H. A. Neidig, R. T. Yingling, K. 1. Lockwood, and T. G. Teates Lebanon Valley College Annville, Pennsylvania
I I
Interaction in Chemical Systems 11.
The KCI-methanol-water
This is the second in a series of articles dealing with interactions in chemical systems. The purpose of this paper is to present experimental data and the interpretation of the data as source material for interested individuals who might wish to develop their own experiments on interaction. An integral part of the study of each chemical system is the construction of a microscopic structural model from the experimental data obtained from a macroscopic examination of the system. The first article of the series described an investigation of interaction in a chemical system composed of two liquids, methanol and water (1). This paper deals with interaction in a chemical system composed of a solid, KC1, and two liquids, CHIIOHand 8 0 . For the purposes of this paper, "interaction" is defined as the deviation of any property of a system from ideality. The KCI-MeOH-H,O, KC1-HzO, and KCl-MeOH systemswere investigated using a titration experimental design (2). Throughout the investigation, the volume of solvent used was held constant and the mass of potas-
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sium chloride was varied. For the KCl-MeOH-H,O system sets of mass-volume, time-temperature, and solubility data were collected for the solvent compositions, 25,50, and 75% (per cent masa) methanol. The same data were collected for the KC1-H20 and the KCl-MeOH systems. Procedure Reagent grade anhydrous methanol and distilled water in tile indicated massea were used to prepare the solvent. Pulverized reagent grade potassium chloride wsa used. A 100.00-g portion of solvent was added to a 180-ml tall form beaker in a 9- X 9- X l4om cardboard box. Timstemperature readings to O.l°C were rewrded every 30 seconds for 5 minutes during the premixing period. For those assignments in which the aptem in it8 6nsl state had two phases, the solvent was heated before the KC1 was added to a temperature, i,such that (1 25'C) approximated the anticipated AT for the syatem being studied. Immediately after the &minute premixing time, the arnrigned maaa of KC1 was added to the solvent while the mixture was rapidly stirred with a glaaa stirring rod. The recording of time-temperature readings was wntinued every 30 sewn& far a. In-rninut,e postmixing time period. The reaction mixture wns
equilibrated in a closed container in a conatant temperature bath at 25.00°C. The mass of a 25.0C-ml portion of the mixture was found. If solid KC1 was present after equilibration, the undissolved solid was removed by suction filtration. The masses of the dry KC1 and of a 25.0&d portion of the filtrate were found.
Using the mass-volume data, the solubility data, and the densities of the reactants reported in the literature (S), the volumes and masses of the reactants, of the reaction mixture, and of the undissolved KC1 were found. The volume change, AV, and the apparent mold volume, *V, of KC1 were calculated (4). From time-temperature curves, the temperature change, AT, was found and used with the heat capacities of the solvent (6) and of KC1 @),the experimentally determined calorimeter constant, and the mass of the reactants to calculate the heat transferred and the enthalpy of solution, AH(real), at 25'C for each composition of the system studied. The secondary data were processed using the Q rejection coefficient (7) for the assignments with fewer than 10 determinations and the standard deviation procedure (8) for data rejection for assignments with 10 or more determinations. The confidence level with the Q rejection coefficientwas 90% and with the standard deviation procedure was 95%. The secondary data for the properties of each of the systems studied were plotted and extrapolated to obtain the magnitude of the property of the system a t the saturation point. The real &differential functions (partial mold quantities) for enthalpy, entropy, and free energy changes, the ideal differential functions, and the excess functions were calculated for the systems studied. Interpretation of D d a
Solubility: The experimental solubility of KC1 in the MeOH-H20 systems was compared with the ideal solubility which was approximated from equation (1).
where XKCI
mole fraction of KC1 in an ideal saturated solution at 25% = average enthalpy of fusion of KC1 far the tempemture range 1045298'K, 5.06 kcal/mole =
Figure 1. Comparison of experlrnsdol and l d e d solubility of potosrlvm chloride a t 25'C. 0 represents Ideal vmluer.
