M. 1. Lyndrup, E. A. Robinson, and J. N. Spencer' Lebanon Valley College Annville, Pennsylvania 17003
The Solubility of Zinc Oxalate A physical chemistry experiment
The solubility product principle as generally presented does not introduce the student to the relations between solubility and solubility product, i.e., the formation of ion pairs, competing side reactions and activity coefficients are usually ignored in favor of simple ion products. The study of the solubility of zinc oxalate is particularly suitable for illustration of the relation between soluhility and solubility product because ion pair formation is pronounced and competing side reactions occur. The data are easily obtained by radiochemical means and only limited measurements of the solubility and the pH of the system are required. From the measured solubility of the zinc oxalate, the pH, and literature values for various equilibria constants the student may determine the concentrations of various species present in the solution. Further the mean ionic activity coefficient may also be found once the concentrations of the charged species are known enabling a calculation of the thermodynamic solubility product. Experimental
Table 1.
Thermodynamic Equilibrium Constants in Aqueous Solution a t 25'C
Ka
Ecluilihrium
. . ..
2~20il) H.Ot(aq)
.
Ref.
. .
+
K . = 1 . 0 x lo-" OHWaq) K is the ratio of the activities of the products to the reactants. "verage of values from ref. d. MOELLER, T., "Qualitative Analysis," (1st ed.), 3fcGraw-Hill Book Co., Inc., New York, 1958, p. 511. d "Stability Constants of Metal-Ion Complexes," Special Puhlication No. 17, London: The Chemical Society, Burlington, House W.l, 1964, p. 362.
The student first prepares a sample of ZnClO,. 2Hz0 containing "Zn. W n emits a gamma ray of 1.11 MeV and is available in 10 pc license exempt quantities. A precipitate of approximately 20-50 mg of ZnC20..2H~0is formed by adding the desired quantity of a Zn(NO& solution containing about 100 mg zinc ion per milliliter to 1 pc of 'SZn in 0.5 ml of H1O. One-half milliliter of a saturated NaCz04 solution is then added and the precipitate of ZnC1O4.2H10 dowed to settle. The supernate is removed and the precipitate washed and dried. A few milligrams of the dried precipitate %resccurrttely weighed and transferred to a volumetrio flask, dissolved in 4 M HCl and diluted to the mark. Usually two samples are prepared in this fashion. Five milliliter aliquots of these solutions which serve as standards are then counted in test tubes in a NaI(T1) scintillation counter. A few milligrams of the remaining precipitate are then transferred to each of three s t o p pered flasks and about 25 ml distilled water added. The samples are then allowed to equilibrate, usually requiring about two days, and 5 ml diquots counted. By comparison to the standard the solubility of the zinc oxalate is found. This solubility thus found includes all forms of zinc in solution because the manner in which zinc enters the solution is of no consequence to radiochemical detection. The solubility measurements on the samples should be continued over a period of days to insure that equilibrium has been attained. The pH of the saturated solution of zinc oxalate is also determined.
overall solubility. From the K values listed in Table 1, the measured solubility and pH of the solution, a determination of the possible species present in solution is made. The pH of a saturated solution of zinc oxalate is 5.4. By using thc pH and equilibria considerations the analytical concentration of Zn, ST,.*+ is seen to be
Calculations
[Cp04P-] = [Zn8+1 - [Zn(CzO,)lz-l
Once the student has determined the solubility of zinc oxalate he is asked to find the solubility product of zinc oxalate. The student may he given a table such as Table 1 consisting of equilibria data for various zinc and oxalate containing species. The student must then determine which species contribute to the
1
To whom all correspondence should he addressed.
+ [ZnCaO,] + [Zn(CIO.)zz-]
ST,"%+ = [Zn2+]
(1)
and the analytical concentration of oxalate ion is Sc?oi- = [C~O,l-] [HzC~O,] [HCsOa-I
+
+
+
[ZnCaO,]
+ 2[Zn(CxO,)r'-I
(2)
In order to determine K,, the student must find [Znf+] and [C20a2-]as well as the activity coefficients. This is easily done by an iterative procedure. In the course of the iterations the student will also determine [HC20a-1, [H2C204], [ZnC20n], and [Zn(C204)zZ-I. Because the analytical zinc and oxalate concentrations must be equal eqns. (1) and (2) may be combined to give
- [HCD-I [H,CsO,I
(3)
By substituting the expression for K8 and K4 and rearrangingeqn. (3), eqn. (4) results.
where the denominator is a constant for the given pH. Equation (4) in conjunction with Volume 49, Number 9, September 1972
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Table 2.
