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Chapter 2: Problem 39

Chlorine has two naturally occurring isotopes, \({ }^{35} \mathrm{Cl}\) (abundance \(76 \%\) ) and \({ }^{37} \mathrm{Cl}\) (abundance \(24 \%\) ), and it occurs as diatomic (two-atom) molecules. In a mass spectrum, peaks are seen for the molecule and for the separated atoms. (a) How many peaks are in the mass spectrum? (b) What is the \(m / e\) value for the heaviest particle and for the lightest particle?

Short Answer

Expert verified
There are 5 peaks in the mass spectrum. The heaviest particle has an \(m/e\) value of \(74\), and the lightest particle has an \(m/e\) value of \(35\).

Step by step solution

01

- Understand the Isotopes and Their Abundances

Chlorine has two isotopes: \({}^{35}Cl\) with an abundance of 76\% and \({}^{37}Cl\) with an abundance of 24\%. Both isotopes will contribute to the mass spectrum.
02

- Determine Possible Atomic Mass Peaks

Since each isotope contributes a peak, the mass spectrum will have two peaks at \(m/e = 35\) for \({}^{35}Cl\) and \(m/e = 37\) for \({}^{37}Cl\).
03

- Calculate Molecular Mass Peaks

Chlorine occurs as diatomic molecules: \({}^{35}Cl_2\), \({}^{37}Cl_2\), and \({}^{35}Cl{}^{37}Cl\). The masses will be: 1. \({}^{35}Cl_2\) at \(35 + 35 = 70\) 2. \({}^{37}Cl_2\) at \(37 + 37 = 74\) 3. \({}^{35}Cl{}^{37}Cl\) at \(35 + 37 = 72\). Thus, peaks will be at \(m/e = 70, 72,\) and \(74\).
04

- Count the Number of Peaks

Combining the atomic and molecular peaks: 1. Atomic peaks: \(35\) and \(37\) (2 peaks) 2. Molecular peaks: \(70, 72,\) and \(74\) (3 peaks). Therefore, there are a total of 5 peaks in the mass spectrum.
05

- Identify the Heaviest and Lightest Particles

The heaviest particle is \({}^{37}Cl_2\) with a mass of \(74\) The lightest particle is \({}^{35}Cl\) with a mass of \(35\).

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Key Concepts

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

mass spectrometry
Mass spectrometry is a technique used to determine the mass-to-charge ratio ( m/e ) of ions. It helps identify different atoms and molecules based on their mass and charge. The process involves ionizing chemical compounds to generate charged molecules or molecule fragments and measuring their mass-to-charge ratios.
  • The sample is introduced into the mass spectrometer.
  • It gets ionized, typically by losing an electron.
  • The ions are then sorted and detected by their mass-to-charge ratio.

This technique is instrumental in analyzing the composition of a substance by providing detailed insights into the mass and abundance of isotopes and molecules present in the sample.
isotopes
Isotopes are atoms of the same element that have different numbers of neutrons, giving them different atomic masses. For chlorine, there are two naturally occurring isotopes:

    • lower solution

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