Lebanon Valley College Annville, Pennsylvania
The purpose of this paper on interaction and the one to follow in the next issue is to present experimental and theoretical information that can serve as source material for people interested in developing an experiment involving the study of interaction. These papers will contain experimental data obtained from an extensive laboratory investigation, illustrat,ionsof dierent methods of data processing, and considerations of the theoretical implications and significance of the data. One of the features of these presentations is the construction of a model for a chemical system and the testing of the model using the experimental data collected. When two or more substances form a solution, the degree of interaction between the components will dcternline the extent to which the structure and bondiug of the substances are altered. By studying the properties of a solution the type and degree of interaction can he established. Some of the different types of interaction are given in Table 1. There are numerous experimental procedures that can be used to investigate interaction in chemical systems. Although the measurements of such properties as freezing point, boiling point, osmotic pressure, and vapor pressure are made for the purpose of demonstrating the deviation of a property of a solution from ideality, the data from these same types of st,udies could be used to consider interactions if desired. In the literature, frequent reference is made to the use of qualitative arguments developing an interaction interpretation of data such as heat capacity, refractive index, and dielectric constant. Quantitative considerations of interaction have been developed using The investigation reported here constitutes in part some of the laboratory work completed by a group of six high school teachers, two college students, and four college professors who participated in an eight-week conference at Lebanon Talley College during the summer of 1963. This conference wa? conducted to design and develop laboratory experiments and was held in conjunction with the laboratory development program of the Chemical Bond Aooroach Proiect conducted under the aus~icesof the National -.~r Science Foundation. The work on interaction was continued during the first semester of the 1963-64 academic year by the authors of this paper and by the students enrolled in a sophomore chemistry course a t Lebanon Valley College. The suthors wish to express their appreciation to Barry B. Barnhart, Paul C. Billett, David H. Deck, Harold F. Emmitt, Robert S. Hamilton, James E. Livengood, William N. Stakely, and Ronald S. Treiohler for collecting the majority of the primary data used in this paper. The comments and suggestions given by L. E. Strong were very useful in developing the section on the interpretation of the data. Acknowledgment is also made to the National Science Foundation for the financial support of aportion of this work. 1 Present address: I.ongwood College, Farmville, Virginia. ~
~
methanol-water system
such approaches as solubility determinations, thermochemical, electrometric, and activity measurements, spectrophotometric and conductivity methods. Of a more sophisticated nature are the studies of interaction that have been conducted on the effects of substances on the structure of liquids serving as solvents. Experimental methods used for such investigations include exchange reactions (4), X-ray diffraction studies (6),Raman spectroscopy (6),and NMR methods (7). Nature of the Investigation
The investigation of dipole-dipole interaction in the methanol-water system was carried out by collecting mass-volume and time-temperature data for the formation of a series of methanol-water solutions, each having a different composition. An elementary approach to analyzing the data obtained from such a study could involve a consideration of density and temperature change (AT), or heat transfer (Q), as a function of the composition of the system. More useful information about interaction in the system could he obtained by finding the volume change (AV) and the enthalpy of solution [A?I (solution)] as a function of composition. Of even more significance would be a calculation of the apparent molal volume (+V)and the apparent molal enthalpy (+H).A more sophisticated approach would involve finding the change in partial molal volume (AP) and partial molal ent,halpy With sufficientdata, the enthalpy, entropy, and free energy changes can he calculated. The methanol-water system was investigated for changes in properties as a function of mole fraction using a continuous variation experimental design (8). Seven different compositions were studied ranging from 85% (percent mass) methanol-15% water to 15% methauol-85% water. For each composition, 14 sets of mass-volume and time-temperature data were collected. These primary data were used to calculate such secondary data as densities, apparent molal volumes, and enthalpies of solution. After applying a statistical rejection procedure to the data, a given property of the system was plotted against the conlposition of the system. Each graph was studied to determine which type of interaction was indicated in the syst,em.
(a).
