Exam Questions Ch14 Nmr

Problem 14.1: From the mass spectral and elemental analysis data, you have determined the formula of an unknown compound from a petroleum distillate to be C4H8O. You have limited the possibilities to the four different structures shown below, which all have the formula C₄H₈O.

1. Describe how an IR spectrum would aid in narrowing down your choices. Be specific.

(b) Use the hydrogen NMR spectrum of your unknown (shown) to determine which of these isomers you have.

Problem 14.2: Determine if the nuclear spin (I) for each of the following nuclides is zero, an integer, or a multiple of ½. (See Example 14.1)

Problem 14.3: Determine the nuclear magnetic quantum number (m) for each of the following nuclides.

Problem 14.4: Identify the nuclides from Problem 14.3 that are NMR active. Explain your choices.

Problem 14.5: For each nuclide below, use Equations 14.4 and 14.5 and the data in Table 14.1 to determine the Larmor frequency in a 4.7 T magnetic field.

Problem 14.6: For each nuclide below, use Equations 14.4 and 14.5 and the data in Table 14.1 to determine the Larmor frequency in a 9.4 T magnetic field.

Problem 14.7: Use Equation 14.6 and the equation for the Boltzmann distribution to determine the relative population distribution between m = –½ and m = +½ for a proton at room temperature for the following NMR spectrometers:

Problem 14.8: Determine the relative sensitivity of the spectrometers from Problem 14.7.

Problem 14.9: Using the data from Table 14.1, derive a megahertz-to-tesla conversion for:

Problem 14.10: The Boltzmann equation (see “Compare and Contrast—Population Distribution for Common Spectroscopic Methods”) indicates that one can also affect the relative population of states by adjusting the temperature. Relative to room temperature, at what temperature would you need to be able to collect your spectrum in order to obtain the same signal enhancement achieved by switching from a 60 MHz NMR to a 200 MHz NMR? Discuss the implications.

Problem 14.11: As of the publication of this textbook, the highest commercial field NMR used in research laboratories is a 900 MHz NMR (for ¹H?). What is the magnetic field strength in units of tesla?

Problem 14.12: Determine the nuclear spin quantum number (I) and the nuclear magnetic quantum number (m) for each of the following nuclides. Identify the nuclides that are NMR active and explain your choices.

(a) ¹⁹F (b) ¹¹⁹Sn (c) ¹⁶O (d) ²⁷Al (e) ²³Na

Problem 14.13: What is the Bo field (in tesla) for a ¹H nucleus with a Larmor frequency of 800 MHz?

Problem 14.14: What is the Bo field (in tesla) for a ¹H nucleus with a Larmor frequency of 500 MHz?

Problem 14.15: Using Figure 14.8 as a model, create a field-splitting diagram for ¹³C showing the field splitting (E) in units of MHz for a 2.34 T, 4.73 T, 7.07 T, and 9.46 T magnetic field.

Problem 14.16: There are two fundamental reasons why the signal strength for ¹³C-NMR is much weaker than the signal strength for ¹H-NMR on any given instrument. Explain what those two reasons would be. (Hint: See Table 14.1 and the results for Problem 14.15.)

Problem 14.17: Using Example 14.4 as a guide, determine the resonance frequency difference in Hertz between ¹H signals at 1.5 ppm and 3.5 ppm as measured on an instrument with a Bo field strength of:

Problem 14.18: Assume you have a detector with a baseline spectral resolution of 20 Hz. How far apart (in ppm) must two peaks be to have baseline resolution for a spectrometer with Bo equal to:

Problem 14.19: Determine the ratio of spin active ¹H to ¹³C nuclei in each of the following molecules:

Problem 14.20: A typical ¹H-NMR experiment will incorporate n = 16 data sets into a single signal-averaged experiment. Assuming that the noise is the same and using Example 14.7 as a guide, how many signal-averaged data sets would you need to collect in order to achieve approximately the same S/N ratio in your ¹³C-NMR spectrum as you would in your ¹H -NMR spectrum?

EXERCISE 14.1: Using the n + 1 rule reviewed in Section 14.1, explain the peak splitting pattern for the compound ethyl crotonate. The structure of trans-ethyl crotonate (ethyl trans-2-butenoate) is shown alongside the ¹H-NMR spectrum.

EXERCISE 14.2: From the mass spectral and elemental analysis data, you have determined the formula of an unknown compound from a petroleum distillate to be C3H6O2. You have limited the possibilities to the four different structures shown. Each has the formula C3H6O2.

(b) Use the 1H-NMR spectrum of your unknown shown to determine which isomer you have.

EXERCISE 14.3: What is the Larmor frequency of ¹³C in a 7.07 T magnetic field?

EXERCISE 14.4: What is the Larmor frequency of 13C in a 19 T magnetic field?

EXERCISE 14.5: For each nuclide below, determine the Larmor frequency in a 14.14 T magnetic field.

EXERCISE 14.6: For each nuclide below, determine the Larmor frequency in a 21.21 T magnetic field.

