In the Classroom
Helping Students Assess the Relative Importance of Different Intermolecular Interactions Paul G. Jasien Department of Chemistry and Biochemistry, California State University San Marcos, San Marcos, CA 92096;
[email protected] Intermolecular forces are one of many fundamental concepts taught in introductory chemistry courses. These forces are invoked to rationalize boiling and melting points of pure compounds, as well as the relative solubility of compounds in polar and nonpolar solvents. Later in the organic chemistry course these interactions are also used to rationalize certain chemical reactions. The task of analyzing intermolecular interactions leads to difficulties for many students trying to apply these ideas for the first time. One difficulty is associated with the need to understand the molecular structure and bonding in a compound to determine the primary intermolecular interactions that would occur (e.g., Does the compound have a permanent electric dipole moment? Can the compound H-bond?). A second difficulty arises in trying to assess the relative importance of the different types of interactions. For neutral compounds, most general chemistry textbooks restrict themselves to discussing three basic intermolecular interactions: (i) London dispersion or induced dipole–induced dipole, (ii) dipole–dipole, and (iii) H-bonding (see refs 1–3). Some textbooks also include other interactions, such as dipole– induced dipole interactions (4). If one views the intermolecular interaction as electrostatic in origin, the nature of the interactions includes many more types than those listed above (5, 6). However, these are rightfully considered too advanced for introductory chemistry students. A problem arises when it is explained to the student that H-bonding is the strongest type of intermolecular interaction, followed by dipole–dipole, and finally by the weak dispersion forces. This ordering will often give students the erroneous idea that compounds that H-bond will have the strongest intermolecular interactions and hence the highest boiling points. This idea is further substantiated in the mind of the student by the ubiquitous plots of normal boiling points (Tb) for the HnX compounds, where X is a group 15–17 element. These plots seem to indicate that even the largest molecules in the group have Tb lower than the smallest owing to H-bonding in the latter. In addition, textbooks further inadvertently re-emphasize this idea via tables showing the energies associated with various intermolecular interactions such as in Table 1. Table 1 can easily lead to a misconception based on perfectly logical reasoning. For example, assume a molecule has a typical H-bond strength of 20 kJ mol–1. The energy value of Table 1. Typical Textbook Representation Illustrating the Strength of Intermolecular Forces
Interaction
Energy/(kJ mol–1)
Dispersion
1–10
Dipole–Dipole
H-bond
1222
3–4 10–40
this interaction and the data in the table seem to imply that it is impossible for a nonpolar molecule with only dispersive forces to have intermolecular interactions of the same strength. This may be the explanation for the answers students give to questions such as the following: Which has a higher boiling point, H2O or C50H102? A disproportionate number of student answer H2O, since they reason it has a strong H-bond and a dipole moment, whereas the nonpolar C50H102 molecule has only “weak” dispersive type interactions. Although textbooks mention that dispersive forces have a range of strengths that depend on the “size” of the molecule, students often fail to appreciate what this means. There have been several published articles in the education literature correlating boiling points for series of compounds using molecular properties (7–10). These articles have prompted a series of letters discussing the most appropriate properties for use in such analyses (11–13). Quantitative models were presented to predict the boiling points of certain classes of compounds and were used to analyze the importance of various types of intermolecular interactions. Some of the relationships were based on statistical considerations while others were based on purely theoretical grounds. Within some of these articles is a discussion of the appropriate quantity to represent the dispersive interaction. Although older general chemistry textbooks generally correlated this effect in nonpolar compounds with the molar mass, some newer textbooks more appropriately replace molar mass with electrical polarizability. In the chemistry education literature other properties that have been used to describe the relationship of boiling point and molecular “size” include molar refractive index, surface area, volume, and number of electrons.1 Although the electrical polarizability is the most appropriate for discussing the physical origin of the dispersive effect, the use of this particular quantity introduces a new and potentially difficult concept to students. For instance, how will a student know how the electrical polarizabilities of two compounds compare? A more easily understandable, yet less physically correct quantity, is the molecular surface area. The use of surface area instead of electrical polarizability presents an easily understandable geometric concept to the students. Unlike the other easily understandable concept of molar mass, the use of surface area as a stand-in for dispersive effects allows one to rationalize the boiling point differences in different isomers of a compound (straight-chain vs branched). In addition, the use of surface area is consistent with a simple Velcro analogy for dispersive interactions that has been used by the author to describe the additive nature of dispersive interactions. The analogy with Velcro, although not perfect, does convey the basic idea that each interaction by its nature is weak, however, when found in large numbers can lead to strong adhesion. In this article, a simple model is presented that may be useful to instructors as they try to develop pedagogical tools to help students understand the relative importance and additiv-
