Test Questions & Answers Chapter 13 Mass Spectrometry

Chapter 13

Problem 13.1: Consider the two molecules below (molecule X and molecule Y) as analyzed by MS. Both molecules can be described as a system with three possible frag­ments: fragment A has a molecular mass of 10 amu, fragment B has a mass of 15 amu, and fragment C has a mass of 20 amu. Assume that (1) the charges generated on the fragments are either +1 or +2 and (2) only one bond is cleaved for each fragmentation. List all possible ions that could be generated, and determine which could be distin­guished explicitly and which would have m/z similar to other ions.

Molecule X: A–B–B–C

Molecule Y: C–A–C–B

Problem 13.2: The analytical chemist is often faced with having to make either a qualitative or quantitative determination. Given only what we have discussed so far in this chapter, which type of ion source (hard or soft) would you select for qualitative and which would you select for quantitative analysis? Explain your reasoning.

Problem 13.3: What would be the velocity of a methyl ion (CH₃⁺) if it were acceler­ated across a voltage of 5.0 x 10² volts?

Problem 13.4: What voltage would be needed to accelerate a tert-butyl dication (C₄H₉²⁺) to a velocity of 1.0 × 10⁶ m/s?

Problem 13.5: Demonstrate that the units in Equation 13.4 cancel out properly.

Problem 13.6: Rewrite Equation 13.4 to relate λ to concentration of particles in molarity.

Problem 13.7: Estimate the mean free path of a water molecule (2.8 Å diameter) at standard temperature and pressure.

Problem 13.8: Assuming the water molecule in Problem 13.7 is traveling at about 610 m/s, how many collisions per second is it undergoing?

Problem 13.9: If we want the mean free path of a water molecule (2.8 Å diameter) in a CI system to be 0.10 mm, at what pressure would we need to introduce reagent gas?

Problem 13.10: Using the pressure you found in Exercise 13.9, estimate the mean free path length of the theoretical organic molecule described in Example 13.2.

Problem 13.11: The mass spectrometric analysis of the common pesticide DDT (C₁₄H₉Cl₅) resulted in a base peak of m/z = 352, with the only other major peaks being 317, 235, and 165. Postulate about the type of ionization (EI or CI), the most logical mode of ionization (negative or positive mode); the ionization reaction responsible for the base peak; and the m/z= 317 peak.

Problem 13.12: What is the final velocity of the m/z = 235 ion in Problem 13.11 if an accelerating voltage of 1.3 kV is used in the mass analyzer?

Problem 13.13: Given that the half-life of the ²³⁸U-to-²⁰⁶Pb decay series is 4.47 billion years, how long ago was a zircon crystal formed if the current ²³⁸U concentration is 3.97 ppb and the current ²⁰⁶Pb concentration is 224 ppm? (Hint: Recall that radioac­tive decays follow first-order kinetics.)

Problem 13.14: A common ion formed in the ICP source is Ar₂⁺. This argon ion dimer might interfere with the analysis of what atomic ion?

Problem 13.15: In wastewater analysis, the molecular ions ArCl⁺ and ClOH⁺ are not uncommon. These molecular ions might interfere with the analysis of what atomic ions?

Problem 13.16: What resolution would be necessary in order to resolve peaks from univalent ions having molar masses of 1,058.0 g/mol and 1,058.5 g/mol?

Problem 13.17: Assuming the resolution of the mass analyzer considered in Problem 13.16 is fixed across the mass spectrum, what two m/z values could be resolved with respect to a mean m/z of 111?

Problem 13.18: A certain MS uses a magnetic sector mass analyzer having a fixed ac­celerating voltage of 2.95 kV and a radius of 0.233 m. What magnetic field (in T) must be used to focus a carbon dioxide ion [CO₂⁺] on the detector?

Problem 13.19: If the same mass analyzer as described in Problem 13.18 were used and the accelerating voltage was kept constant, what magnetic field would be required to measure a bis-imidazolium dication, (C₇H₈N₄)²⁺?

Problem 13.20: Assuming the same parameters described in Problem 13.18, what magnetic field range would you need to scan in order to sweep a m/z range of 40 to 4,000 Da?

Problem 13.21: What is the magnitude of electrostatic field (E, in V/m) that would be needed in order to impart a curvature (r) of 0.233 m with a fixed accelerating voltage of 2.95 kV?

Problem 13.22: Calculate the kinetic energy of a univalent ion in the spectrometer described in Problem 13.21.