compared with the volume change, AV(ideal), for the formation of an ideal solution. The AV(idea1) was found by assuming that the formation of an ideal solution would involve a two-step process: KCI(I)
= =
, :;,&
(2)
KC1 (saturated solution)
(3)
,
,
-E -1.5 2 -1.0
temperature of fusion of KC], 1045'K temperature of the solution, 298'K
A more precise method of calculating XKCIis given in reference (10). By using XKC, = 2.23 X lo-) [ohtained from equation (I)], the number of moles of potassium chloride that would he present in the ideal solution a t 2 5 T was calculated. The experimental solubility and the ideal solubility of KC1 in the MeOH-H20 systems are compared in Figure 1. The experimental solubility of KC1 in the systems of low X x . 0 ~ (0.W0.6) deviates appreciably from the ideal solubility. This deviation indicates considerable interaction for these compositions. As Xx.0~ increases (0.6-LO), the experimental solubility a p proaches the ideal solubility so that the amount of interaction appears to decrease. Hence, the KC1 appears to be solvated by the water to a greater extent than it is solvated by the methanol. Volume change: The experimental volume change, AV(real), for the formation of a saturated solution was
+ solvent (1)
KCI(1)
The volume change, AVx, for equation (2) is the difference between the molal volumes of liquid and of solid KC1 at 25'C. The volume change, AV2, for equation (3) is zero because an ideal solution is being formed. Therefore, AV(idea1) will be equal to AVl. A comparison of AV(rea1) and AV(idea1) (Fig. 2) reveals that there is a large volume contraction for systems of X x m ~ 0.0-0.6. For systems of high X r . o ~ , 0.6-1.0, the systems show a very small contraction. These trends suggest that there could be more interaction between potassium ions, chloride ions, and water than between the ions and methanol. However, one of the reasons that AV(rea1) decreases as Xarao=increases is that the quantity of KC1 dissolved in the solvent decreases as the Xx.0~increases.
f.9) \-,
True T
-
KCl(s)
-0.5 0 0.5 0
0.2
0.4
0.6
0.8
1.0
X Y ~ OinHsolvent Figure 2. a t 25'C.
R e d ond ldaol volume change versus mole fraction of methonol 0 represents Idem1 volume changes.
Apparent molal volume: By using the apparent mold volume of KC1 in each of the solvents, the volume change can he considered on a per mole basis of KC1. Thus, ' V K ~shows the volume change in terms of KC1. The change in apparent molal volume of KC1 in satr urated solutions of each of the solvents is shown as a function of the composition of the system (Fig. 3). The apparent molal volume changes indicate that KC1 causes a much greater contraction of volume in forming saturated solutions in methanol than when saturated solutions are formed in Ha0 or MeOH-HpO systems. Volume 42, Number 7, July 1965
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centration of C, that the composition of the solution does not change. For the special case in which the KCI-MeOH-H20 system is saturated with KCl, the free energy change for equation (4) is zero. Thus, for the process [equation (4)] a t the saturation point,
01 0
,
,
,
0.2
, , 0.4
, , 0.6
, 0.8
.
1 1.0
X u a a in solvent Flgvre 3. Apparent mold volume of potasrlvm chloride versus mole fraction of methanol at 2S°C.
The evidence indicates that the interaction between the ions and methanol is greater than between the ions and water or between the ions and mixtures of methanolwater. I n contrast, the volume change suggests greater interaction when the composition of the system has water in excess. Enthalpy of solution: The experimental enthalpy of solution, AH(real), per mole of KC1 dissolved is compared (Fig. 4) with the enthalpy change that would occur for the formation of an ideal solution, AH(idea1). The ideal enthalpy change was calculated on the basis of the two-step process shown in equations (2) and (3). The enthalpy change for equation (2) is the enthalpy of fusion of KC1 a t 25'C. The enthalpy change for equation (3) is zero for the formation of an ideal solution. Thus, the ideal enthalpy change is equal to the enthalpy of fusion of KC1 a t 25'C. The real enthalpies of solution of KC1 in water and in the MeOH-H90 svstems are more endothermic than the ideal enthalpy of "solution of KC1 a t 25'C for systems of Xnzeon= 0.0 to 0.85. On the other hand, the real enthalpy of solution of KC1 in MeOH is less endothermic than the ideal enthalpy of solution of KC1. The relative increasing order of the real enthalpy changes appears to he MeOH < H,O < MeOH-Ht0 systems. Comparison of Enthalpy, Entropy, and Free Energy
