Problem 100 - Chemistry: An Atoms-Focused Approach

Question

Mass spectrometry has proven useful in analyzing the gases emitted from landfills. The principal component is methane \(\left(\mathrm{CH}_{4}\right),\) but small amounts of dimethylsulfide \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{S}\right)\) and dichloroethene \(\left(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}_{2}\right)\) are often present, too. Calculate the masses of the molecular ions formed by these three compounds in a mass spectrometer.

Step-by-Step Solution

Answer

Answer: The masses of the molecular ions are: - CH4: 16.042 amu - C2H6S: 62.128 amu - C2H2Cl2: 96.936 amu

Step 1: Identify the atomic masses of the elements involved in the compounds

To find the atomic masses, we can refer to the periodic table: - Carbon (C) has an atomic mass of approximately 12.01 amu (atomic mass units). - Hydrogen (H) has an atomic mass of approximately 1.008 amu. - Sulfur (S) has an atomic mass of approximately 32.06 amu. - Chlorine (Cl) has an atomic mass of approximately 35.45 amu.

Step 2: Calculate the mass of CH4

Here's the calculation for CH4: 1 Carbon atom: 1 × 12.01 amu = 12.01 amu 4 Hydrogen atoms: 4 × 1.008 amu = 4.032 amu CH4 mass: 12.01 amu + 4.032 amu = 16.042 amu

Step 3: Calculate the mass of C2H6S

Here's the calculation for C2H6S: 2 Carbon atoms: 2 × 12.01 amu = 24.02 amu 6 Hydrogen atoms: 6 × 1.008 amu = 6.048 amu 1 Sulfur atom: 1 × 32.06 amu = 32.06 amu C2H6S mass: 24.02 amu + 6.048 amu + 32.06 amu = 62.128 amu

Step 4: Calculate the mass of C2H2Cl2

Here's the calculation for C2H2Cl2: 2 Carbon atoms: 2 × 12.01 amu = 24.02 amu 2 Hydrogen atoms: 2 × 1.008 amu = 2.016 amu 2 Chlorine atoms: 2 × 35.45 amu = 70.9 amu C2H2Cl2 mass: 24.02 amu + 2.016 amu + 70.9 amu = 96.936 amu So, the masses of the molecular ions formed by CH4, C2H6S, and C2H2Cl2 in a mass spectrometer are: - CH4: 16.042 amu - C2H6S: 62.128 amu - C2H2Cl2: 96.936 amu

Key Concepts

Molecular Ion Calculation

Molecular ion calculation is a crucial step when interpreting the results from mass spectrometry. Mass spectrometry is a technique that helps identify the components of a compound by measuring the mass of ions. To calculate the mass of a molecular ion, we need to know the atomic masses of each element in a compound and their quantities.

For example, in the exercise given, methane \((\mathrm{CH}_4)\) is made of carbon and hydrogen. By multiplying the number of each type of atom by their respective atomic masses, and then summing the results, we determine the mass of the molecular ion of methane as follows:

• 1 Carbon atom: \(1 \times 12.01 \, \text{amu} = 12.01 \, \text{amu}\)
• 4 Hydrogen atoms: \(4 \times 1.008 \, \text{amu} = 4.032 \, \text{amu}\)
• Total for \(\mathrm{CH}_4\): \(12.01 \, \text{amu} + 4.032 \, \text{amu} = 16.042 \, \text{amu}\)

These calculations are repeated for each compound to determine their respective molecular ion masses.

Atomic Mass

Atomic mass is a fundamental concept in chemistry that refers to the mass of a single atom of a chemical element. It's often measured in atomic mass units (amu), where one amu is defined as one twelfth of the mass of a carbon-12 atom. Understanding atomic mass is crucial when calculating molecular ion masses in mass spectrometry.

In mass spectrometry, knowing the precise atomic mass of each element involved helps in calculating the correct molecular ion mass.

• Carbon (C) has an atomic mass of approximately 12.01 amu.
• Hydrogen (H) has an atomic mass of about 1.008 amu.
• Sulfur (S) has a heavier atomic mass of roughly 32.06 amu.
• Chlorine (Cl) is even heavier, with an atomic mass close to 35.45 amu.

These values allow chemists to accurately compute the mass of larger compounds for analysis, revealing crucial insights into the molecular structure of substances being studied.

Landfill Gas Analysis

Landfill gas analysis is important for environmental regulation and safety, providing essential data on the gases emitted from landfills. These gases can include methane, dimethylsulfide, and dichloroethene, and analyzing their composition helps in understanding the potential impact on air quality.

Mass spectrometry is one technique used in landfill gas analysis, offering rapid and precise identification of the gases present. By identifying and calculating the mass of molecular ions, scientists can determine the concentration of each gas type. This information is essential for monitoring landfill gas emissions and ensuring they are within safe limits.

• Methane (\(\mathrm{CH}_4\)) is often the main component and a major focus because of its significant greenhouse effect.
• Dimethylsulfide (\(\mathrm{C}_2\mathrm{H}_6\mathrm{S}\)) may be present in smaller amounts but still needs monitoring.
• Dichloroethene (\(\mathrm{C}_2\mathrm{H}_2\mathrm{Cl}_2\)), also present in trace amounts, is monitored due to its potential environmental impact.

Thus, landfill gas analysis helps in assessing both environmental impact and compliance with environmental regulations.