A Visual Method of Teaching Mass Balance Relationships to Undergraduate Quantitative Analysis Students Pete E. Poston Western Oregon State College, Monmouth, OR 97361 Solving complex equilibria problems is central to the undergraduate quantitative analysis course. The student is taught a method that is based on a series of steps used to define and solve the problem (1,2). General Problem-Solving Steps 1. Identify all of the relevant chemical species and write down balanced chemical equations. 2. Identify the number of unknowns. 3. Write down a system of linearly independent equations involving the equilibrium concentrations of the unknowns. The number of independent equations has to at least equal the number of unknowns. It is in this step that the charge balance and mass balance expressions are required. 4. Make simplifyingapproximations and solve the system of equations. I t has been my experience that the mass balance equation is conceptually the hardest to understand and derive, although there are plenty of other intellectual hurdles here to overcome! This is where a visual approach to obtaining the mass balance expression could be useful. As a n illustration, consider the equilibrium calculation of the molar solubility of CaC204in a n HCI solution with a pH of 4.0. The relevant chemical equations for step 1follow. CaC204= ca2++ ~~0:-
(1)
~~0:-+ H' = HC204-
(2)
HC204-+ H' = H2CZ04
(3)
The mass balance equation can be obtained visually by first writine down on the chalkboard, or on a n overhead transparency, a set number of CaC204molecules, say 10 of them. Now tell your students that since calcium oxalate is a sparingly soluble salt, only a small percentage ol'the molecules w ~ l actually l disiiociate and become solva~ed.Indi-
~ i ~ u 1. r eDissociation of calcium oxalate into calcium and oxalate ions.
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Journal of Chemical Education
Figure 2. Protonation of the oxalate ion. cate this by showing the equilibrium dissociation of perhaps four out of the original 10 (Fig. 1). I t would be simple to illustrate this by using superimposable transparencies for each figure. Now continue the process by protonating perhaps two of the resulting C204" species (Fig. 2). Finally, protonate one of the hydrogen oxalate ions to produce oxalic acid (Fig. 3). The entire process illustrates dia-
Figure 3. Protonation of the HC204- Ion.
grammatically how different species are produced and undergo further reactions in solution. At this point, mention that a mass balance relationship must exist because all of the species on the right originated from the H2C204molecules on the left. Count them up for the students by first covering up the HC20k and H2C204 molecules with vour hand (Fig. 3) and ask the auestion: "Does not the eqklibriurn con&ntration of Ca2' ions equal the eauihbrium concentration ofoxalatc ions:'" Write down eq 4 61the students: [ca2+I = [ c,o,?
+ [HC2O47
As a final step, physically count up the number of Ca2+ ions (41, the number of C 2 0 p ions (21, the number of HC20a-ions (11, and the number of H2C204molecule~(1). This illustrates that the numbers on the left balance the number of species on the right.
(4)
Now move your hand and cover only the H2C204species. It should be evident that two oxalate ions have been replaced by two HC204-ions such that eq 5 is valid now: [ca2+I = [czo4?
Finally, illustrate by entirely removing your hand, that one HC204ion is replaced by a H2CzO4molecule so that eq 6, the mass balance equation, is now valid:
(5)
Literature Cited 1. Dex R.A,: Underwood, A. L. QuonfifvtivaAnalysis, 6th ed.: Prentiee-Hall: New Jersey, 1991; p 116.
2. Skoog, D. A,: Wesf D.M.:HoUer. F J. FundmntalsofAnalytiml Chemistry, 6th ed.; S a n d e r s CollegePublishvlg Fort Wmth. 1992; p 158.
Volume 71 Number 2 February 1994
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