-
Tnhle Intermtion . - ..1. . . Tvaer .,-.-of .~ ~~~- - ~ -
Type of interaction
Chemical system
Dipole-dipole Ion-dipole Ion-ion Ion paim Locslised hydrolysis
Methanol-ethanol Potassium hydroxide-water Mercury(I1) ion-iodide ion LeFe(CN)swater Potassium acetate-water
Reference
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(a
(8)
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Procedure
After the assigned masses of reagent grade anhydrous methanol and distilled water were equilibrated in closed containers in a constant temperature bath a t 25.00°C, the reagents were poured simultaneously into a 180-ml tall-form beaker containing a thermometer graduated in O.l°C units. Time-temperature readings were recorded every 30 sec for 10 min after mixing. The beaker and contents were covered with aluminum foil and placed in a constant temperature bath. When the temperature of the reaction mixture reached 25.00°C, the mass of a 25.00-ml sample of the mixture was found. The masses of the reactants used in the calculations were the masses transferred. Using the primary data and the densities of the reactants reported in the literature (9),the volumes and masses of the reactants and the reaction mixtures were found. The A V , +VH20,,,, and +Vu.oHwere calculated (10). From time-temperature curves, AT for the system was found by extrapolation (11). Using the A T , the heat capacity of the reaction mixture reported in the literature ( I f ) , the experimentally determined calorimeter constant, and the mass of the reaction mixture, Q and AH (solution) at 25.00°C were calculated for each composition of the system studied. I n addition, the partial molal enthalpies of solution were found (IS). The secondary data were processed using the standard deviation method for data rejection (14). For a chemical system composed of two miscible liquids, the AV or *V and A T , Q , or AH (solution) for the system can be used to consider interaction. Three major generalizations can be advanced for this purpose and are summarized in Table 2. Table 2.
Relationship of thermodynamic functions
Ideal
AV, AT, Q, and AH
Solvation
AV, Q, and AH 0 AV, AH, and Q > 0 AT < 0
Association
=
0
'Vt 'V,
VI V, %I' < V, 'v, < V R *V, > V , 'V* > V , = =
Mass-Volume Data
Volume change: For all compositions studied, a negative volume change was found indicating that the type of interaction is solvation. A graph of AV against mole fraction of methanol, XaaeoH(Fig. 1) indicates that the maximum interaction appears to = 0.35. occur a t X,. Apparent molal volume: These data show that the apparent molal volume of water is less than the molal volume of water for all compositions studied. There fore, the predominant type of interaction is solvation. The plot of +VH,oagainst X,,,, (Fig. 2) indicates that the maximum interaction occurs in the solutions that have a large concentration of methanol while the plot of 'VMsOE against XM.OEshows that the maximum interaction occurs a t XLI~OH = 0.20 to 0.25. Although the composition where maximum interaction appears to occur is not the same for AV and for 'V,,,. and
/
AV versus mole fraction of methanol.
'VH,O,the difference might be expected.
AV is the arithmetical mean of the differences between the apparent molal volumes of methanol and of water and their respective molal volumes, weighted according t o the number of moles of methanol and of water in the solution. Therefore, AV represents the combined contribution of the structural changes in water and in methanol. The apparent molal volumes resolve AV into its component parts: that due to the structural changes associated with methanol and that associated with water.
Generalizations on Interaction in a System of Two Miscible Liquids
Type of interaction
310
X~ma Figure 1.
Journal of Chemical Educafion
Figure 2. Apparent molal volumes versus mole fraction of methonol (0indicates per mole of woter and 0 indicates per mole of methanol.)
Thermochemical Data
Inspection of the data for AT and Q indicates that the predominant type of interaction is solvation. However, there would be little value in plotting either property against mole fraction because neither function is expressed in terms of moles. Enthalpies and partial molal enthalpies of solution are more useful. From the enthalpies, information about both the predominant type of interaction and the degree of interaction is obtained. Enthalpy of solution: The enthalpies of solution per mole of methanol, per mole of water, and per mole of solution are all negative for all compositions studied. Solvation is the predominant type of non-ideal interaction. The AH (solution) per mole of solution is equal to the arithmetic mean of the AH (solution) per mole of water and the AH (solution) per mole of methanol, weighted according to the mole fractions of the components. The plots of these enthalpies of solution against XaeoHshow a region of maximum interaction a t X u . 0 ~ = 0.25.
