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Chapter 2: Problem 17

Chlorine consists of two isotopes, chlorine- \(35(75.77 \%\) abundance) and chlorine- 37 ( \(24.23 \%\) abundance). Draw a graph of the mass spectrum obtained from a sample of \(\mathrm{Cl}_{2}\) gas.

Short Answer

Expert verified
Graph peaks at masses 70, 72, and 74 with respective intensities 57.44%, 36.72%, and 5.87%.

Step by step solution

01

Identify Isotopes and Their Abundances

Chlorine has two isotopes: chlorine-35 with 75.77% abundance and chlorine-37 with 24.23% abundance. These percentages will help us find the relative peaks in the mass spectrum.
02

Calculate Relative Intensities for Single Chlorine Atoms

For a single chlorine atom, the isotopes show peaks at their respective mass numbers, 35 and 37, with intensities proportional to their abundances. Thus, for chlorine-35, the intensity is 75.77, and for chlorine-37, it is 24.23.
03

Identify Possible \\( ext{Cl}_2\\) Molecule Combinations

In a sample of \( ext{Cl}_2\) gas, the molecule can consist of a combination of the isotopes: 35-35, 35-37, and 37-37. We need to calculate the masses for these combinations.
04

Calculate Masses of the \\( ext{Cl}_2\\) Molecules

The molecular masses of the \( ext{Cl}_2\) gas combinations are: 70 for 35-35, 72 for 35-37, and 74 for 37-37. These reflect the sum of atomic masses of the chlorine atoms in each pair.
05

Calculate Relative Abundances for Each Molecule

Use the formula \(\text{Relative abundance} = (\text{Abundance of first isotope}) \times (\text{Abundance of second isotope})\). For Cl-35/Cl-35: \(75.77\% \times 75.77\% = 57.44\%\); for Cl-35/Cl-37: \(2 \times 75.77\% \times 24.23\% = 36.72\%\); and for Cl-37/Cl-37: \(24.23\% \times 24.23\% = 5.87\%\). The 2 multiplier in the second calculation accounts for the two possible arrangements.
06

Draw the Mass Spectrum

On the x-axis, plot the masses (70, 72, 74) and on the y-axis, plot their respective calculated relative abundances. So, points are at (70, 57.44%), (72, 36.72%), and (74, 5.87%). Ensure proper scaling to reflect the difference in abundance clearly where the peak at 70 is the highest and 74 is the lowest.

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Key Concepts

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

Isotopic Abundance
Isotopic abundance refers to the percentage of a particular isotope present in a natural sample of an element. For chlorine, which has two stable isotopes, the isotopic abundance helps determine the characteristics observed in mass spectrometry.
  • Isotopic Contribution: Chlorine-35 represents 75.77% of the natural mixture, while chlorine-37 consists of 24.23%.
  • Mass Spectrum Peaks: The peaks in a mass spectrum directly reflect these isotopic abundances. Higher abundance results in taller peaks for each isotope.
Understanding isotopic abundance is crucial for visualizing and interpreting the mass spectrum. It helps in determining how each isotope contributes to the overall spectrum of chlorine gas.
Chlorine Isotopes
Chlorine's two main isotopes are chlorine-35 and chlorine-37. These isotopes differ in the number of neutrons, which affects their mass. Here's how they influence the mass spectrum:
  • Chlorine-35: This isotope has a mass number of 35. Due to its higher abundance, it plays a major role in the mass spectrum of chlorine gas.
  • Chlorine-37: With a mass number of 37, this isotope is less abundant. Its peak in the spectrum is smaller compared to chlorine-35.
The presence of these isotopes determines the formation of different molecular combinations in chlorine gas, which are reflected as various peaks in a mass spectrum analysis.
Chlorine Gas Analysis
Analyzing chlorine gas through mass spectrometry reveals information about the molecular composition and isotopic distribution.
  • Molecular Combinations: Chlorine gas molecules can be a mix of the isotopes, forming combinations like 35-35, 35-37, and 37-37.
  • Mass Calculations: These combinations result in distinct mass peaks, calculated as 70 (35-35), 72 (35-37), and 74 (37-37).
  • Relative Abundances: The relative abundance is calculated using the product of the isotopic abundances. For instance, 35-35 has the highest, while 37-37 has the lowest occurrence.
In a mass spectrum, these combinations create distinct peaks, showcasing how isotopic distribution influences the observed data and providing insight into the molecular make-up of chlorine gas.

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