Journal of Chemical Education • Vol. 85 No. 9 September 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Classroom
ity of the various types of intermolecular interactions. It should be noted, that the intent of this work is not to develop a means to accurately predict the boiling points of these compounds, but merely present a semi-quantitative model to represent the relative importance of the various interactions in the overall intermolecular interaction. As such, it is not recommended that the mathematical model be presented in class, but that the ideas should first be distilled by the individual instructor into a form that may be easily digested by students. Model In keeping with the description of intermolecular forces as being composed of dispersive, dipole–dipole, and H-bonding, only these three quantities will be used in a multiple linear regression (MLR) analysis (14). Thus, the equation resulting from the MLR will have the following form:
Table 2. Fitting Functions from MLR Analysis R
α1/ (K Å–2)
α2/ (K D–1)
α3/ K
α4/ K
All
0.929
1.11
—
—
202
All
0.958
1.07
20.6
—
173
All
0.982
1.09
21.4
24.8 155
All (minus alcohols)
0.986
1.13
20.7
14.8 150
All (minus amines)
0.982
1.10
21.0
26.9 156
All (minus ketones)
0.982
1.12
20.5
25.4 152
All (minus aldehydes)
0.982
1.10
19.6
26.1 154
Fitted Molecules
Tb B1 SA B2 N B 3 BH B 4
In this equation, SA is the molecular surface area in Å2, μ is the permanent electric dipole moment in Debye (D), and BH is a dimensionless indicator variable for hydrogen-bonding. Although the values of the fitting constants (αi) will depend on the particular units used, they provide a means by which qualitative information can be extracted and communicated to the students. The compounds used in the analysis consisted of straightchain compounds of 11 alkanes, 12 aldehydes, 10 alcohols, 11 ketones, 12 amines, and 11 ethers.2 Boiling points were obtained from the NIST WebBook (15). All statistical analyses were performed using the SPSS 13.0 program for the Macintosh operating system (16). Molecular electric dipole moments and CPK surface areas based on space filling models3 (17–19) were computed from the results of geometry optimizations using a simple AM1 wavefunction as implemented in the Spartan ’02 program (17). This semi-empirical method is sufficient to yield the accuracy needed for the physical properties used in this model. It should be noted that Mebane et al. (8) used the more sophisticated measure of solvent accessible surface area in their work, however, the CPK surface area is sufficient for the semi-quantitative accuracy desired here. To assess the potential variation of these physical properties with molecular orientation, a number of low energy conformations found through Monte Carlo sampling of the potential energy surface were investigated. Changes in molecular surface area with conformation are very minor; however, in the case of dipole moment, a few cases showed deviations of up to 5–10 percent.4 Lastly, the ability of a compound to H-bond was represented by an indicator variable that followed the general rules for H-bonding in general chemistry, that is, an H atom covalently bonded directly to N, O, or F. Initially only a variable distinguishing H-bonded systems from non-H-bonded systems was tried, but it was observed that there was a large difference in the data from the amines and alcohols (Table 2). Therefore, the indicator variables used were 0 (no H-bond), 1 (H-bond in amines), and 2 (H-bond in alcohols). Other more complex equations might lead to better predictive power for the boiling points of compounds in these classes. However, the goal here is only to provide information on the relative importance of these
three terms in a form that beginning students in general and organic chemistry will be able to understand. Table 2 displays the coefficients for a number of different fits along with the values of R from the MLR analyses. Including only the surface area term in the fit accounts for 86% of the variance in the data. This is not unexpected, given that in fitting the boiling point for each class of compounds separately, the area term accounts for 98% of the variance in boiling point within each group. Using only the surface area and dipole moment terms accounts for 92% of the variance, while including all three “intermolecular interaction” terms in the function accounts for 96%. In all cases, the fitting coefficients and equations reported are all statistically significant ( p < 0.001). Furthermore, the fitting coefficients varied only slightly when changes in the dipole moment values were made in the data or when whole classes of compounds were removed from the data set. (The only large difference is seen for α3 in one fit and is due to the BH weighting of 1 vs 2 for alcohols and amines). Overall, the equation that best fits all the data is Tb
1.1
K 2
Å
SA 21
K N D
25 K BH 155 K