Representative Student Data
. . Standards Sample Background
708 248 16
2.82 X lo-' 0.950 X lo-"
...
.
,
...
...
...
...
5.4
22
a Standard is prepared by adding a known amount of ZnCnO,.2H2O (about 2.5 mg) to a 50-ml volumetric flask and diluting to the mark with 4 M NCI. The precipitate is prepared from 1 ~c "Zn, 0.3 ml Zn(NO>). solution (100 mg Zn(NOs)t/ml), and 0.5 ml saturated solution NazC204. b About 10,000 total counts are collected.
and
may be used for iterative purposes. ranc,o. is. taken - - . ~ . to be unity. For the first iterations the activity coefficient is assumed to be unity. Equations (4), (5), and (6) are used to iterate for K..,. the solubilitv nroduct written without activity coefficients. his" i's accomplished by first estimating a reasonable value for K.,,. Substitution of Sa. and K.,, into eqn. (6) allows the first estimate for [Zn2+]. Once [Zn2+] is known [Zn(Cz04)22-]is found from the third term of eqn. (6). By using this value for [Zn(C204)22-] in eqn. (4) along with [Zn2+] and [HaO+], [C204-] is found. Then using [Zn2+]and [C20a2-]K.,, is calculated. If the calculated K.,, does not agree with the original estimate of K,,,, the iteration is performed anew choosing a different value for K.,,. If the student is prudent a surprisingly small number of approximations are required. The iteration is continued until the estimated K.,, and the calculated K,,, agree to the nearest 0.1. Three figures should be used for iterative purposes. For Sz. = 1.63 X the results of these first iterations are [Zn2+] = 4.3 X M [ZnCz041= 1.2 X 10-'M [Zn(C2O4)sa-]= 1.9 X 10-' M [C104*-] = 3.8 X
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Journal of Chemical Education
[HC20r-I = 3.0 X 10- M [HnCzO,] = negligible
Thus the [Zn2+]is less than 30% of the total concentration of zinc containing species. The ion pair accounts for more than 70% of the zinc containing species. The literature values for the solubility of zinc oxalate range from 4.2 X to 1.68 X M (1-3) and the K., from 1.3 X to 7.5 X lo-# (2-5). Student data generally falls into this range. The experiment may easily be expanded to determine the effect of pH on the concentration and nature of species produced by the dissolution of zinc oxalate, the effectof ionic strength, temperature, or addition of a common ion such as oxalate. The conditions of the experiment determine the equilibria necessary for consideration; thus students could be assigned different sets of conditions and class data pooled. The iteration procedure may also be computerized.
M
Having found these quantities [HCzOa-] and [HrCsOa] are found from K3 and K4. The best estimate for K.,, is 1.7 X lo-'. It is easily shown that all relations expressed by eqns. (1) through (6) are.self consistent under the assumptions made. The value for K, will be slightly off due to the number of significant figures used for the estimates.
642
Having made the first estimates for the concentrations the student finds the ionic strength by summing over the charged species in solution. By using the Debye-Huckel relation y+ is found. The value found for r+ is substituted into eqns. (4) and (6) and the iterations repeated for a new K,,. The activity coefficients of the uncharged species are assumed to be unity. When the new K., is found a new ionic strength is calculated using concentrations as found from eqns. (4), (5) and (6). A new y* is found and the iteration repeated. Usually only one or two iterations are required. The ?+ found using 8%.= 1.63 X 10-4 is 0.940 and the thermodynamic K., is 1.6 X lo-'. The internal consistency of all equations may again be shown with KZ being slightly off for the same reasons given as above. The concentrations of the various species are found to be
Literature Cited (1) O s ~ w * T., . Bull. Chem. Soe. Japan, 23, 244 (1950). W. J.. A N D VOBBDROX, C., J. Amer. Chem. Soe., 59, 2414 (2) CLAYTON,
\."".,.
W.
,1017,
(3) Vossunax,
W. C., A N D BECKXAN, J . F.. J. A m w . Chem. Soe., 62,
1028
IlQL", ~-".-,.
(4) M o ~ m e nT., . "Quslitstive Anslyais," 1st ed., McGraw-Hill Book Co..
Inc., New York, 1958, o. 517:. , AND SUIT". G. F., Quantitative Analysis." John Wiley & (5) D r ~ m H., Sons. Ino.. New York. 1952, p. 489.
