Test Bank Answers Understanding The Nmr Experiment Ch.21

Chapter 21

Problem 21.1: Using Equation 21.1, determine the intrinsic line width in hertz of an excited state with a lifetime of:

Problem 21.2: For the line width found in Problem 21.1(a), determine the min­imum ppm separation that could be resolved for the following NMR field strengths:

Problem 21.3: By degassing your sample, you were able to lengthen the relaxation time of your desired signal from 0.2 to 6 seconds.

(a) By what factor will your line width decrease as a consequence?

(b) If your experiment required a signal-averaged scan of 64 scans in order to achieve the desired S/N ratio, how much longer will your experiment take as a result of degassing the sample?

Problem 21.4: In general chemistry, you learned that the integrated first-order rate equation has the form ln(A)_t = -kt + ln(A)_o. Using Equation 21.2 as a starting point, derive an analogous equation for M_o.

Problem 21.5: Rework Problem 21.3, assuming a delay between successive scans of 5 × T₁.

Problem 21.6: The following data were collected for an inversion recovery ex­periment. I_τ is the peak intensity with a delay between the 180° and 90° pulse of t. Determine the value of T₁.

Problem 21.7: The following data were collected for an inversion recovery ex­periment. I_τ is the peak intensity with a delay between the 180° and 90° pulse of t. Determine the value of T1.

Problem 21.8: Show the derivation of Equation 21.5 from Equation 21.1.

Problem 21.9: You have an NMR spectrum taken on a 400 MHz NMR with a nom­inal peak width at half-height of approximately 1.8 ppm. Use Equation 21.5 to estimate the value of T₁. Hint: You will need to use Equation 14.6 to convert ppm into hertz.

Problem 21.10: The following data were collected for a Hahn spin-echo experiment. I_τ is the peak intensity with a delay between the 90° and 180° pulse of t. Determine the value of T₂.

Problem 21.11: The following data were collected for a Hahn spin-echo experiment. I_τ is the peak intensity with a delay between the 90° and 180° pulse of t. Determine the value of T₂.

Problem 21.12: Repeat the analysis of J-coupling from Example 21.3 for a b-hydrogen in propane.

Problem 21.13: Using the J-coupling tree diagram (Figure 21.13), sketch the antici­pated splitting pattern for the b-protons from Example 21.4.

Problem 21.14: Using Figure 21.15 as a reference and model, sketch the expected splitting pattern for the M nucleus. Assume that J_MX is 0.05 ppm and that the peak is centered at 3.5 ppm.

Problem 21.15: Label each peak in the 1H-NMR spectrum of ethanol (see Figure 21.16). Explain your rationale for the peak assignments using expected J-coupled splitting patterns. What are the chemical shift values (in hertz) for the J-coupling constants? Recall that for a 200 MHz NMR, 1 ppm is 200 Hz.

Problem 21.16: Other NMR-active nuclei include ¹⁹F, ²⁹Si, ⁵⁷Fe, ⁷⁷Se, ⁸⁹Y, ¹⁰³Rh, ¹⁰⁷Ag, ¹⁰⁹Ag, ¹¹¹Cd, ¹¹³Cd, ¹¹⁷Sn, ¹¹⁹Sn, ¹²⁵Te, ¹²⁹Xe, ¹⁶⁹Tm, ¹⁸³W, ¹⁸⁹Os, ¹⁹⁹Hg, ²⁰⁷Pb, ²⁰³Tl, and ²⁰⁵Tl. Do a library search using the American Chemical Society database (pubs.acs. org) to find an application of NMR using one of these other nuclei. Write a short summary of your findings or give a brief presentation to your class.

Exercise 21.1: By degassing your sample, you were able to increase the relaxation time of your desired signal from 0.1 to 4 seconds.

(a) By what factor will your line width decrease as a consequence?

(b) If your experiment required a signal averaged scan of 500 scans in order to achieve the desired S/N ratio, how much longer will your experiment take as a result of degassing the sample?

Exercise 21.2: Using your answer from Exercise 21.1, determine the percent improvement in resolution in ppm for the following NMR field strengths:

Exercise 21.3: Is T₁ relaxation a first-order or second-order process? Write out the integrated rate equation that describes a T₁ relaxation process.

Exercise 21.4: What are the two names often given for a T₁ relaxation process? Which is the descriptively more accurate term?

Exercise 21.5: Is T₂ relaxation a first-order or second-order process? Write out the integrated rate equation that describes a T₂ relaxation process.

Exercise 21.6: What are the two names often given for a T₂ relaxation process? Which is the descriptively more ac­curate term?

Exercise 21.7: Why is it sometimes desirable to degas an NMR sample before collecting the spectrum?

Exercise 21.8: Discuss two ways an NMR spectroscopist can manipulate a sample in order to increase the spectral resolution.