Le Chatelier's Principle Applied to the Temperature Dependence of Solubility Richard S. Treptow Chicago State University, Chicago, IL 60628 Le Chatelier's principle is a well known generalization stating how changes of condition affect systems a t equilibrium (I).In a previous paper I proposed a brief, yet unambiguous way of phrasing i t (2): A eyzrrm or equilihrium resists attempts to change na lure, prrssurr, ur conrentraticm oia reagrnf.
trmpwa-
General chemistry texts often cite the principle when discussing the temperature dependence of solubility. It predids that solubility will increase with temperature if dissolution absorbs heat and, conversely, that solubility will decrease with temperature if dissolution liberates heat. The validitv of the nrinciole when annlied to ionic com.. pounds in water bins heen questioned by nodner ( 3 ) .He points out that the enthsloies ot solution usualiv rahulated in reference books refer io infinitely dilute sol;tions, and he cautions that such values have little relevance to the situation involving a solute in equilihrium with saturated solution. Bodner ~ r o n e r l vfocuses attention on enthalpies of solution a t saturation. Even then, his examination ofliterature data does not confirm the principle for many compounds. He offers several possible explanations for the apparent anomalies. One explanation, which is not explored, refers to the complicating factor that some ionic compounds exist as hydrated solids when equilibrated with saturated solution. Subsequent papers by Fernindez-Prini and by Brice defend the principle with largely theoretical arguments (4). Both authors reiterate that the narameter of most imoortance is enthalpy of solution a t satbration. ~urthermore,'inthe case of ionic comnounds in water. thev ooint out that enthalnv .. .. of solution varies unpredictably as one proceeds from lower to higher concentration. Except for a few examples, this matter is not pursued in any comprehensive fashion. This paper extends the work of previous authors by conducting a detailed examination of experimental results available in the literature. Le Chatelier's principle is tested, using appropriate thermodynamic data, for predicting the temwmture dependenre of soluhilitr tin ionic compounds in water. Care is &ken to identify correctly the actual hydrate solid equilibrated with saturated solution and to base predictions solely upon its enthalpy of solution at saturation. Heats of Solution Defined Imagine a calorimetry experiment in which solute in small amounts is added to 1mole of solvent until no more can dissolve. The total heat absorbed or liberated in the dissolving nrocess is continuouslv measured. If we maintain conditions of constant temperatureand pressure this hear rhange is AH, theenthaluvolsululion. In [his oaoer AH is rcferred toas the heat of soiuiion. We, thereby, foilow the sign convention that heat of solution is negative for exothermic dissolution. Figure 1shows a hypothetical plot of AH versus amount of solute added for the experiment just described above. Recall that AH is the total heat change of the system. It isnot amolar quantity unless we choose to divide by the amount of solute added at any point. The amount of solute added is expressed in the d o t as moles solute per 1mole solvent: it covers arange from iiltinite dilutton to sn;uration. For many compounds plots such as this are nunlinr:lr. This means that hear uiso-
I
I
I
I
I
l
l
Mole S o l u t e / l Mole Solvent Figure 1. Hypothetical heat-of-50lution plat fa & pwpose of defining& heats of solution. Each AH is the slope of a line shown.
various
lution per mole of solute varies with concentration and that we must define several different beats of solution, as will now he done. Integral heat of solution, AHi, is defined as the total heat change for a mole of solute when that mole dissolves to form a solution of particular concentration. Mathematically, AHi is the slope of a straight line from the origin to any point on the plot of Figure 1. Differential heat of solution, AHd,is the incremental heat change per mole of solute at any particular concentration. I t is the slope of the plot at any point. The symbols AH! and AH&, represent the differential heat of solution a t infinite dilution and saturation, respectively. I t should he clear from their definitions that AHi and AHd are molar quantities. The two become identical at infinite dilution; at other concentrations they are identical only if the plot happens to be linear. Our graphical treatment of data follows that suggested by Glasstone and Lewis (5).The heat of solution definitions are standard with these and other authors. Le Chateller's Principle Tested The only parameter of importance when testing the principle is AHL, the molar heat of solution when a small amount of solute dissolves in solution at the point of saturation. Since AHL, values are rarely found as such in the literature, we have determined them by constructing AH plots and measuring their slopes a t saturation. Thermodynamic data for constructing the plots were taken from standard references (6-8); the data were treated by calculationmethods described in the Appendix. Solubility versus temperature plots have also been constructed, once again using data from the literature (9, 10). Figure 2A shows AH plots for selected ionic compounds in water a t 25%. increases with the amount of dissolved solure for each compound; this means that dissolution ahsorhs heat. The plow have positive slope for all coticentrariuns and, most impbrtant~y,a t their saturation points. (Each compound's saturation concentration is marked by a pointer on Volume 61
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I 01
0.2
0.3
DL
Mole LiCIII Mole H20
Mole Solute/l Mole H20
Temperature. 'C Figure 3. Heat of solution (A) and solubilty (8)plots for LiCl and its hydrates. Ths f m l a wH20 stands fw LiCI.nH&. AH plots are at 25% at Wt temperatue the solid equilibrated with solution is LiCI.H&: its solubility is M e d by a painter
Temperature. ' C kgure 2. Heat of solution (A)and solubility (8)plots far some ionic compounds which do not formhydrates at 25'C. AHpiots are at 25% each compound's solubility at that temperature is marked by a painter ( A 1.