Problem 13.23: Determine the time of flight for an 800 m/z ion accelerated across 6.5 kV and allowed to drift through a length of 2 m.

Problem 13.24: If the instrument used to measure the 800 m/z ion, as described in Problem 13.23, has a resolution of 15,000, what is the expected peak width for that ion?

Problem 13.25: Demonstrate that the units in Equations 13.23 and 13.24 cancel each other out.

Problem 13.26: What is the resonance orbital radius of the CH₃⁺ with a v_xy of 3.0 x 10⁴ m/s in a 7.035 T mag­netic field? What is the precession frequency?

Problem 13.27: To avoid collision with the cell walls, what is the maximum pulse width for a 2 V excitation signal that could be used for a 2 cm cell in a 7.035 T magnetic field?

EXERCISE 13.1: Consider the electron ionization source depicted in Figure 13.4. What do you think would be the effect of decreasing the voltage between the filament and the target? What effect would using an unheated filament have?

EXERCISE 13.2: What would be the velocity of an imidazo­lium ion (C₃H₄N₂⁺) if it were accelerated across a voltage of 22.3 kV?

EXERCISE 13.3: What voltage would be needed to accel­erate an imidazolium ion (C₃H₄N₂⁺) to a velocity of 4.2 × 10⁵ m/s?

EXERCISE 13.4: Given that the half-life of the ²³⁵U-to-²⁰⁷Pb decay series is 704 million years, how long ago was a zircon crystal formed if 1.0 g of the crystal contains 4.32 ng of ²³⁵U and 1.92 ng of ²⁰⁷Pb?

EXERCISE 13.5: What would the age of the zircon crystal in Exercise 13.4 be if the amounts of ²³⁵U and ²⁰⁷Pb were reversed?

EXERCISE 13.6: Explain the function of the quadrupole ion deflector seen in Figure 13.15.

EXERCISE 13.7: What is the mass of a univalent ion if it acquired a velocity of 5.5 × 10⁵ m/s when accelerated across a potential of 1,250 V?

EXERCISE 13.8: Which method of ionization would you suggest for each of the following samples? Explain your reasoning.

(a) Dioxin, a byproduct of the bleaching of paper by chlorine

(b) Horseradish peroxidase

(c) Steel shavings

EXERCISE 13.9: Naphthalene, a polyaromatic hydrocarbon (C₁₀H₈), was analyzed by MS using chemical ionization and a quadrupole mass analyzer. The base peak occurred at m/z = 129, and the largest ion mass in the spectrum was seen at m/z = 156. Explain these observances.

EXERCISE 13.10: To what excited state radius will ions in an ICR chamber be moved if a 2.5 V radio frequency signal is applied for 500 μs across a 2.3 cm cell while a 4.71 T field is applied?

EXERCISE 13.11: What is the maximum time the pulse de­scribed in Exercise 13.10 could be applied to avoid having ions collide with the cell walls?

EXERCISE 13.12: What is the maximum voltage that could be applied for 500 μs in the cell described in Exercise 13.10 to avoid having ions collide with the cell walls?

EXERCISE 13.13: Your ICM-MS spectrometer has a res­olution of 175 when the average mass of univalent ions is around 120 Da. Would the molecular ion Ar–Br⁺ interfere with the analysis of any elemental ions? Explain your answer.

EXERCISE 13.14: What resolution would be necessary in order to resolve peaks from divalent ions having molar masses of 1,000 g/mol and 1,001 g/mol?

EXERCISE 13.15: Assuming the resolution of the mass an­alyzer considered in Exercise 13.14 is constant across the mass spectrum, what two m/z values could be resolved if around a mean m/z of 2.5 × 10³?

EXERCISE 13.16: Estimate the resolution of the mass an­alyzer used to obtain the spectrum seen in Figure 13.2(a).

EXERCISE 13.17: Estimate the mean free path of an eth­anol molecule (0.44 nm diameter) at 25^oC and 1.0 torr.

EXERCISE 13.18: Assuming the ethanol molecule in Exercise 13.17 is traveling at about 555 m/s, how many col­lisions per second is it undergoing?

EXERCISE 13.19: If we want the mean free path for an eth­anol molecule in a CI chamber to be 0.098 mm, what pres­sure would be required in the chamber?

EXERCISE 13.20: Given the NMR and mass spectra shown, determine the molecular formula and structure of the compound.

EXERCISE 13.21: Given the NMR and mass spectra shown, determine the molecular formula and structure of the compound.