A PHASE RULE EXPERIMENT: THE SYSTEM LEAD NITRATE-SODIUM NITRATE-WATER E. L. HERIC University of Georgia, Athens
A m o w the physical chemistry laboratory texts currently in print, there are a number of experiments devoted to heterogeneous equilibrium and the phase rule, including several involving ternary systems. The interpretation of the triangular diagram commonly used in representing ternary systems (1) is on occasion a source of difficulty to the student, especially when both liquid and solid phases are involved. The experiments on ternary systems in the current texts are invariably concerned with systems containing liquid phases only. These experiments call for the student to indicate on a phase diagram the hinodal curves and tie lines as determined experimentally by a method such as titration. There the experiment ends. Although such systems are of importance in themselves, their value in helping the student understand phase diagrams is limited. It appears that a laboratory exercise involving the study of the less easily interpreted solid-liquid type of system might be of more value t o the student. Two such experiments have been described by O'Brien and co-workers: potassium chloride-hydrochloricacid-water (2) and sodium bromide-hydrobromic acid-water (3). The method outlined involves analysis by chemical means of fractions of each of the phases present a t equilibrium. This is a disadvantage in that it requires the labor of a pair of students over a six to eight hour period in order to establish some half-dozen pairs of points representing solidsolution equilibrium. In the experiment t o be described the analytical procedure is reduced t o a minimum, determination of total anhydrous solids. This is accomplished by extension of t,he wet residue method of Schreinemakers (4) and the method of algebraic extrapolation (5) so that a knowledge of the composition of two synthetic samples on the same tie line is used t o fix the latter.
figure 1. The S m t e m b a d Nitrate-Sodium Nit..te-W.ta.
While the principles involved are presented in terms of the system lead nitrate-sodium nitrate-water, it will be apparent that the method is not specific and might be applied t o many ternary systems in which one of the components is easily separable from the others. The author has evidence that with several refinements the method may also he a suitable tool for research, especially for some of those systems where the usual methods of analysis are not satisfactory. In the discussion below, the following symbols will be used: a, b, c = weight per aent of respectively water (A), sodium
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nitrate (BI. and lead nitrate (.C ,),: b,, el = values of b and e in a first series of synthetic samples along the section a, = i (constant); b,, er = values of b and c in a second series of synthetic samples along the section m = j (constant); a,,. b,,. e. = valuos of a, . b,. and c for ooints on the solubilitv curve;
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b = for a synthetic sample, the fraction of the solids b +.c whleh is B. =
The phase diagram of the system at 25' is given in Figure 1 (6). On the diagram there have been superimposed two sections a t a, = i and a2 = j, representing two series of synthetic samples. Along each of the sections a is a constant, while b and c vary. For each sample 011 a section there is a value of a, for the solution obtaining a t equilibrium. The relationship is shown in Figure 2 in terms of a plot of a, versus p. Each of the t ~ v ocurves is seen to consist of three branches. If the phase rule and visual examination of the samples at equilibrium are combined with the curves in Figure 2, certain conclusions concerning the system can be reached without previous knowledge of its phase diagram. The ternary system is considered t o be at a constant pressure and temperature, so the phase rule fixes F, the degrees of freedom (variance), as where P indicates the number of phases present ( 1 ) . Since the system cannot possess a lesser variance than zero, the number of possible phases is restricted to one, tmo, or three. The physical appearance of the samples a t equilibrium will show each t o consist of at least two phases, at least one of these being a liquid. The nature of the system is defined further by the form of the curves in Figure 2. Consider a, versus pl. The branches from (0, d) t o (w, z) and from (x, z) to (1, e) represent samples whose solution compositions vary continuously as p varies. Such behavior indicates a two phase region. Another feature of this plot is that these two branches do not form a continuous curve but show a discontinuity between (w, z) and (a,z) JOURNAL OF CHEMICAL EDUCATION
lines must be established by the extrapolation of the generally non-linear a, versus p curves t o a, = z in Figure 2, the latter method appears t o be less accurate here. Extrapolation of the solubility curves is rendered less arbitrary by the restriction that the value of a, is fixed a t z. After the solubility curve has been established, the tie lines used for that purpose may he extrapolated in the opposite direction in order t o fix the identity of the solid phases in equilibrium with the solution. If this is done graphically it will be apparent that the average composition of the solid corresponds to one or the other of the anhydrous salts. Assuming then that the solid is anhydrous, the tie lines may be used t o obtain an indication of the quality of the data, since they should intersect precisely a t the points corresponding to the pure anhydrous salts. The method is again that of similar triangles. I n the region where Cis the apparent solid, for example, a,
- a2 ba - ba
ad NPU.. 2.