EXERCISE 14.7: What is the magnetic field strength in units of tesla for a 600 MHz NMR instrument?

EXERCISE 14.8: What is the magnetic field strength in units of tesla for a 700 MHz NMR instrument?

It is conventional to describe the MHz of an NMR with respect to the resonance frequency of ¹H.

EXERCISE 14.9: Using Figure 14.9 as a model, create a field-splitting diagram for ³¹P showing the field splitting (E) in units of MHz for 2.34 T, 4.73 T, 7.07 T, and 9.46 T magnetic fields.

EXERCISE 14.10: Using Figure 14.9 as a model, create a field-splitting diagram for ¹⁹F showing the field splitting (E) in units of MHz for 2.34 T, 4.73 T, 7.07 T, and 9.46 T magnetic fields.

EXERCISE 14.11: There are two fundamental reasons why the signal strength for ¹³C-NMR is much weaker than the signal strength for ¹H-NMR on any given instrument. Explain what those two reasons would be. (Hint: See Table 14.1 and the results for Problem 14.15.)

EXERCISE 14.12: Determine the resonance frequency difference between two resonances in an NMR spectrum taken on a 300 MHz instrument. If the two ¹H signals of interest are at 2.4 ppm and 3.0 ppm, what is the frequency difference between the two peaks?

EXERCISE 14.13: Determine the resonance frequency difference between two resonances in an NMR spectrum taken on a 500 MHz instrument. If the two 1H signals of interest at 7.75 ppm and 7.90 ppm, what is the frequency difference between the two peaks?

EXERCISE 14.14: Determine the resonance frequency difference in hertz between ¹H signals at 2.20 ppm and at 2.30 ppm as measured on an instrument with a Bo field strength of:

EXERCISE 14.15: Determine the resonance frequency difference in hertz between ¹H signals at 4.45 ppm and at 4.60 ppm as measured on an instrument with a Bo field strength of:

EXERCISE 14.16: Assume you have a detector with a baseline spectral resolution of 15 Hz, comment on the resolution of the peaks in Problem 14.17 at each field strength (a–c).

EXERCISE 14.17: Assume you have a detector with a baseline spectral resolution of 10 Hz, comment on the resolution of the peaks in Problem 14.17 at each field strength (a–c).

EXERCISE 14.18: Determine the relative population distribution between m = –½ and m = +½ for a proton at room temperature for the following NMR spectrometers:

EXERCISE 14.19: Determine the relative population distribution between m = –½ and m = +½ for a proton at a temperature of 280K, for the following NMR spectrometers:

EXERCISE 14.20: Determine the relative population distribution between m = –½ and m = +½ for a proton at a temperature of 310K, for the following NMR spectrometers:

EXERCISE 14.21: Determine the ratio of spin-active ¹H to ¹³Cnuclei in each of the following molecules:

(a) Pentane (C5H12) (b) Ethylene diamine (C2H4(NH2)2) (c) Acetaldehyde (C2H4O)

EXERCISE 14.22: Determine the ratio of spin-active 1H to 13C nuclei in each of the following molecules:

(a) Glycerol (C3H8O3) (b) Heptane (C7H16) (c) Lysine (C6H14N2O2)

EXERCISE 14.23: What is the S/N ratio enhancement when ¹H-NMR experiment incorporates n = 64 data sets into a single signal-averaged experiment rather than n = 16 data sets?

EXERCISE 14.24: What is the S/N ratio enhancement when ¹H-NMR experiment incorporates n = 128 data sets into a single signal-averaged experiment rather than n = 64 data sets?

EXERCISE 14.25: Repeat the calculations from Exercises 14.12 and 14.13 with ¹³C-NMR. Describe how the enhancement effect compares between ¹H and ¹³C.

EXERCISE 14.26: If you were interested in observing nuclei other than ¹H or ¹³C in an MRI, which of these biologically available elements would be possible candidates?

(a) Oxygen (b) Calcium (c) Selenium

EXERCISE 14.27: If you were interested in observing nuclei other than ¹H or ¹³C in an MRI, which of these biologically available elements would be possible candidates?

(a) Iron (b) Sulfur (c) Nitrogen

EXERCISE 14.28: In an MRI, the patient is placed inside a central opening, the bore, of the magnetic field. The patient’s body is aligned with the magnetic field (Bo) along the z axis. The magnetic field runs from head to toe. Is this the same relative position as an NMR tube inside an NMR? Explain using diagrams. Be sure to consider the gradient coils and their function in your answer.

EXERCISE 14.29: In an MRI instrument, there are gradient coils that modify the external magnetic field, creating gradients in the field. These gradients can be set up to image sections of the body along the sagittal, transverse, or coronal planes. Use the internet to find MRI images of tissues that represent these sections and describe the perspective of the image on the tissue. This article, from the National High Magnetic Field Laboratory at Florida State University, may help you get started; you can find it at http://www.magnet.fsu.edu/educa­tion/tutorials/magnetacademy/mri/fullarticle.html.