5 -0.6 0
.3 -0.4
?j-0.2 0
0.2
0.4 Xxmx
0.6
0.8
1.0
Figure 3. (a) Enthalpy of solution per mole of water and per mole of methanol. (0indicates per mole of woter and 0 indicatsr per mole of methanol.)
Rgure 3. (b) Enthdpy of solution per mole of solvtlon versus mole frodion of methond
Partial molal enthalpy of solution: The partial molal enthalpy of solution per mole of water was obtained by plotting the AH (solution) per mole of methanol against the mole ratio (nE,o/nar.o~). For a given mole ratio, the slope of the curve is d(AH)/d(na,o). The partial molal enthalpy of solution per mole of methanol was obtained in a similar manner. The partial molal enthalpies of water and of methanol plotted against X H ~ O(Fig. H 4) indicate that the predominant type of interaction is solvation.
should be able to develop a reasonable mechanism regardless of the rigidity with which the data are processed. If it is desirable to stress the idea of interaction, one approach that has proved to be very successful is to have the students develop a model for the chemical system based on a series of assumptions and to test the model using the data collected. The construction of models for water and for aqueous solutions has been the subject of a number of papers. Born (15) was one of the first individuals to advance a model for a solution. Bernal and Fowler (16) advanced the tetrahedral model for the structure of water. In contrast to this model, Pauling (17) has suggested that water is a clathrate-like structure involving dodecahedra arranged in random ways relative to each other. The sphere-in-continuum model for an aqueous solution has been proposed by Fuoss (18). Other models for aqueous solutions have been advanced by Buckigham (19), by Frank (80), and by Diamond (21). Marchi and Eyring (22) have recently applied the significant structure theory to water. The model for water that they propose shows reasonable agreement with experimental data. Gurney (25),Davies (24), and Hunt (65) have included in their presentations models for the structure of water and of aqueous solutions. A structural model for the methanol-water system can be constructed on the basis of five assumptions. These assumptions are: (1) In water in the pure liquid state, a water molecule is tetrahedrally bonded to four other water molecules through hydrogen bridge bonding. In Figure 5, the bondmg of a water molecule is shown to occur a t the two positions on oxygen (Position 1 and 2 in Fig. 5) and through each of the two hydrogens (Positions 3 and 4 in Fig. 5) giving a total of four bonding sites for each water molecule. The number of
Model Proposed and Tested
If one wishes to emphasbe solution formation, a very useful approach is to have the students present a possible mechanism for the solution process a t the molecular level based on their experimental data. The students
Figure 5.
Figure 4. PorHol mold enthalpies of soluHon versus mole frastlon of methanol. (0indicahs the enthalpy changes per mole of water, end 0 Indicates the enthalpy changes per mole of methanol.)
bonding sites that will be occupied in a water molecule will decrease with an increase in temperature. At 25"C, it is assumed that a majority of the bonding sites of the water molecules are filled. Thus, the predominant structure in water is assumed to be tet,rahedral. (2) In methanol in the pure liquid state, a methanol molecule is bonded to two other methanol molecules through hydrogen bridge bonding giving a chain structure. In Figure 6, the bonding of a methanol molecule is shown to occur a t the one position on oxygen (Position 2 in Fig. 6) and through the hydrogen of the hydroxyl group (Position 3 in Fig. 6). It is assumed that the hydrogens of the methyl groups do not participate in hydrogen bridge bonding. There is not enough hydroxyl hydrogen available in methanol to bond Position 1on the oxygen of the methanol molecule. Thus, only
iU Hydrogen bridge bonding in woter in the pure liquid rtote.