The enthalpy, entropy, and free energy changes for the KC1-MeOH-H20 system can he most meaningfully compared by considering them as partial molal functions. Equation (4) applies to the addition of solid KC1 KCl(s)
-
KCl(solution, CJ
(4)
to such a large quantit,y of solution of KC1 with a con-
Several methods are available for obtaining partial molal functions from experimental data (11). The partial molal enthalpy change per mole of KC1 is essentially the slope of a graph of real enthalpy of solution per mole of solvent versus moles of KC1 per mole of solvent. The partial molal enthalpy change for a given solvent can be obtained for solutions of KC1 a t different concentrations and can be extrapolated to the saturation point to give the partial molal enthalpy change a t the saturation point. The differential dissolution process can he considered as occurring in two steps represented by equations (2) and (6). KCI(1)
-
KCl(saturated soh)
(6)
The enthalpy change for equation (2) is 3.56 kcal/mole of KC1 a t 25'C (18). When forming an ideal solution, the ent.hdpy change for equation (6) is zero. Therefore, the ideal partial molal enthalpy change is equal to 3.56 kcal/mole of KC1 a t 25'C. The entropy change for equation (2) a t 25°C is 0.98 cal/mole-deg (IS). For an ideal solution, the entropy change for equation (6) is
ASISW~, = -R
(7)
in X K C ~
where XKCIis the mole fraction of KC1 in a saturated solution a t 25'C. The ideal partial molal entropy change is the sum of the entropy changes for equations (2) and (6). Excess functions for the systems may then be defined
where f represents a function, that is, entropy or enthalpy. The real partial molal enthalpy change was obtained by extrapolation and the real partial molal entropy change was obtained by using equation (5). The excess partial molal free energy change was obtained from To compare the real and ideal partial molal functions, ~l-f(real), d ( i d e a l ) , AS(real), and AS(idea1) are plotted against XM,OH (Figs. 5 and 6).
I $ 54
22 u
3
.E
17 2 II
a
0
0.2
0.4
0.6
0.8
1.0
Xar.ox in solvent Figure 4. Eiperimsntol and ideal entholpy of rolvtion per mole of dissolved potosium chloride versus mole froction of methonol a t 2S°C. .~reprorontr ideal vdues.
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1
G 0
0.2 Xy.on0.4 in solvent 0.6
-
0.8
1.0
Figure 5. Comparison of A&dl and AHlideoll for the potordum rhoride-methanol-water system. 0 indicakr the ideal valuer.
The relationships which exist between the values of ~H(rea1)and AH(idea1) shown in Figure 5 are the same as the relationships between AH(real) and AH(idea1) as discussed with Figure 4. However, the interpretation given with Figure 4 applies to the two-step integral process represented by equations (2) and (3), but with Figure 5 the two-step differential process is involved as represented by equations (2) and (6).
KC1-MeOH-H20 solutions. TAS(excess) suggest that KC1 produces the smallest increase in randomness when it is dissolved in a saturated KC1-MeOH solution. &@excess) indicates the combined structural and bonding effects of dissolving KC1 solid in saturated 102-MeOH-H20 solutions. ~6(excess)in Figure 7 indicates that KC1 is solvated to a greater extent by water than by methanol. Further Consideration of the Data
X X ~ O in E solvent Figure 6. Comparison of ASlreall and AS%dea~for the potassium chloride methanol-water system. indicate* the ideal valuer.
All of the values of &S(real) are positive, indicating that an increase in randomness occurs when solid KC1 is dissolved in the saturated KC1-MeOH-H,O solutions. However, &.$(real) for water and for the MeOH-H,O systems are more positive than the corresponding &$ideal) up to Xmeoe = 0.85. The increase in randomness in these systems is greater than the increase calculated for the formation of a n ideal solution. For methanol, &.$(real) is less than the &.$(ideal),indicating that the increase in randomness in the KC1-MeOH system is less than that calculated for the formation of an ideal solution. The excess functions of enthalpy, free energy, and entropy partial molal changes are shown in Figure 7. AR(excess) is a measure of the type and extent of nonideal bonding in the saturated KC1-MeOH-H20 solutions. Figure 7 indicates that the extent of non-ideal bonding of KC1 with the solvents increases in the order MeOH-H20 < H 2 0 < MeOH. TAS(excess) is a measure of the type and extent of non-ideal structural changes (changes in randomness) which occur when KC1 solid is dissolved in saturated
Figure 7.
