(a) A research chemist used a mass spectrometer to study the two isotopes of an element. Over time, she recorded a number of mass spectra of these isotopes. On analysis, she noticed that the ratio of the taller peak (the more abundant isotope) to the shorter peak (the less abundant isotope) gradually increased with time. Assuming that the mass spectrometer was functioning normally, what do you think was causing this change? (b) Mass spectrometry can be used to identify the formulas of molecules having small molecular masses. To illustrate this point, identify the molecule which most likely accounts for the observation of a peak in a mass spectrum at: 16 amu, 17 amu, 18 amu, and 64 amu. (c) Note that there are (among others) two likely molecules that would give rise to a peak at 44 amu, namely, \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\). In such cases, a chemist might try to look for other peaks generated when some of the molecules break apart in the spectrometer. For example, if a chemist sees a peak at 44 amu and also one at 15 amu, which molecule is producing the 44 -amu peak? Why? (d) Using the following precise atomic masses: \({ }^{1} \mathrm{H}(1.00797\) amu \(),{ }^{12} \mathrm{C}(12.00000 \mathrm{amu}),\) and \({ }^{16} \mathrm{O}(15.99491 \mathrm{amu}),\) how precisely must the masses of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\) be measured to distinguish between them? (e) Every year millions of dollars' worth of gold is stolen. In most cases the gold is melted down and shipped abroad. This way the gold retains its value while losing all means of identification. Gold is a highly unreactive metal that exists in nature in the uncombined form. During the mineralization of gold, that is, the formation of gold nuggets from microscopic gold particles, various elements such as cadmium (Cd), lead (Pb), and zinc \((\mathrm{Zn})\) are incorporated into the nuggets. The amounts and types of the impurities or trace elements in gold vary according to the location where it was mined. Based on this knowledge, describe how you would identify the source of a piece of gold suspected of being stolen from Fort Knox, the federal gold depository.

Step by step solution

01

Understanding the Increasing Ratio in Isotope Peaks Over Time

The increasing ratio of the taller peak to the shorter peak might be due to isotopic enrichment. With time, more quantity of the abundant isotope is detected as compared to the less abundant one, thereby increasing the ratio.

02

Identification of Molecules Using Mass Spectra

The molecules associated with the given atomic mass units (amu) could be: 16 amu - \( \mathrm{O} \), 17 amu - \( \mathrm{OH} \), 18 amu - \( \mathrm{H}_2\mathrm{O} \), 64 amu - \( \mathrm{SO}_2 \).

03

Identifying Molecule With 44 amu and Additional 15 amu Peak

From the two given molecules \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\), both have mass 44 amu. But \( \mathrm{C}_{3} \mathrm{H}_{8} \) can break into a fragment with mass 15 amu (\(\mathrm{CH}_{3}\)), thus, the molecule producing the 44 amu peak, in this case, is \( \mathrm{C}_{3} \mathrm{H}_{8} \).

04

Precision in Measurements to Distinguish Two Molecules

The masses of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\) can be calculated as 44.063 amu and 43.993 amu respectively, based on given atomic masses. To distinguish between them, the measurement needs to have a precision up to the fourth decimal place.

05

Identifying Stolen Gold

The origin of a gold piece can be determined by studying the patterns of trace elements or impurities incorporated during the gold nugget formation. Each location will have a unique pattern of these trace elements due to different geochemical environments. So, by comparing it with the known profiles of various gold sources, the origin of the stolen gold piece can potentially be traced.

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