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two thirds of the honding sites on a methanol molecule or two sites would be expected to be filled. The predominant stmcture in liquid methanol is assumed to he a chain stmcture. The methanol molecules are unsaturated in terms of hydrogen bridge bonding having a t least one hondmg site per methanol molecule unoccupied. (3) The dipole moments of water and methanol molecules are considered to be point charges and the attraction between molecules is due to electrostatic forces. In liquid water, liquid methanol, and methanol-water solutions, there would he dipole-dipole attractions hetween the molecules. This would imply that the waterwater bonds, the methanol-methanol bonds, and the methanol-water bonds would each have characteristic energies, EHK-a,o, EM.~H-M.oH, and Emon-are. (4) The addition of methanol to water or methanolwater systems of high mole fraction of water could result primarily in the suhstitution of methanol molecules for water molecules in the water structure. The water is saturated in terms of filled honding sites. The substitution of methanol for water could occur a t each of the four filled honding sites of each water molecule or a t Positions 1, 2, 3, and 4 in Figure 5. The process could be represented by H,O(H,O).
+ MeOH 2 HzO(H,O)~M~OH + H,O
(1)
The extent of substitution will depend on the mole fraction of methanol in the system. (5) The addition of water to methanol or methanolwater systems of high mole fraction of methanol could result in the substitution of water molecules for methanol molecules in the methanol structure. Also, addition of water molecules to the unoccupied sites of the methanol molecules could occur. The substitution of water for methanol could occur a t each of the two filled bonding sites in a methanol molecule or a t Position 2 and 3 in Figure 6. This process is represented by equation (2). At the same time, a water MeOH(Me0H).
+ H20d M~OH(IM~OH)(H%O) + MeOH
(2)
molecule may add to the unoccupied bonding site on the oxygen of a methanol nlolecule as represented by eqnation (3). MeOH(MeOH)?
+ HaO e MeOH(MeOH)n(H*O)
(3)
The extent of suhstitution and of addition will depend on the mole fraction of water in the system. The usefulness of the model can he determined by testing its validity in terms of the experimental data. This procedure represents an attempt to use macroscopic data to test a model that provides a microscopic view of the system.
Figure 6.
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Hydrogen bridge bonding in methanol in the pure liquid stole.
Journal of Chemical Education
The testing of the validity of the model can be begun by considering the effectof adding water to methanol on the volume of water and of methanol. From Figure 2, the *VHL0decreases rapidly as X M ~ Oincreases H until Xaaeoa = 0.6. On the other hand, the *VM.OHdecreases rapidly as XMeoHdecreases until XMeoH= 0.25. After this point, *Vx.oH increases. At mole fractious above 0.6, the 'VH~Ocontinues to decrease but a t a slower rate. These data suggest that the addition of a small quantity of methanol to water alters the structure of the methanol appreciably with the predominant structure of the solution being that of water. The methanol molecules would be present in the solution in a new configuration involving water molecules rather than in the form of chains. At the same time, a small portion of the water structure will be altered by the interaction of methanol and water molecules. Thus, the addition of methanol to water has disrupted both the water structure and the methanol structure as they would exist in the pure liquid state. Under such conditions, a methanol molecule is probably solvated with water molecules so that the three bonding sites in a methanol molecule (Positions 1, 2, and 3 in Fig. 6) might be filled with water molecules. When the quantity of methanol added to water is increased, there would be a decreasing quantity of water available to solvate the methanol molecules. This process would continue to destroy the water structure giving rise to a new confignration. When a large quantity of methanol is added, a point is reached a t which the number of water molecules is insufficient to occupy all of the bonding sites in methanol so that the solution now contains the methanolwater configuration as well as the chain structure of methanol. From these considerations, it would appear as if the mass-volume data are reasonably consistent with the proposed model. Next, consider the compatibility of the model and the thermochemical data. The model is tested on the basis of two processes as shown in equations (4) and (5). Water or methanol is added to a methanol-water solution of sufficient quantity that the composition of the solution does not change. The change in partial molal enthalpy for equation (4) is equal to the enthalpy of a mole of water in a methanol-water solution minus the enthalpy of a mole of water in the pure liquid state.