its AH plot.) Since their AH&,values are all positive, Le Chatelier's principle predicts each compound will become more soluble with temperature. Figure 2B shows the solubility curves needed to verify this prediction. Indeed, the effect of temperature is to increase solubility in every case. The compounds selected for Figure 2 have several characteristics in common: (1) the anhydrous solid dissolves endothermically a t all concentrations, (2) the phase that equilibrates with saturated solution at room temperature is the anhydrous solid, and (3) hydrates either do not form or form only below room temperature. Compounds behaving in this way include: NaCl KC1 KBr KI
KHzPO4 KHSOI KCNS K2Cr207
NH4HzPO4 (NH~zHPOI
In keeping with Le Chatelier's principle, each of these becomes more soluble with temperature. We next consider compounds that form hydrates at room temperature. Figure 3 illustrates LiCl and its several hydrates.' Depending upon temperature, the solid equilibrated with saturated solution can be any of four compounds; hence, the solubility curve has four segments. The family of AH plots (Fig. 3A) a t 25'C reveals that anhydrous LiCl dissolves exothermically, hut dissolution becomes more endothermic with each solid as the extent of hvdration increases. LiCLHqO is the solid which exists in equikhrium with saturated solution a t 25OC (Fig. 3B). Hence, it is the one compound of this series for which the dataallow a test of Le Chatelier's principle. The AH lot shows AHd for LiCI.H?O is neeative for dilute solupositive vdue tion; hut positive at saturation. From
tee
AHL
Solution concentrations in this and subsequent figures are based upon anhydrous solid, even when the solid phase is hydrate.
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Journal of Chemical Education
Temperature. 'C Figure 4. Heat of solution (A)and solubility (8)plats far KOH and its hydrates. The formula .nH20 stands for KOH.nH@ AHplots are at 25% at that temperature the solid equilibrated with salution is KOH.2H20; its solubility is marked by a pointer ( A ) . we predict LiCI.HzO will become more soluble with temperature. The solubility plot shows this does occur; the principle is upheld. The data of Figure 3 do not allow a test of the principle for a compound such as LiC1. Its AH plot is at too low concentration and temperature to predict the solubility curve.
Table 1. Heats of Solutlon and Temperature Dependence of Solublllty for Selected Ionic Compounds Temp. Compound
(OC)
AM*, (kJ/mole)
Solubility Temp. (Wt. %). depend."
LiCI.HgO
LiBr9H20 NaCl
NaBr.2H20 NaOH+l20
Na&Odm)r Na2SOq10H20 Mole
KF9H20 KC1 K8r
MnSO&/ I Mole H20
KI KOH.~HIO
KYPOI KHSOI KCNS K2Cr201
AgF.2H20 NHIH2PO. 1NHArHPOa
Temperature. .C Figure 5. Heat of solution (A) and solubility (8)plots for MsSOl and its hydates. t sat 17%: at that tern The formula .nH,O stands for MnSOd.nH20. . . A ~ ~ l oare peratwe MnSOcH20. MnSO..4H2O,and MnSOc5H20all can equilibrate with solution; each compound's solubility is marked by a pointer ( A ).
'SOIUbilitieO are expressed as weight per cent of the anhydrous solid. 4 Plus (+) indicates solubility increaser with temperature and minus I-)mat It d%creases. The symbol im) indimtesthe solid and ita saturated ~olutionexist in metastable egullibrium at thB temperature listed.
