Determination of Equilibrium Constants using NMR Spectrscopy

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1 CHEM 331L Physical Chemistry Laboratory Revision 1.0 Determination of Equilibrium Constants using NMR Spectrscopy In this laboratory exercise we will measure a chemical equilibrium constant using key proton signals in a Nuclear Magnetic Resonance (NMR) spectrum. Those doing the traditional P Chem experiments will examine a keto-enol tautomerism, while those doing the biophysical experiments will look at the cis-trans equilibrium for a peptide bond. In each case, the relative concentration of the equilibrium species can be determined from the NMR signal strength. The relative concentrations can then be leveraged to determine the desired equilibrium constant. Solvent effects on the equilibrium constant will be examined. In general, we write the equilibrium constant K c for a chemical reaction: a A + b B c C + d D as: K c = (Eq. 1) Recall, each concentration [i] is the equilibrium concentration of species i relative to the standard concentration of 1 Molar; c i o = 1M. Thus, K c is unit-less. Once K c has been determined, the Standard Gibbs Free Energy change for the reaction can be calculated: G o (T) = - RT ln K c (Eq. 2) This can then be interpreted in terms of the Enthalpic ( H o ) and Entropic ( S o ) effects of the chemical reaction: G o = H o - T S o (Eq. 3) Traditional Experiment Aldehydes and Ketones typically exist in solution as a mixture of keto and enol tautomeric forms:

2 With a few important exceptions the keto form heavily dominates the equilibrium. For example, when dissolved in Water, only about 0.01% of Acetone molecules exist in the enol form. Although the enol form is the minor form, many reactions depend on the formation of this tautomer as an important intermediate. Also, the enol form of -ketoesters and -diketones can be stabilized by formation of a internal hydrogen bond: The equilibrium constant for the tautomerization reaction can be written as: K c = (Eq. 4) The solvent plays an important role in determining K c. This can occur through specific solutesolvent interactions such as hydrogen bonding or charge transfer. In addition the solvent can reduce solute-solute interactions by dilution and thereby change the equilibrium if such interactions are different in eno-enol, enol-keto, or keto-keto dimers. Finally the dielectric constant of the solution will depend on the solvent and one can expect the more polar tautomeric form to be favored by polar solvents. Experiments in Physical Chemistry, 8 th Ed. Shoemaker, Garland, and Nibler The protons of the keto and enol forms are in distinctly different chemical environments that can be distinguished via NMR spectroscopy. The relative strength of the NMR signals will be proportional to the concentration of each different form. Thus, the equilibrium constant for the reaction can be determined by measuring the integrated NMR signals for the enol vinyvl and keto methylene protons of each form. We will measure K c for the following dicarbonyl compounds: Acetylacetone Ethyl acetoacetate This will be done using the relatively non-polar solvent CDCl 3 and the more polar DMSO-d 6.

3 Biophysical Experiment Naturally occurring -amino acids are the monomeric building blocks of proteins and small peptides. Because the peptide bond has a resonance form that exhibits significant C=N double bond character, rotation about this bond is restricted. This means the peptide bond can exist in both the cis and trans isomeric forms: The equilibrium constant for the isomerization reaction can be written as: K trans = [trans] / [cis] (Eq. 5) Biologically, the trans isomer dominates because of the energetically unfavorable interaction between the R groups in the cis isomer. However, Proline residues are special because their side-chain forms a secondary -amine group. For this reason, both the cis and trans isomers are energetically roughly equivalent.

4 We will use N-acetyl-L-proline as a model for peptide bonds involving Proline and will measure the equilibrium constant for the cis-trans isomerism. The NMR signals of the and protons are sensitive to the cis-trans isomerization. The relative strengths of the NMR signal will be proportional to the concentration of each different form. Thus, the equilibrium constant for the reaction can be determined by measuring the integrated NMR signals from and protons of each form. NMR Spectra in General The proton at the heart of the Hydrogen atom, like the electron, exhibits behavior reminiscent of a spinning top. And, like the electron, its spin is quantized; limited to the states of Up and Down. In the presence of a strong external magnetic field (H o ), the energy of the two spin states splits; the stronger the field the greater the splitting. A photon whose frequency is such that its energy matches the energy difference between the spin states can be absorbed: E = E photon = hc / In NMR spectroscopy, these photons will lie in the Radio Frequency region of the electromagnetic spectrum. Now, this would be rather uninteresting if all the Hydrogen atoms in a molecule had nuclei that absorbed at exactly the same frequency. We would observe a single absorbance peak. However, locally, each Hydrogen atom is in a different environment. These environmental differences will

