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