Two compounds which merit sl~erialmention are KOH and NaOH. Laboratory rxperirnce reminds us that these hydroxides generate nmsidrmhle heat when dissolved in water. Naive application of Le (:hatelier's principle leads to the prediction that soluhility will decrease with ttmprrvture. Just the oppnsite is true. Figure 4 provides theexplanation, using KOH as the examnle. We see that the anhvdrous jolid does dissolve exotheriically. However, K O H . ~ H ~ Othe , phase which eouilibrates with saturated solution a t 2 P C . dissolves endoth&nically at saturation. Its solubility predi'ctahly increases with trmperatttre. Anhydrous KOH equilibratrs with saturated solution only above 99OC.2 The NaOH system hehaws similarlv. The ~ h a s rouilibrated e with saturated sulution a t 25°C i i N ~ O H . H ~ O iis; AH'&,is positive and its solubility increases with temperature. The behavior displayed in Figures 3 and 4 is typical of many ionic compounds. The common characteristics of these compounds are: (1)the anhydrous solid dissolves exothermically for all concentrations, (2) hydrates form over a broad temperature range including room temperature, (3) the particular solid equilibrated with saturated solution becomes progressively one with less water of hydration as temperature increases, (4) heats of solution become more endothermic with extent of hydration of the solid, and (5) the hydrate which equilibrates with saturated solution a t room temperature dissolves endothermically, a t least a t saturation. Compounds displaying these characteristics include: ~
~
~
~~
LiCl [LiCl.H20] LiBr [LiBr.%HaO]
NaOH [NaOH.HtO] KOH [KOH.ZHzO]
Mg(N0ah [Mg(N03)2.6HzO) Ca(N03h [Ca(N03)~4H20]
The hydrate shown in brackets after each anhydrous solid is the phase that equilibrates with solution a t room temperature.
Le Chatelier's principle predicts each of these hydrates will increase in solubility with temperature, and such is observed. Having not yet found a compound whose solubility decreases with temoerature. our attention turns to MnSOd and its hydrates. FigLre 5~ shows AH plots a t 17°C. The pattern resembles that already discussed for LiCl and KOH. Figure 5B reveals that MnS045HzO is the most stable phase a t 1I0C. Its solubility increases with temperature in agreement with its positive AH&,. A special feature of this family of compounds is that MnSOd.H20 becomes less soluble with temperature. At 1I0C i t ;xi& in metastable equilibrium with solution, as shown by the dashed line in Figure 5B; its AH$ is seen from Figure 5~ to be negative. Hence, we have an uncommon example of a compound with exothermic heat of solution a t saturation and solubility which decreases with temperature. Le Chatelier's principle is upheld nonetheless." Table 1 presents a summary of all ionic compounds for which adeauate data for testine.. the principle were found in . standard refrrrncrs. Tu he lisied, a cumpound must hr the actual i,hase which eouilihratesu~ithsaturntrd solutilm .it ihe tempe;ature of the Ak plot. For each such compound we list the temperature, AH$,,the solubility, and the observed temperature dependence of solubility. In every case, the sign of AHit correctly predicts the temperature dependence. Note that only two compounds out of twenty-five dissolve exothermicallv a t saturation and correspondinglv become less soluble with temperature.
KOH.YO appears as a "finger" on the solubility curve because it is a congruently melting solid. The fact that the equilibrium is metastable does not detract from these arguments. Metastability simply means another solid that has greater thermodynamic stability than the one in question exists.
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Table 2.
lonlc Compounds Whose Water Solublllty Decreases wlth Temoerature
(7) Dean. John A,. (Edilorl, "Lange's Handbwk of Chemistry."12th d., McCraw-Hill Bwk Co., New York, 1979,pp. 9-4 Lo 9NX slso9fh ed., 1956,pp. 1577-1630, I81 Weast,%bertC..(Editorl,"HandbookofChemistryandPhysi~"59thd.,CRCPl~, West Palm Beach. FL, 1979,pp. D-67 to D~77. (91 Unke, William F.. (Editor),"Solubtlities of ha-eand Metal-OmmicCompounds," 4 t h d . . D. Van Noatrand Co., Princeton, 1958,Vol. I: with Scidell. AtherLon, 1966,
.-., .11.