A Plot of o, .,em"*
0 s t the sectiom a, = ;-a
=j
corresponding t o a region of constant a,. This discontinuity could be the result of an invariant point a t the intersection of the two branches of the solnbiiity curve. However, it could also indicate the existence of a third branch, corresponding t o another two phase region exhibiting an essentially constant water content in the solution phase. The uncertainty here will be resolved by the nature of the tie lines. The interpretation of the plot of a, versus p2 is the same as that given for a, versus p1 except that the two end branches are terminated a t (v, z) and (y, z). The curves in Figure 2 may now be used t o construct the phase diagram of the system. While the solubilities of the binary systems AB and AC are given directly by the values a, = e and a, = d respectively, it is necessary t o consider both curves in order to establish additional points on the solubility curve. Consider, for example, the points (f,h) and (g, h). These correspond respectively to synthetic samples of composition (al, b2, e2) and (al, b,, el), both having the same solution composition (a,, b,, c,). The points representing these three compositions thus lie on a common tie line in the phase diagram. It follows from the theorems.of similar triangles that
a,,= b, a, - az
- bi - c, - ci b, - b2 CL - c*
(2)
Since the only unknowns in (2) are b, and c, the coordinates of the point (a,, b,, e,) are readily determined. Additional points on the solubility curve may be determined in a manner similar to that just described. When this is done it will be apparent that the tie lines passing through the synthetic samples corresponding to the points (v, z) and (w, z), and the points (x, z) and (y, z), intersect (within experimental error) at a common point on the solubility curve. This is sufficient t o establish that the system possesses a single invariant point and not a third branch of the solubility curve. Although tie lines have been used to establish that an invariant point does exist, the coordinates of this point are best fixed by extrapolation of the two branches of the solubility curve itself, rather than by the use of the tie lines from Figure 2. Since these particular tie VOLUME 35, NO. 10, OCTOBER, 1958
(3)
where ba is the experimentally indicated value of bin the solid phase. Typical results obtained by combining the experimental nrocedure described below with the calculations described above are given in Table 1. A point on the solubility curve has been obtained for each synthetic sample prepared. The indicated nature of the solid phase in equilibrium with each solution point is also TABLE 1 Equilibria i n the System N a N 0 3 - P b ( N 0 d - H z 0 at 25' by the Method of This Experiment Solid composition (assumed anhydmus) % by weight NaNOs Pb(NOa)z
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Solution composition % by wei ht iVaN01 pb(A'd3)r--
.. .
.~ .-
~~
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.4eeepted values (6): " 47.9, 0.0, 52.1; "0.3, 15.5, 44.2 (invariant point);' 0.0,37.2,62.8.
Na NO,
PbINO,), Figu.o 3.
The solubility cuwe of the syatsm Lend Nitrat.-Sodfurn
Nitrmte-wete.
Curvee are from accepted d u e s ( 8 ) ; points are erperimental values from Table 1.
given. The points are compared graphically with the accepted values in Figure 3. The agreement appears t o be satisfactory for the purpose intended. The equilibrium temperatures were 25.0 O.l°C.
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THE EXPERIMENT
Apparatus and Materials: 60-ml. glass stoppered bottles, 50-ml. volumetric flasks, 2-ml. Mohr type pipets, 10-ml. volumetric pipet, reagent grade sodium nitrate and lead nitrate, distilled water, thermostat (25'). . . Procedure: This experiment is designed for a pair of students working as partners. I n order t o fit it conveniently into laboratory periods of the usual length it is advisable that the bottles and pipets be previously cleaned and allowed t o dry. The synthetic samples t o be prepared are given below. Since the purpose of samples 1-5 is t o iix the values of a, for the individual salts and the invariant point, their compositions may actually he varied within rather wide limits. The values given here are intended t o serve as a guide. The components in these samples should be weighed to the nearest gram. If the instmctor feels it is detrimental t o the purpose of the experiment if the student knows in advance that these points lie in the designated regions, the weights of these samples may be adjusted so that they lie precisely upon the sections corresponding t o the remaining samples below. Obviously this would have no effect upon the value of a, for these points. For samples 6-17, which establish all other values of a, along the solubility curve, the compositions of the samples are more critical. The solids shoulkl be weighed t o within 5 mg. of the amounts specified, which refer t o apparent weights (in air). A convenient procedure is to weigh about 0.1 g. short on a trip balance, and then bring t o the desired weight with a more sensitive balance. The method requires much less effort than might be supposed. The pipet used in preparing samples 6-17 should be calibrated for the weight of water delivered, duplicate results agreeing to within 5 mg. Thermostatted water should be used for both calibration and sample preparation. Drying of the solids used in preparing samples G17 is recommended. 1. 2. 3. 4. 5. 6. 7. 8. 9.
10. 11. 12. 13. 14. 15. 16. 17.