Given the crude model used here, the equation does a good job at predicting the relative boiling points, not the absolute values. It should also be noted that the coefficients determined are appropriate only for the data set studied here. However, the present goal is to simply gain insight into the relative importance of the three terms in determining the boiling points of the molecules studied. One might be tempted to associate the relative size of the coefficient of the surface area-related term with the absolute contribution of this effect. However, it is instructive to interpret this equation at the limit of zero dipole moment and no ability to H-bond. If one tries to assign a physical meaning to the constant term (α4) in this limit, one could interpret this as being due to the baseline dispersive effect and any other electrostatic effects not included in the fitting equation. Therefore, some of
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 9 September 2008 • Journal of Chemical Education
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In the Classroom Table 3. Comparison of Surface Areas with Boiling Points for Some Alcohols and Alkanes Alcohol
CPK Area/Å–2
Tb/K
Comparison CPK Hydrocarbon Area/Å–2
C2H5OH
82.0
351.5
C6H14
157.3
341.9
C3H7OH
103.9
370.3
C7H16
179.1
371.5
C4H9OH
125.8
390.6
C8H18
201.0
398.7
C5H11OH
147.6
411
C9H20
222.9
423.8
C6H13OH
169.5
430
C10H22
246.0
447.2
C7H15OH
191.4
448
C11H24
267.88
468
C8H17OH
213.3
468
C12H26
289.75
489
C9H19OH
235.1
485
—
—
Tb/K
—
the dispersive effect is folded into the constant term (α4). On the other hand, the coefficient for the dispersive term (α1) is the only one of the three fitted molecular properties that has any appreciable dependence on molecular size.5 Comparisons that may be useful to students involve this “size” dependent term. Implementation As mentioned previously, it is not recommended that students be asked to use the fitting equation. If so, it could potentially become just one more formula in which to plug-in numbers with little understanding. Instead, it is suggested that instructors give students some general ideas extracted from this equation to help them understand the additive nature of intermolecular interactions. For instance, the MLR equation seems to indicate that all other things being equal in two molecules (i.e., surface area and dipole moment), the ability of a compound to H-bond increases the boiling point by about (25 K)(2) = 50 K for an alcohol. A similar increase in boiling point for a molecule of the same surface area, but not able to H-bond could be attained by the molecule possessing an electric dipole moment about (25 K)(2)∙(21 K D‒1) = 2.4 D larger than that of the alcohol. From the information contained in the MLR equation, one could also estimate how big a hydrocarbon with a zero electric dipole moment might need to be to give a comparable boiling point to a molecule with a non-zero dipole moment. For instance, pentanal (C5H10O) has a calculated dipole moment of 2.75 D, a molecular surface area of 139 Å2, and a Tb = 376 K. A dipole of this size would add (21 K D‒1)(2.75 D) onto the boiling point compared to a nonpolar molecule. However, this increase in boiling point could be accounted for by a nonpolar molecule having an increased surface area of (21 K D‒1)(2.75 D)∙(1.1 K A‒2) = 53 Å2. This corresponds to a hydrocarbon molecule with an area of 139 + 53 = 192 Å2. Referring to the data from this work (Table 3), this corresponds to a hydrocarbon with surface area between 179 Å2 (C7H16, Tb = 371.5 K) and 201 Å2 (C8H18, Tb = 398.7 K), as predicted. If one does not have a means by which to estimate surface areas, the following rule of thumb can be used: a CH2 group has a surface area of about 22 Å2. Thus for a comparable boiling point the nonpolar molecule
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would need 2–3 more CH2 groups or an additional molar mass of 28–42 g mol–1. Once again, this puts one in the range of a C7 hydrocarbon as was obtained above. Other examples that could be presented are the cases of some alcohol molecules. To have a comparable boiling point to an alcohol molecule with an electric dipole moment of 1.7 D, a nonpolar molecule would need an additional surface area of [(21 K D‒1)(1.7 D) + (25 K)(2)]∙(1.1 K A‒2) = 78 Å2. Table 3 presents a short comparison of boiling points between alcohols and alkanes. Although the hydrocarbon compared to the alcohol does not have a surface area exactly 78 Å2 larger, the table does show that the basic idea presented in the equation does qualitatively hold. It should be noted, that the relationship holds less well for larger systems, since at some point a large molecule with a polar functional group starts to look very similar to an alkane (8) and the H-bonding ability of the molecule becomes insignificant in determining Tb. Once again, it is not recommended that students perform calculations with this approximate equation. However, instructors may want to develop a set of illustrative examples that they can present to students to impress upon them how the intermolecular interactions are additive in nature. For example, one very qualitative way to relate the effect of surface area or molar mass on Tb is to note that the addition of each CH2 group increases Tb by 20–30 K. In whatever manner the instructor chooses to use this information, the approximate nature of above analysis should be emphasized to the student. Limitations The calculations illustrated above are approximate, but rough estimates such as those presented emphasize to the students that the intermolecular effects are additive and vary with molecular “size”. In addition, the point may be demonstrated more emphatically that even a nonpolar molecule with no permanent electric dipole moment or the ability to H-bond can have a “high” boiling point. Since the simple hydrides (i.e., HnX, where X is a group 14–17 element) were not used in the training set for the model suggested here, it is not appropriate to try to apply the current model to these systems. The analysis here is meant to help students understand the trends in boiling point of the typical “larger” straight-chain molecules they would expect to see in general chemistry and also in organic chemistry. Therefore no special effort was made to try to include small hydride systems, many with low boiling points, in the current analysis. Extension to More Advanced Courses The current work is intended to provide a pedagogical tool for instructors in helping students understand the role of intermolecular interactions in determining Tb. However, it could easily be modified to provide a computational exercise in quantitative structure–property relationships (QSPR) or quantitative structure–activity relationships (QSAR) that is suitable for upper-level chemistry students. Several such exercises have been reported in this Journal (20–22). Students could either be provided with boiling points and property data or do a literature search or semi-empirical
Journal of Chemical Education • Vol. 85 No. 9 September 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Classroom
quantum chemical calculations to obtain these data to be fitted. This should be determined based upon the amount of time the instructor wishes to allocate to this investigation. After obtaining these data, students could make use of any number of statistical packages readily available at most universities. In most cases, undergraduate students are not familiar with the methods needed to perform the full analysis, but are familiar with some aspects. Therefore, it is recommended that the final MLR fitting be done with close instructor supervision. The author has successfully used a variant of the method described in this article as a computational experiment in his upper-level physical chemistry laboratory. In that exercise, students are given a small number of organic compounds and a list of potential properties that might be related to boiling point. Students then use the Spartan program to calculate a number of molecular properties and tabulate their results. They use a simple linear regression analysis to determine which properties are most related to Tb and to determine which properties are related to each other. This initial data analysis can easily be done with a simple spreadsheet program such as Excel and helps students narrow down the final properties to try in their MLR analysis. The overall process helps teach them not to include strongly correlated parameters in a fit, since this will lead to linear dependencies. Lastly, with instructor assistance, students are guided to discover their best fit with the smallest number of parameters and try to use their chemical knowledge to interpret why these parameters may be correlated with Tb. Conclusion A crude model has been developed to provide a semiquantitative estimate of the relative effects of dispersion, dipole– dipole interactions, and H-bonding on the boiling points of a series of straight-chain organic compounds. Although it is not predictive in terms of the absolute boiling points of these compounds, this model provides a framework that may be useful to instructors and students in comparing the strengths of the three basic types of intermolecular interactions. It is not claimed that the coefficients of the three intermolecular interaction terms are unique or anything more than rough estimates, but the model may help students to more fully understand the additivity of intermolecular interactions. Lastly, the use of the results from this model may help specifically address the fact that dispersion effects increase with molecular size, which although stated in many texts is often not emphasized sufficiently. Acknowledgments The author would like to thank Michael Schmidt and the referees for their many valuable suggestions. Their comments improved this report tremendously. Notes 1. For the compounds studied in this work the aforementioned quantities had pair-wise Pearson correlation coefficients of greater than 0.995. This indicates that any of these would be suitable quantities for use in the mathematical model used here. 2. The specific compounds and data used are available in the online material. CH4 was omitted from the list of fitted alkanes, since
its high symmetry and close packing ability make it anomalous even among the alkanes. 3. The CPK surface areas were based on the space filing volumes as parameterized in the Spartan software. These are based on the original idea of Corey and Pauling (18) and Koltun (19). As stated in the Spartan User Manual, “As the atom sizes have been chosen to reproduce experimental X-ray crystal packing data, space-filling models are intended to portray overall molecular size. Space-filling models closely approximate electron density surfaces.” 4. The coefficient of the μ term in the MLR equation is not particularly sensitive to the exact value of μ used. 5. The calculated values of the electric dipole moments of the polar molecules are essentially independent of the size of the molecule for all but the smallest systems in each class.
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Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Sep/abs1222.html Abstract and keywords Full text (PDF) Links to cited URLs and JCE articles Supplement Data used in this work are available in Microsoft Excel format
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