"8
1101 Stephen,H.,snd Stsphen,T.,(Edifors1,"Solubiliti~aof lnorganiesnd OrganieCompounds." The Macmillan Co., New York, 1963. Vol. 1,Part 1,pp. 96364
Appendlx Constructing the AH plots of this paper required knowledge of integral heats of solution as a function of concentration. An excellent source of such data is the compilation of Landolt-Barnstein (6).For example, this reference lists AHi for NaCl over the concentration range from infinite dilution to near saturation. Specifically, when 1 mole NaCl dissolves in 9.5 moles Hz0 at 25'C, AH'is 1.874 kJ1mole NaCI. The dissolution can he written:
Summary and Discussion W e find Le Chatelier's principle valid for predicting t h e effect of temperature on solubility for all compounds tested. When applying t h e principle, care must he taken to identify the actual solid phase equilibrated with solution and t o examine only its differential heat of solution a t saturation. Some useful generalizations emerge from this study:
Expressed in terms of 1mole solvent the enthalpy change is 0.1973 kJ, which is plotted in Figure 2Aat the concentration 0.105 mole solute11 mole Hz0. Integral heats of solution for some compounds were determined from standard heats of formation (7). AHi can he calculatedwhen AH1 is known for the pure compound and the compound in aqueous solution. In the case of KHSO4, for example, AH1 is -1158.1 kJImole KHSOlfor the pure solid and -1143.8 kJ1moleKHSO~fartheeompound in solution with 20 moles H20. The integral heat of solution for the dissolution is obtained hy taking the difference
1) Anhydrous solids that dissolve endothermically either do not
AH' = AHLKHSO~IPOH~OI - AHC,KHSO~(~~ form hvdrates or form them well onlv below room temoerature. The result is 14.3 kJIreole KHSO4: In terms of 1 mole solvent the 2) Anhvdrous solids that dissolve exothermieallv , form hvdrates ,~~~~~~ enthalpy change is 0.715 kJ, which is plotted in Figure 2A at the at nmm tempernture. I t is the hydrate that equilibrates with concentration 0.05 mole solute11mole H20. dnturated wlution. Ilydratesdissolve with liberationof It.% heat Determining integral heats of solution is mare involved in the case than their respective anhydrous solids. They usually dissolve of hvdrated solids. AHi for a hvdrate can be calculated if we know both endothermically, particularly at saturation. AHi for the anhydrous solid and AHdehyd,the heat of dehydration of 3) As a result of (1) and (2) most compounds havepositivedifferthe hydrate. Consider LiC12H20 for example. AHt for the dissoluential heats of solution at saturation. In keeoine with Le Chation telier's principle their solubilities increase w'ithttemperature. LiCl.2 HnO(s) + 18Hz0(1) LiCI(20HzO) Compounds whose solubilities decrease with temperature ~
~
~
~~
-
are exceptions to t h e generalizations just stated. Tahle 2 lists all such exceptional compounds t h a t were found (9,10). Excluded from the listing are salts of organic acids, complex salts, a n d compounds for which t h e solid phase equilibrated with solution is n o t well identified. Although I will n o t speculate whv temoerature causes some comnounds t o lose soluhilitv. i t is wortk noting t h a t oxyanions prkdominate in Tahle 2 al;d t h a t all anions renresented form strong- hvdroeen bonds with " water. In actual practice, of course, solubility d a t a are easier t o obtain than differential heats of solution. It is unlikely t h a t a chemist would ever have t o resort t o usine t h e latter t o predict the former. It is reassuring, nevertheless, to know that [his study leaves Le (.'hatelier's principle affirmed.
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Literature Cited 111 L.Cha~lier.H., Cornpt. Rend, 99,786 (1884). (21 Treplow, Riehsrd S.,J. C H E W EDuc.,57,417 11980). (31 Bcdner.GoargeM.. J. CHEM. E D U C .I17 , ~ ~(19801. . 1" FernBndez-Plini. R.. J. CHEM.EDVC., 59,550 (1982);Brico.L. K., J, CHEM.EDUC., 60. 387 (19831.
IS1 Glaslone, Samuel, and Lewis. David. "Elements of Nastrand Co., Princeton, 1960. pp. 52-86.
Physical Chemistry." D. Van
16) Landolt-Bbrnstein, "Numerical Oats and Fundional Relationahips in Science and T e ~ h n u l o ~New , " Series, Springer-Verlag,Berlin, 1976, Group IV. Val. 2. pp. I-
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Journal of Chemical Education
--
can he calculated by separating the reaction into two steps LiCL .2HzO(s) LiCl(s) + 2H20(1) LiCl(s) 20H20 LiCI(20H20)
+
The first step is dehydration of the hydrate. Its enthalpy change can be calculated from heats of formation as follows:
+ ~ M L H * o (-I )AH~,UCI.ZH~O(~I AHdehyd = MP,L~CI(~) Using literature values AHdshyd is 32.3 kJImale LiC1.2H~0(7). The second step is the dissolution of anhydrous solid, for which AHi is -34.6 kdlmole LiCI (5).Combining the two steps AHi;cim20 = AHdchyd+ AHLcI gives -2.3 kJ1mole LiC1.2HzO. In terms of 1mole solvent this enthalpy change is -0.12 kJ, which is plotted in Figure 3A a t the eoncentration 0.005 mole LiClll mole HnO. The example just diwusred ilh-tmte- a general r i t u d m : the heat of aolurion uf n hydra@ is rhe sum irf (he heat uf solution 111its anhy. drous solid plus its heat of dehydration. This is true for both integral and differential heats of solution. Since heats of dehydration arealways positive, the heat of solution of a hydrate must always be more positive than that of its anhydrous solid. As has been previously discussed the AH plotsof Figures 3A, 4A, and 5A become progressively more endothermic with extent of hydration.