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10 ml. A 15 e. B 15 g. C 10 ml. A 10 ml. A 22 g. B 8 g. C 17 g. B 13 g. C 10 ml. A 14 g. B 16 g. C 10 ml. A 10ml.A + 1 4 . 2 5 0 g . B + 0 . 7 5 0 g . C 10ml.A 13.000g.B 2.000g.C 10ml.A +12.000g.B 3.000g.C 10ml.A+ 8.000g.B+ 7.000g.C 4.005 g. B 11.000 g. C 10 ml. A 10ml.A+ 1.505g.B+13.500g.C 1 0 m l . A + 2 8 . 8 7 5 g . B + 1.120g.C 10ml.A + 2 7 . 7 2 0 g . B 2.280g.C 1 0 m l . A + 2 7 . 0 0 0 g . B + 3.000g.C 8.000g.B +22.005g.C 10ml.A 5.650g.B+24.360g.C 10ml.A 10 ml. A 2.280 g. B 27.725 g. C
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The samples are stored in the glass stoppered bottles. Constant agitation of these samples in order to attain equilibrium is not necessary. A more convenient, and equally effective, method is t o warm the samples to about 60°, and then store them in the thermostat for a period of two hours with only an occasional gentle swirling action in order to prevent caking of
the solids. Caking is a possible source of error for those samples with a large fraction of solids. After the samples have been weighed, the flasks are cleaned, rinsed with acetone, and oven dried. When it is time to withdraw fractions of the samples the flasks are cooled in a desiccator and weighed to the nearest milligram. Taring is convenient for weighings involving the flasks. About 2 ml. of solution is removed from a sample with a pipet provided with a filter. The pipet should be above sample temperature so that no solid is deposited upon its walls. The fraction is drained into the flask, which is then stoppered and weighed again t o the nearest milligram. The procedure is repeated until a fraction of each sample bas been placed in a flask. A dry pipet is required for each sample. Although desirable, duplicate determinations are not suggested because of the lengthy nature of the experiment. A comparison of results obtained in this laboratory shows good agreement between different sets of data based upon single determinations. The flasks containing the fractions are heated t o evaporate the water, cooled in a desiccator, stoppered and weighed to the nearest milligram. The fractions are completely evaporated overnight a t 130'. Calculations: From the experimental values of a, and B a t the two sections a plot resembling Figure 2 is constructed. To obtain results of the order indicated above, however, would require a plot of Figure 2 as such t o he excessively large. I t is more convenient simply to omit the invariant region, and t o plot on a single sheet of paper the four branches such as (0, d) t o (w, 2). As a further aid to reduction in size of the plot the two branches t o the right are plotted in terms of 1-g rather than 0. A 65-cm. length of graph paper 50 em. wide in l a m . divisions is suggested. The experiment provides an opportunity t o introduce the student t o the use of the spline, a useful device unknown to too many of our science graduates. Care should be exercised in the drawing of these curves since in certain regions of concentration the results are sensitive t o relatively small changes in a, and 8. Other ternary systems might he preferable for this reason, but it seems important that the student see the limitations of the method as well as its advantages. The opportunity for error could be lessened by selecting two sections farther apart but not without introducing added difficulties in the experimental procedure. Using the plot of a, versus B the phase diagram of the system is constructed by the method outlined above. If a point on the solubility curve is established for each of the samples prepared, the curve is adequately defined over its entire extent. I n calculating the true weights of each sample component, corrections for the buoyancy of air should be introduced where they are significant. The student is referred t o Seidell (7) or t o the original literature (6) for a comparison between the accepted values and his own. The instructor may quickly obtain an indication of the quality of the student's experimental technique by comparing the values of a, for the samples 3, 4, and 5, all of which should agree within experimental error. The following pairs of points may also be used in the same way, since each pair lies on a single tie line: 8 and 14, 9 and 15. JOURNAL OF CHEMICAL EDUCATION
LITERATURE CITED
(4) SCHREINEMARERS, F. A. H., 2.phys. Chent., 11, 80-1 (1893).
(1) PRUTPON,C. F., A N D S. H. MARON,"Fundamenta] prin. ciplen of Physical Chemistry," revised ed., The Mitemillan Company, New York, 1951, 415-27. 12) O'BRIEN. S. J.. AND C. L. KENYY.J. CHEDI.EDUC.. 14., 573-4 (1937).'
( 5 ) HILL,A. E., A N D J. E. RICCI,.I. Am. Chem. Soc., 53,4306-8 (1931). (6) GLASSTONE. S., A N D H . ?*I. SAL'NDERS, J . Chern. Soc., 123, 2136 (1923). (7) BEIDELL,A,, "Solubilities of Inorganic and Metal Organic Compounds," 3rd ed., D. Van Nostrand Company, Inc., New York, 1940, Vol. 1, 846, 1403.
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(3) O'BRIEN,S. J., C. L. KENNY,AND R. J. F U X J.~ CHEM. Eouc., 17,5iG-7 (1940).
VOLUME 35, NO. 10, OCTOBER, 1958