When water is added to a methanol-water solution, the model suggests that some or all four of the water molecules on the four bonding sites of a water molecule could be displaced by methanol molecules. According to Assumption (4), the number of methanol molecules bonded to water will be proportional to XM,OH. For compositions where XM.OHis low, it would be expected that not all of the water molecules will be substituted by methanol molecules a t the hydrogen bonding sites on a water molecule. When Xmeonis large, the majority of the water molecules being added should be solvated by methanol. If this description based on the model of the effectof adding water to methanol is correct, the experimental partial molal enthalpy change for water should be in agreement with that calculated from the bond energies for the components of the system.
2. The composition of the system nhere there is maximum interaction is at a mole ratio of three water molecules to one methanol molecule. 3. The addition of methanol to water appears to cause a collapse of hoth the water and the methanol structures resulting in the formslcion of a new structure of lower enthalpy. 4. The solvation of methanol with water a t small Xwma involves the addition of water a t the unsaturated bonding site of methanol as well as substitution of water molecules for methanol molecules. At large X m m , the primary process is suhstitution with little if any addition occurring. 5. The addition of water to methanol appears to cause a When the partial molal enthalpies of solution of water collapse of both the water and the methanol structures resulting are plotted against X M ~ Othe A ,resulting curve as shown in the formation of a new structure of lower enthdpy. 6. The solvation of water with methanol at all Xn.on inin Figure 4 is a straight lme and the slope ~ A L T / ~ X M ~ ~ E volves predominantly the substitution of water molecules by is a constant. Because the slope is constant the bondmethanol molecules at the bonding sites on a water molecule. ing of methanol molecules with the water is occurring in 7. The strength of the water-methanol bonds is greater than s regular fashion. Thus, the data support the assumpthat resulting from the asso&tian of water molecules or from the association of methanol molecules. The methanol-methanol tions on which equation (7) was developed, and the bonds are stronger than the water-water bonds. partial molal enthalpy changes per mole of water sup-
The change in the partial molal enthalpy of water (AR) in terms of bond formation and bond rnpture when water is added to a methanol-water solution of X M ~isHgiven by equations (6) and (7) which were developed from the assumptions.
port the proposed model. When methanol is added to methanol-water solutions, either substitution (eq. 2) or addition (eq. 3) can occur. If addition occurs, the enthalpy change will be much larger than if a substitution process is involved. The slope of the curve in Figure 4 indicates that as Xn20increases the partial molal enthalpy of methanol increases with a marked increase in the rate of change. These data suggest that when methanol is added to methanolwater solutions of large XM.~H substitution is the predominant process occurring. When methanol is added to methanol-water solutions of large XHIO hoth addition and substitution occur. The strength of the bonds in the methanol-water system can be compared to the strength of the bonds in methanol and in water. The basis for this comparison is the change in partial molal enthalpies of solutions based on the processes given in equations (4) and (5). Because enthalpy change is a measure of bond energy, the AFZ for equation (4) is a measure of the difference between the bond energies per mole of water in a methanol-water solution of a given composition and the bond energies per mole of water in the pure liquid state. The AR for equation (5) may he viewed in an analogous manner in terms of methanol. From the plot of the change in the partial molal enthalpies, the sign of the slopes of the curves in Figure 4 indicates that the methanol-water bonds are stronger than the water-water or the methanol-methanol bonds. In addition, the methanol-methanol honds are stronger than the water-water honds since the slope (-bBH20/ ~XM.OH) for water isgreater than the slope (+dflM,oH/ ~ X M . ~ for H ) methanol in excess methanol where water appears to interact with methanol mainly by suhstitution (eq. 2). These data tend to support the proposed model. This interpretation of the data is only valid if there are no new types of bonds formed in the solution such as a water-methyl group bond. Although Benjamin and Benson(26) have reported the same relative bond strengths as these data support, they raise a question as to the possibility of bonding between a methyl group of methanol and water molecules. On the basis of the information obtained from this investigation, the following statements might he made about the interaction in the methanol-water system. 1. There is non-ideal interaction in the methanol-water system, and the interaction invdves predominantly solvation.