5 lead to slight differences in the magnetic field experienced by the proton and will cause the splitting to vary slightly. This will lead to differences in the frequency of the absorbed photons. For instance, protons near the exterior of a Benzene ring experience a deshielding due to a locally induced magnetic field arising from the circulation of the electrons. This causes the spin state splitting to increase and shifts the absorbance frequency. This Chemical shift effect is measured in machine independent units of. The chemical shift is highly correlated with molecular structure and will provide us with an important clue as to the environment in which each proton finds itself. Finally, neighboring protons can influence the environment of each other via a mechanism called spin-spin coupling. Consider two neighboring protons A and B. A will observe that B can occupy its two possible spin states. Whether B is spin Up or Down will influence the spin states of A; the coupling is through the chemical bonds connecting the Hydrogen atoms. One case will cause A to absorb at a slightly higher frequency and the other a slightly lower frequency. This will lead to a splitting of A s absorbance into a doublet. If A couples to two Hydrogen atoms, then the splitting will occur again and a triplet will be observed; etc. So, spectral information concerning Chemical Shift and Coupling will provide important clues about the molecular environment of each Hydrogen atom in a molecule. In this lab, this information will provide us with the relative concentrations of the equilibrium species needed to calculate the equilibrium constant K c /K trans.

6 Procedure Traditional Experiment 1. Prepare a 0.20 mole fraction solution of Acetylacetone in CDCl 3 containing TMS in a 5 ml volumetric flask. 2. Prepare a 0.20 mole fraction solution of Acetylacetone in DMSO-d 6 containing TMS in a 5 ml volumetric flask. 3. Prepare a 0.20 mole fraction solution of Ethyl acetoacetate in CDCl 3 containing TMS in a 5 ml volumetric flask. 4. Record the NMR spectrum for each solution. The enol vinyl proton signal occurs in the = 5.1 to 5.7 region of the spectrum. The keto methylene proton signal occurs in the = 3.4 to 3.8 region. Integrate the relative strengths of these signals for each case. Do this at least three times for each signal. This will allow for an estimation of the error in these values. Biophysical Experiment 1. Dissolve about 5 mg of N-Acetyl-L-Proline in ~0.7 ml of Acetone-d 6 containing TMS. 2. Dissolve about 5 mg of N-Acetyl-L-Proline in ~0.7 ml of a 45:55 mixture of Benzene-d 6 and CDCl 3 containing TMS. 3. Dissolve about 5 mg of N-Acetyl-L-Proline in ~0.7 ml of D 2 O; acidic solution. 4. Dissolve about 5 mg of N-Acetyl-L-Proline in ~0.7 ml of D 2 O to which a small amount of NaOH has been added; basic solution. 5. Record the NMR spectrum for each solution. Identify the signals due to the and protons of the Proline residue. Integrate the relative strengths of theses signals for each case. Do this at least three times for each signal. This will allow for an estimation of the error in these values.

7 Data Analysis 1. Calculate K c /K trans for each solvent. Include an appropriate error estimate. 2. Calculate G o for each solvent. Include an appropriate error estimate. 3. Discuss the effect of solvent (and ph for the biophysical expt.) on K c /K trans. What do your results suggest about the relative polarity of the two forms?

8 References Cook, Gilbert and Feltman, Paul M. Determination of Solvent Effects on Keto-Enol Equilbria of 1,3-Dicarbonyl Compounds Using NMR, J. Chem. Ed. 84 (2007) Shoemaker, David P.; Garland, Carl W. and Nibler, Joseph W. (2009) Experiments in Physical Chemistry, 8 th Ed. McGraw-Hill, New York. Streitwiesser, Andrew and Heathcock, Clayton H. (1981) Introduction to Organic Chemistry, 2 nd Ed. Macmillan, New York. van Holde, Kensal E.; Johnson, W. Curtis; and Ho, P. Shing. (2006) Principles of Physical Biochemistry, 2 nd Ed. Pearson, New Jersey. Williams, Kathryn R.; Adhyaru, Bhavin; German, Igor; and Alvarez, Eric. The Cis-Trans Equilibrium of N-Acetyl-L-Proline: An Experiment for the Biophysical Chemistry Laboratory, J. Chem. Ed. 79 (2002) 372.

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