Comparison of A%excerJ,
~ A % r c e s ~ ,and AG(Fxcrs~1for
the potorsivm chloride-methanol-water system.
The data obtained can be examined to determine if a structural model for the KC1-MeOH-H20 system can be constructed by extending the model developed for the MeOH-H20 system (1). The extended model must account not only for dipole-dipole interactions but also ion-dipole interaction. The MeOH-H20 model developed previously was based on the followingassumptions. Methanol in the pure liquid state consists mainly of chains of methanol molecules. Each methanol molecule has two occupied bonding sites and one unoccupied proton acceptor site. Water a t 25'C consists mainly of tetrahedrally bonded water molecules. Each water molecule has four bonding sites which are assumed to be completely occupied in most water molecules. Examination of the experimental data in terms of the structural model lead to the following generalizations. For the MeOH-H20 systems with low XNL~OH, the predominant structure of the solvent is the water structure. The majority of the bonding sites of both the water molecules and the methanol molecules are filled. For the MeOH-H20 systems with high XM.OE, the methanol structure predominates with many of the methanol molecules Laving one unoccupied bonding site. The MeOH-H20 bonds are stronger than the H20-H20 bonds or the MeOH-MeOH bonds. The extension of the MeOH-H20 structural model to the KC1-MeOH-H20 system must rationalize the observed relationships between the experimentally determined solubility and the calculated ideal solubility. In order to determine why the solubility of KC1 in methanol is less than in water, the changes in the structure and bonding which occur when KC1 is dissolved in methanol and water must be considered. By resolving this matter, the applicability of the MeOH-H,O structural model to the KC1-H20-MeOH systems can be determined. One approach is to consider the enthalpy changes for the different systems and relate these changes to those of the bonding in the systems in terms of the structural model. The relative &R(excess) values suggest that the change in bond energy which occurs when solid KC1 is dissolved in a saturated KCl-MeOH solution is greater than the change in bond energy which occurs when KC1 solid is dissolved in a saturated KC1-HIO solution. This difference could be explained by assuming that the potassium ion could interact with the unoccupied proton acceptor site of a methanol molecule to release energy. I n order for a potassium or chloride ion to bond to one of the four bonding sites on a water molecule, an H20-HzO bond must be broken. The decrease in enthalpy associated with the substitution of a potassium or chloride ion for a water molecule on one of the bonding sites of a water molecule would be less than the enthalpy decrease associated with the addition Volume 42, Number 7, July 1965
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of a potassium or chloride ion to an unoccupied bondmg site in methanol. In the MeOH-H20 systems having excess water, potassium and chloride ions must interact with methanol or water by substitution. The MeOH-Hz0 hond is stronger than the H,O-H,O bond. Therefore, the decrease in enthalpy associated with the substitution of a potassium or chloride ion for a methanol molecule on a bonding site of a water molecule is less than the enthalpy decrease in the KC1-H20 system. As the XxeoHin the solvent increases in the systems with excess water, the percentage of MeOH-H20 bonds increases and AR(excess) becomes less negative. In MeOH-H20 systems containing excess methanol, the methanol structure predominates and AR(excess) becomes more negative, possibly due to the fact that the potassium ion can now interact with the unoccupied proton acceptor sites on methanol molecules by addition. The examination of the enthalpy data revealed that the MeOH-H20 structural model could be extended to include the iou-dipole interactions in the KC1MeOH-H20 system. If only the changes in bonding in the system are considered, the solubility of KC1 would be expected to decrease in the order MeOH > H,O > MeOH-H20 systems with low Xr.oe. Thus, consideration of the enthalpy data does not resolve the soluhility question even though the MeOH-Hz0 model appeared to be extended successfully. Another approach to this problem is to examine the entropy changes in view of the structural changes as suggested by the MeOH-H20 structural model. The relative T~S(excess)values suggest that the ordering effects produced by dissolving KC1 in a saturated KClMeOH solution are greater than the