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Chapter 10: Problem 19

Naturally occurring Fe consists of \(5.8 \%^{54} \mathrm{Fe}\) \(91.7 \%^{56} \mathrm{Fe}, 2.2 \%^{57} \mathrm{Fe}\) and \(0.3 \%^{58} \mathrm{Fe} . \mathrm{Fe}(\mathrm{CO})\) (10.12) loses \(\mathrm{CO}\) molecules in a sequential manner in the mass spectrometer. What do you expect to observe in the mass spectrum of \(\mathrm{Fe}(\mathrm{CO})_{5} ?\)

Short Answer

Expert verified
Expect mass spectrum peaks at decrementing intervals of 28 amu starting from 196 amu.

Step by step solution

01

Calculate Molar Mass of Fe Isotopes

To understand the mass spectrum, calculate the molar mass of each isotope based on its natural abundance. Given, the isotopes are \( ^{54}\mathrm{Fe} \), \( ^{56}\mathrm{Fe} \), \( ^{57}\mathrm{Fe} \), and \( ^{58}\mathrm{Fe} \) with percentages 5.8%, 91.7%, 2.2%, and 0.3% respectively. So, the masses are approximately 54, 56, 57, and 58 amu.
02

Determine the Molar Mass of CO

To find the expected mass peaks in \(\mathrm{Fe(CO)}_5\), we need the molar mass of \( \mathrm{CO} \). Carbon \( (^{12}\mathrm{C}) \) has a mass of 12 amu, and oxygen \( (^{16}\mathrm{O}) \) has a mass of 16 amu. Therefore, the molar mass of \( \mathrm{CO} \) is \( 12 + 16 = 28 \) amu.
03

Calculate the Initial Mass of \(\mathrm{Fe(CO)}_5\)

Compute the mass of \(\mathrm{Fe(CO)}_5\) for each Fe isotope. For example, the mass with \(^{56}\mathrm{Fe}\) is \( 56 + 5 \times 28 = 196 \) amu. Similarly, evaluate for the other isotopes.
04

Determine Mass Changes as CO is Lost

Sequential removal of \(\mathrm{CO}\) from \(\mathrm{Fe(CO)}_5\) reduces its mass by 28 amu per \(\mathrm{CO}\). Hence, calculate the masses for each \(\mathrm{Fe(CO)}_n\) (for n from 1 to 5) for all isotopes, e.g., \(^{56}\mathrm{Fe(CO)}_4\) will be \( 168 \) amu.
05

Predict Mass Spectrum Peaks

The mass spectrum will show peaks at the calculated masses: initially for each \(\mathrm{Fe(CO)}_5\), then for each subsequent loss of \( \mathrm{CO} \). The peaks will diminish by multiples of 28 amu for each losing \(\mathrm{CO}\). For \(^{56}\mathrm{Fe(CO)}_5\), expect 196, 168, 140, 112, and 84 amu. Repeat for other isotopes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isotope Abundance
When discussing isotopes, it's essential to grasp their natural abundance. Isotopes are variations of an element, with the same number of protons but different numbers of neutrons in their nuclei. This results in different atomic masses. Understanding isotope abundance helps in predicting the composition of a sample and its behavior in chemical processes.
For instance, consider iron isotopes in the original exercise. We have:
  • 54Fe with an abundance of 5.8%.
  • 56Fe, which is the most abundant, making up 91.7%.
  • 57Fe is less common, comprising 2.2%.
  • Finally, 58Fe with a minimal presence of 0.3%.
This information is crucial in mass spectrometry, a technique used to analyze and identify isotopes in a sample.
Molar Mass Calculation
Calculating the molar mass of an element or compound is foundational in chemistry. It helps in predicting the behavior and interaction of molecules. The molar mass is the sum of the atomic masses of all atoms in a molecule. It is measured in atomic mass units (amu).Calculating for Compounds:
  • First, determine the molar mass of individual elements within the compound.
  • Next, sum these values considering the number of each atom in the compound.
For instance, the molar mass of CO is derived by adding the mass of carbon (12 amu) and oxygen (16 amu), yielding 28 amu. When dealing with compounds like \(\mathrm{Fe(CO)}_5\), multiply the molar mass of CO by 5 and add the molar mass of iron. This gives insight into reaction stoichiometry and conservation of mass in chemical equations.
Mass Spectrum Analysis
Mass spectrum analysis allows scientists to study the distribution of different isotopes in a substance. By ionizing chemical substances and sorting the ions based on their mass-to-charge ratio, a mass spectrometer provides a spectrum showing the presence of different isotopes. Interpreting a Mass Spectrum:
When you look at a mass spectrum from a device like a mass spectrometer, each peak represents ions of a particular mass. The height and position of each peak indicate the abundance and mass of the ions. For the exercise in question:
  • Each isotope, like \(^{56}\mathrm{Fe(CO)}_5\), has a distinct peak based on its total mass.
  • Peaks vary as CO groups are sequentially removed from the compound.
  • The mass decreases correspondingly with the release of each CO unit.
Mass spectrum analysis provides a detailed insight into the isotopic composition and rearrangements within a sample.
Iron Isotopes
Iron is a common element with several naturally occurring isotopes, each contributing to our understanding of iron in various natural and industrial processes. The isotopes of iron such as \(^{54}\mathrm{Fe}\), \(^{56}\mathrm{Fe}\), \(^{57}\mathrm{Fe}\), and \(^{58}\mathrm{Fe}\) are each identified by the number of neutrons they possess.Role of Iron Isotopes:
  • Iron isotopes are pivotal in geological and environmental studies.
  • Isotopic analysis is useful in examining meteoric compositions and tracing processes in ancient rocks.
Understanding these isotopes aids in applications beyond just their atomic and structural analysis. It includes practical applications in medicine, like the role of iron metallurgy in treatment techniques, and industry, where their isotopic compositions determine ore refinement processes.

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Most popular questions from this chapter

Suggest what peaks might be present in the mass spectra of (a) \(\mathrm{F}_{2}\) and (b) \(\mathrm{Cl}_{2}\)

Compound \(\mathbf{D}\) contains \(68.13 \% \mathrm{C}, 13.72 \% \mathrm{H}\) \(18.15 \%\) O, and shows a parent ion in its mass spectrum at \(m / z=88 .\) Determine the molecular formula of \(\mathbf{D}\).

In its mass spectrum, a compound A shows a peak from the molecular ion at \(m / z=78 .\) What further information from the parent ion allows you to distinguish between A being \(\mathrm{C}_{6} \mathrm{H}_{6}\) and \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{Cl} ?\)

A compound \(\mathbf{Y}\) contains \(58.77 \%\) C and \(27.42 \%\) N. From an exact mass determination, the molecular weight of \(\mathbf{Y}\) is found to be \(102.11576 .\) Suggest a likely composition for \(\mathbf{Y}\).

(a) Compound \(\mathbf{Z}\) is a liquid at \(298 \mathrm{K}\) High-resolution mass spectrometry gives an exact mass of \(61.01638,\) and \(\mathbf{Z}\) contains \(19.7 \%\) C \(, 4.9 \%\) \(\mathrm{H}\) and \(22.9 \% \mathrm{N} .\) Suggest a possible formula for \(\mathrm{Z}\) (b) The low-resolution mass spectrum of Z shows intense peaks at 61,46,30 and \(15 .\) Deduce a possible structure of \(\mathbf{Z}\)
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