Other features of the methanol-water systen~can he developed from the proposed model, but the considerations presented should illustrate the use of a strnctural model in conjunction with this type of laboratory investigation. The interpretation of the data requires the students to relate volume and enthalpy changes to hydrogen bonding, solvation, and interaction. The model might be considered to he naive and an oversimplification of salvation compared to cont,emporary theories of interaction in solution. However, the Droposed model does provide a means of interpreting the data collected for the methanol-water system, and affords an opportunity to consider hydrogen bridge bonding, structure, and interaction in a more quantitative fashion than is usually. done. References (1) BJEBRUM,N., Z. Ano~g.Allgem. Chm., 109, 275 (1920). (2) BJERRUM, N., KgL Danske. V i Dmkab., 7, No. 9 (1926):
"Selected Papers,"
Einar Munksgaard, Copenhagen,
1948. (3) ROBINSON, R. A., AND HARNED, H. .4., Chm. Rev., 28, 419 (1941). (4) BALDWIN, H. A., AND TAUBE,H., J. Chem. Phys., 33, 206 (1960). (5) BRADY,G. W., AND ROMANOW, W. J., J . Chm. Phys., 32, 306 (1960). G. E., J. Chm. Phys., 36, 90 (1962). (6) WALRAFEN, (7) MEIBOOM, S., J. Chm. Phys., 34, 375 (1961). (8) JOB,P., Ann. Chem., 9, 113 (1928). (9) TIMMERMANS, J., "The Physico-chemical Constants of
Binary Systems in Concentrated Solutions," Interscience Publishers, Inc., New York, 1960, Vol. 4, p. 161. (10) PITZER,K. S., AND BREWER,L., "Themodymmies," 2nd ed., McGraw-Hill Book Company, Inc., 1961, p. 205. (11) SHOEMAKER. D. P.. AND GARLAND. C. W.. "Emeriments in Physical 'chemistry," Mc~rak- ill ' ~ o o dCompany. Inc., New York, 1962, p. 111. TIMMERMANS,J., "The Physicc-chemical Constants of Binary Systems in Concentrated Solutions," Interscience Publishers, Inc., New York, 1960, Yal. 4, p. 169. PITZER, K. S., AND BREWER,L., "Thermodynamics," Znded., McGraw-HillBook Company, Inc., 1961, p. 384. PA-TT, L. G., "Probability and Experimental Errors in Science," John Wiley and Sons, Ine., New York, 1961, p. 88. BORN,M., Physik. Z.,1, 45 (1920). BERNAL,J. D., AND FOWLER, R. H., J . Chm. Phys., 1,515 (1933).
PAULING,L., "Nature of the Chemical Bond," 3rd ed., Comell University Press, Ithaca, New York, 1960, p. 464. SADEK,H., AND FUOSS, R. M., J . Am. Chm. Soe., 72, 301 (1950).
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(19) BUCKINGHAM, A. D., Discxis8ion Faraduy Soe., No. 24.151 (1957). (20) FUNK. H. S., A N D WEN, W. Y., DibmSim Faraday Sot,, No. 24, 133 (1957). (21) DIAMOND, R. M., J . Phys. C h m . , 67, 2513 (1963). (22) MAECHI,R. P., AND EYRING, H., J. Phy8. chem., 68, 221 (1964).
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(23) GURNEY, R. W., "Ionic Processes in Solution," McGrswHill Book Company, Inc., New York, 1953. (24) D ~ v m s ,C. W., "Ion Association," Butterworths, London, 1962, Chap. 14. (25) HUNT, J. ,P., "Metal Ions in Aqueous Solution," W. A. Benjarnm, Inc., 1963, Chap. 3. (26) BENJAMIN, L.,AND BENSON,G. C., J. Phy8. Chem., 67, 858 (1963).
