the value of the"spi'h only" magnetic moment expected for the complex and calculate the cwstal field stabilization enerev for the complex. Given a hbie of pound and higher state s.&hols for the various d electronic svatems, the studcnt is asked to list the allowed electronic trakitions for the complex in aqueous solution and then to assign these transitions, given the uvvisible spectra of the complex. Other questionsinclude predicting whether the complex is inert or labile to substitution reactions, and describing the mechanism which the complex will follow in such a reaction. Students have returned favorable comments t o this type of exam a t the introductory and advanced level. They have indicated that this approach illustrates the application of general principles to an actual and specific compound.
b
This presentation is largely mathematical: it takes on greater chemical significance where ionic concentrations are small, as with weak acids. However, the approach to eqns. (1) and (2), for example, is valid generally. The table shows that the quadratic equation of Levy and Byersl is valid down to and loe6mol dm-J, the mol dm-3. At c = about c = deviations from the results given by eqn. (2) are 0.2% and 7.7% respectively. Levy, M., and Byers, I. D., J. CHEM. EDUC., 56,526 (1979). 2Bairstow, L., Aero Mem No. 514 (1914); Pennington,R. H. "Introductory Computer Methods and Numerical Analysis," Maemillan Co, New York, 1965.
Student G r a d e r s Richard Steiner University of Utah Salt Lake City, UT84112 Two problems which I have repeatedly incurred when teaching large lecture sections are lack of personal contact with students and a lack of understanding of the difficulties involved in grading exams. I have made progress in alleviating both of these problems by adapting Reichert's use of student graders' to my organic chemistry class (Amer. J.Phys., 40,336 (1972)). Volume 57. Number 9, September 1980 1 669
On Fridays I have a short quiz on the week's work. The grading of these quizzes was done in my office by 5-6 members of the class. During these grading sessions we discussed the quiz and the week's work. Graders had an opportunity to ask questions, defend their own answers, work problems at the blackboard, and explain concepts to their peers. These exchanees allowed me to assess where difficulties lav and to engage in dialogue with almost every student in the class. Once the initial barrier was breached. students came in more often on their own. This program theiefore served very adequately to increase rapport between teacher and student. Once students were actively involved in the grading process and themselves exoerienced trvina ambiauous an. -to made . swers, assigning values to degrees of correctness, &d intermeting imoossible to read and/or follow answers, they were much iess prone to argue vociferously over a few points:Many students commented that being involved in grading radically changed their outlook on exams. I observed a marked increase in neatly presented, precise answers.
If a molecule or ion contains one element not included explicitly in the rules, its oxidation number is found by difference. For example N is +5 in N03- because each 0 is -2, and the sum for all four atoms is -1. The rules will take care of all situations encountered in general chemistry and more. They will be qualified in higher level courses but serve well at the time they are presented and used.
-
Calculators in Freshman Chemistry George Wiger California State University, Dominguez Hills Carson, CA 90747
Elementary Oxidation-Number Rules
A recent article in the Journal [56,526 (1979)] addressed the difficulties arising from the presence of calculators in freshman chemistrv courses. The nrohlems noted are certainlv cause for concern, and the solution suggested is clearly one means of response. I would like to suggest an alternative. I have gradually come to perceive the danger of calculators as a oaDer tieer. Indeed. I now view the handheld calculator as a gekx?"hoon for the teaching of freshman chemistry. In particular, the pocket calculator has placed mathematics in its proper position as a tool in the mastery of chemistry rather than an obstacle in its study. Interpolating with log tables to solve pH problems undoubtedly yields a better feel for logarithms than does the "keystroke" approach, hut does it teach more about acidity or hydrolysis? What about significant figures, clearly a calculator related problem? I would like to suggest that it is not necessarily true that students ten years ago, by not violating significant figure rules, demonstrated an understanding of the restrictions. Given the tools available, YOU could not produce answers with excess significant figures. Here calculators mav.be oerformine a service hv underlinine. the need for a strong emphasis on the significant figure relationshios in the teachine of chemical couceots. There is an additional area where c&ulators are a defkite plus in the classroom. The advent of the calculator has facilitated the coverage and testing of fundamental chemical relationships involving moderately complex calculations. Much more is available to the students, since much less time needs to he devoted to numher crunching. Given the above perspective, the way to proceed is straightforward. Make the calculator related problems obvious to the students. Then proceed in the traditional fashion, with emphasis on the understanding of relationships and their underlvin~concents rather than on numericallv correct answers. '?here is udthing novel in this approach akd that is my basic tenet: we have overreacted to the nresence of calculators. If we simply teach systematic approaches to problem solving, require extensive supporting work to be shown, and explain the analysis of answers in nonquantitative terms, the pocket calculator will play its proper and valuable role.
Eugene M. Holleran Neil D. Jespersen St. John's University Grand Central and Utopia Parkways .Jamaica. NY 11439 A survey of many general chemistry textbooks leads to the conclusion that a less confusing introduction to oxidation numbers would be desirable. When a student first encounters oxidation numhers his theoretical background is minimal, so he is presented with a list of rules to memorize. In most cases these rules are either inadequate or too complex. We present the following list which is short, simple, unequivocal, and easy for the student to learn and to use. Oxidation Number Hierarchy (1) The sum of the oxidation numbers of all the atoms in a molecule or ion must equal the total charge (zero for neutral mole. 1 -1 ....,
Luarr,.
(2) Metallic atoms of groups 1A and 2A have midation numbers of +1 and +2., resoectivelv. (3) Hand F are assigned orGation numbers of +1 and -1, respec-
.
tively. 0 is assigned an oxidation number of -2. ( 5 ) Atoms of group 7A are assigned oxidation numbers of -1. (6) In binary compounds, atoms from groups VIA and VA are assigned oxidation numbers of -2 and -3, respectively. First and foremost, i t should be noted that this list is a hierarchy. As a result, if two rules conflict, the rule that occurs first takes precedence. This process gives 0 = -1 in H202, Br = +5 in BrOs-, 0 = +2 in OF*, 0 = -%in Li02, etc. If a conflict occurs within the same erouo. the liehter element follows the rule, so that, for exampie, I is +1 i L 1 ~ 1 . Aoolication of the first rule would eive an oxidation number of +?for Fe in Fe3+, +1for Hg in HlgZ2+,and, in general, an oxidation numher of zero for any uncombined element (as for S in Ss). The subsequent rules then apply to combined elements. (4)
+
670 1 Journal of Chemical Education
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