ordering effects produced by dissolving KC1 in a saturated KC1-H20 solution. In methanol, a potassium ion could interact with more than one unoccupied proton acceptor site. This would result in the methanol chains being bonded together by means of a potassium ion and would account for the decrease in the excess partial molal entropy. On the other hand, water in the pure liquid state is highly bonded and highly structured. The dipoledipole bonds in water are broken when potassium and chloride ions interact with water molecules. The highly ordered water structure breaks down, resulting in an increase in the excess partial molal entropy. The increase which occurs in the TAS(excess) in MeOHH,O systems containing excess water, suggests that methanol and water interact in these solvents to produce a solvent structure which is more highly ordered than the water structure. The consideration of the entropy data indicates that the MeOH-H,O structural model could be extended to the KC1-MeOH-H20 system. If solubility were a function only of the structural changes which occur when KC1 solid is dissolved in the solvents, the solubility would be expected to decrease in the order: MeOHH20 systems with low X M ~>HHz0 > MeOH-H20 systems with high XMaH> MeOH. Although the extension of the model appeared to he satisfactory, the solubility question was not resolved. Because the excess solubility is determined by the non-ideal changes both in bonding and in structure, an examination of free energy changes in the systems might 372
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be more profitsble than a consideration of entropy or of enthalpy. AG(excess) gives the decreasing order for the solubility of KC1 in the solvents: He0 > MeOHH20 systems with low X M ~>HMeOH-H20 systems with high X n a ~> MeOH. The interaction in the KC1-MeOH system is certainly not ideal as evidenced by the large negative N(excess) value. It is primarily the entropy change (the ordering effect) which occurs when KC1 is added to KCI-MeOH solutions that is responsible for the low solubility of KC1 in methanol. The entropy change is also largely responsible for the high solubility of KC1 in water. The free energy change data indicate the feasibility of extending the MeOH-H20 structural model to the KC1-MeOH-H20 system. In addition, the changes in bonding and in structure as reflected in the free energy changes for the systems offer an appropriate explanation for the observed solubilit,y of KC1 in water, in MeOHHzO, and in methanol. Summary
The following observations can be made regarding the nature of the interaction in the KCI-MeOH-H20 system: (1) Potassium chloride interacts to a greater extent with water than with methanol. (2) The type of interaction involved in the KC1-H20 system is predominantly solvation. (3) A greater change in bond energy occurs when potassium and chloride ions bond to methanol molecules than when they hond to water molecules. (4) A greater ordering effect occurs in the system when potassium and chloride ions hond to methanol molecules than when they bond to water molecules. (5) The enthalpy and entropy changes which occur when KC1 solid is dissolved in MeOH-H,O suggest that the methanol and systems with low XM.OH water molecules interact in these MeOH-H,O systems to form a more strongly bonded and a more highly structured system than in water and in methanol. (6) The entropy changes that occur when KC1 solid is dissolved in KCI-MeOH-H20 solutions are primarily responsible for the observed trend in solubilities. Bibliography (1) NErDIa, H.A., ETAL., THIS JOURNAL, 42,309 (1965). (2) "Investigating Chemical System," Webster Division, MeGraw-Hill Book Company, Inc., New York, 1963, p. 20. (3) TIMMERMANS, J., "The Physiw-chemical Constants of Binary System in Concentrated Solutions," Vol. 4, Interscience Publishem, Inc., New York, 1960, p. 161. (4) PITZER,K. S., AND BREWER,L., "Thermodynamics," 2nd ed., McGraw-Hill Book Company, Inc., 1961, p. 205. (5) ~ M M E R M AJ., N Op. S , tit., p. 169. (6) "Handbook of Chemistry and Physics," 42nd ed., The Chemical Rubber Publishing Co., Cleveland, Ohio, 1960, p. 2272. (7) DEAN,R. B., AND DIXON,W. J., And. C h . , 23, 636 (1951). (8) P ~ R A T T L., G., "Pmbahility and Experimental Errors in Science." John Wilev and Sans. Inc.. New York. 1961, p. 88. (9) JONES,W. H., "Janaf Interim Thermochemieal Tables," Val. 2, The Dow Chemical Co., Midland, Michigan, 1960. K., S., AND BREWER, L., op. cit., p. 228. (10) P ~ Z E R K. S., AND BREWER, L., op. eit., p. 205. (11) PITZER, (12) JONES,W. H., OP. cit. (13) JONES,W. H., op. tit.
