How is the melting point of a molecular compound affected by its structure?

Transcription

1 How is the melting point of a molecular compound affected by its structure? Pre-experiment Questions (Please come to class prepared to discuss your answers to questions 1-4.) 1. Compile a table, Table 1, containing the structure and melting point for each of the following molecules: pentane, diethyl ether, butanol, dodecane, and icosane. (You may find the NIST Chemistry WebBook to be helpful.) 2. Examine the data in Table 1 and look for trends in melting points. At the molecular level, what structural parameters seem to affect the melting point, and how? Propose at least two parameters that could explain some of the variability in melting point. 3. Some of your parameters would have to be measured in a lab or computational experiment. Propose at least two numerical parameters that we could determine just by examining the Lewis structures of the molecules, and describe the effect of each parameter on the melting point. 4. We have been thinking about melting point at a molecular level. Let s scale up to the macroscopic world. How would the values of each of your parameters affect the thermodynamic function ΔfusH? 1

2 In class discussion 5. Summarize how you could use your parameters to predict the melting point of a molecule. 6. Derive an equation for melting temperature as a function of ΔfusH and use it to justify your model. Experiment: part one Suppose that you have: hexane, octane, decane, t-butanol, 2,2-dimethylpropanol, 1- butanol, 1-pentanol, 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol, cyclohexanol, 1,4- butanediol, 1,6-hexanediol, cis-1,4-cyclohexanediol, and 1,8-octanediol in the lab. 1. Propose two experiments to test your model from question 5. (Be sure to identify the parameters you are using to predict the melting point of a molecule.) On the whiteboard, write a one-sentence description of each experiment, its expected outcome, and how you will analyze your data. Check with your instructor before going on to step Look up the melting point for the compounds in your experiment. The NIST WebBook is an excellent source of data. Thinking About the Data 3. Below your description, draw the molecules involved. 4. Annotate the molecules with the values of their model parameters. 5. Annotate your structures with their melting points in kelvin. 6. Does the melting point data confirm the predictions? 2

3 7. Present your results to the class and discuss in what way your data either confirms or refutes your model. 8. Consider any outlying data point. In what way does it deviate from the trend? 9. Based on your model look up the appropriate thermodynamic property (preexperiment question 6) to see if it will explain any anomalous data. 10. Propose an additional structural property that would explain the data set. Justify your answer with the melting point equation. 11. In order to develop a quantity that correlates with this property, is there an equation that generally relates this additional parameter to the thermodynamic function that affects melting point? 12. Summarize the overall relationship between the structural parameter, the thermodynamic parameter, and melting point. Additional Information We can use Boltzmann s equation to calculate the entropy of a system: S = R ln W Here W is the number of microstates contained in a macrostate. Flexible molecules can adopt multiple conformations, generating entropy. Sconformation = R ln Wconformation The number of conformations is function of the number of rotatable bonds; this parameter is usually given the symbol τ. A bond is rotatable if it is a single bond that is not in a ring. (We are simplifying a bit here; bonds in large rings can rotate, and resonance can affect rotation. We will ignore those complications in this experiment.) Because hydrogen atoms are so light, the entropy generated by the rotation of a methyl group is negligible, so terminal bonds are not considered rotatable. 3

4 Consider the Newman projection of butane shown below. Butane has one non-terminal single bond, so τ = 1. Note that there are three conformers. This is true for all rotatable bonds, so we can calculate the total number of conformations from τ: Wconformation = 3 τ Thus, the conformational entropy is a function of the number of rotatable bonds: Sconformation = R ln (3 τ ) Thus, the conformational entropy is a linear function of τ: Sconformation = τ R ln (3) Experiment: part two Suppose that you have: methylcyclobutane, neopentane, 1,1-dimethylcyclopentane, bicyclo[3.1.0]hexane, trans-bicyclo[3.3.0]octane, and cubane in the lab. 1. Build each of these the molecules in Spartan, webmo, or another program and rotate them in 3-D. 2. Propose an experiment to test your model. (Be sure to identify the parameters you are using to predict the melting point of a molecule.) On the whiteboard, write a one-sentence description of your experiment and its expected outcome. Check with your instructor before going on to step Look up the melting point for the compounds in your experiment. Thinking About the Data 4. Below your description, draw the molecules involved. 5. Annotate the molecules with the values of their model parameters. 6. Annotate your structures with their melting points in kelvin. 7. Present your results to the class and discuss in what way your data either confirms or refutes your model. 4

5 8. Consider any outlying data. How does it deviate from the trend? 9. Propose an additional model parameter that would explain the data set. 10. Compare ΔfusH of two molecules to assess whether or not this thermodynamic function is consistent with the melting point for this additional parameter. 11. Based on the melting point data, what does this indicate about the difference in entropy of the solid and liquid state for a symmetric molecule? Explain. 12. Would a highly symmetric molecule have more orientations in the liquid state than an asymmetric molecule? Why or why not? 13. Would a highly symmetric molecule have more orientations in the solid state than an asymmetric molecule? Why or why not? 14. Summarize how your answers to questions 12 and 13 are consistent with your answer to question 11. 5

6 Additional Information One way to quantify symmetry is the use the rotational symmetry number, σ. The value of σ is equal to the number of indistinguishable orientations. This is illustrated for twodimensional objects shown below. Symmetric objects can fit into a lattice in more than one way; in this case, the triangles have three-fold symmetry. Asymmetric objects may still be able to form a lattice, but each object can fit into the lattice in only one way; in this case, σ = 1. 6

7 Post-experiment Questions 1. What are the values for n, h, σ, and τ for cis-1,3-cyclobutanediol? 2. In many applications we need a compound to be a fluid; that is, a liquid or gas. For instance, we might need to move it through a pipeline. What features favor a molecule existing in a fluid state rather than the solid state? 3. Suppose we need a liquid with a wide working range: that is, we want large difference between the boiling point and the melting point. What molecular features would enable this? 4. Proteins that contain a large proportion of the amino acid proline can have unusually thermal stability; it takes a surprisingly high temperature to denature them. Explain why this is so. 7

8 References (1) Dannenfelser, R.-M.; Yalkowsky, S. H. Estimation of Entropy of Melting from Molecular Structure: A Non-Group Contribution Method. Ind. Eng. Chem. Res. 1996, 35 (4), (2) Gilson, M. K.; Irikura, K. K. Symmetry Numbers for Rigid, Flexible, and Fluxional Molecules: Theory and Applications. J. Phys. Chem. B 2010, 114 (49),