Problem 69 - Chemistry: An Atoms-Focused Approach

Question

Earth's atmosphere contains many volatile substances that are present in trace amounts. The following quantities of trace gases were found in a 1.0 mL sample of air. Calculate the number of moles of each gas in the sample. a. \(4.4 \times 10^{14}\) atoms of \(\mathrm{Ne}\) b. \(4.2 \times 10^{13}\) molecules of \(\mathrm{CH}_{4}\) c. \(2.5 \times 10^{12}\) molecules of \(\mathrm{O}_{3}\) d. \(4.9 \times 10^{9}\) molecules of \(\mathrm{NO}_{2}\)

Step-by-Step Solution

Answer

Answer: The number of moles for each gas are: a. Ne: approximately \(7.31 \times 10^{-10}\) moles, b. CH4: approximately \(6.97 \times 10^{-11}\) moles, c. O3: approximately \(4.15 \times 10^{-12}\) moles, d. NO2: approximately \(8.14 \times 10^{-15}\) moles.

Step 1: Identifying the given information

The number of \(\mathrm{Ne}\) atoms given is \(4.4 \times 10^{14}\). Our task is to convert this amount to moles.

Step 2: Applying the formula

To find the number of moles of \(\mathrm{Ne}\), we need to divide the number of atoms by Avogadro's number: moles of \(\mathrm{Ne}\) = \(\frac{4.4 \times 10^{14}}{6.022 \times 10^{23}}\)

Step 3: Calculating the result

By dividing the given number of atoms by Avogadro's number, we obtain the number of moles of \(\mathrm{Ne}\). The result is approximately \(7.31 \times 10^{-10}\) moles. #b. Number of moles of CH4#

Step 1: Identifying the given information

The number of \(\mathrm{CH}_{4}\) molecules given is \(4.2 \times 10^{13}\). Our task is to convert this amount to moles.

Step 2: Applying the formula

To find the number of moles of \(\mathrm{CH}_{4}\), we need to divide the number of molecules by Avogadro's number: moles of \(\mathrm{CH}_{4}\) = \(\frac{4.2 \times 10^{13}}{6.022 \times 10^{23}}\)

Step 3: Calculating the result

By dividing the given number of molecules by Avogadro's number, we obtain the number of moles of \(\mathrm{CH}_{4}\). The result is approximately \(6.97 \times 10^{-11}\) moles. #c. Number of moles of O3#

Step 1: Identifying the given information

The number of \(\mathrm{O}_{3}\) molecules given is \(2.5 \times 10^{12}\). Our task is to convert this amount to moles.

Step 2: Applying the formula

To find the number of moles of \(\mathrm{O}_{3}\), we need to divide the number of molecules by Avogadro's number: moles of \(\mathrm{O}_{3}\) = \(\frac{2.5 \times 10^{12}}{6.022 \times 10^{23}}\)

Step 3: Calculating the result

By dividing the given number of molecules by Avogadro's number, we obtain the number of moles of \(\mathrm{O}_{3}\). The result is approximately \(4.15 \times 10^{-12}\) moles. #d. Number of moles of NO2#

Step 1: Identifying the given information

The number of \(\mathrm{NO}_{2}\) molecules given is \(4.9 \times 10^{9}\). Our task is to convert this amount to moles.

Step 2: Applying the formula

To find the number of moles of \(\mathrm{NO}_{2}\), we need to divide the number of molecules by Avogadro's number: moles of \(\mathrm{NO}_{2}\) = \(\frac{4.9 \times 10^{9}}{6.022 \times 10^{23}}\)

Step 3: Calculating the result

By dividing the given number of molecules by Avogadro's number, we obtain the number of moles of \(\mathrm{NO}_{2}\). The result is approximately \(8.14 \times 10^{-15}\) moles.

Key Concepts

Moles Calculation

In chemistry, calculating moles is a crucial step when dealing with atoms and molecules. It all starts with Avogadro's number, which is a constant known to be approximately \(6.022 \times 10^{23}\). This number is fundamental because it relates the number of atoms or molecules in one mole of a substance.
Calculating moles requires dividing the known number of particles (atoms or molecules) by Avogadro's number. This simple formula, \[ \text{moles} = \frac{\text{number of particles}}{6.022 \times 10^{23}}\]helps chemists convert between microscopic particles and macroscopic amounts that can be measured.
This conversion is vital for scientists to weigh or measure elements and compounds for experiments or production. Understanding this concept is the key to unlocking many more complex topics in chemistry.

Trace Gases

Trace gases are those constituents of the atmosphere that exist in amounts smaller than 1% by volume. Despite their small concentration, these gases play significant roles in atmospheric processes.
Gases like neon \((\mathrm{Ne})\), methane \((\mathrm{CH}_4)\), ozone \((\mathrm{O}_3)\), and nitrogen dioxide \((\mathrm{NO}_2)\) are examples of trace gases discussed in this exercise.
- Neon is a noble gas and is chemically inert, used in lighting.- Methane is a potent greenhouse gas, significantly affecting Earth's temperature.- Ozone plays a crucial role in absorbing harmful ultraviolet radiation from the sun.- Nitrogen dioxide is a significant air pollutant, contributing to the formation of smog.Understanding trace gases and their impact on our environment is essential for atmospheric chemistry studies, as they often indicate pollution levels and climate change impacts.

Atmospheric Chemistry

Atmospheric chemistry involves studying chemical processes in Earth's atmosphere. This field examines how elements and compounds interact in the air we breathe.
The presence and concentration of trace gases highlight various chemical reactions that occur constantly within the atmosphere. These gases can interact under the influence of sunlight, temperature, and pressure, forming new compounds.
- Understanding these reactions is critical in predicting weather, understanding climate change, and addressing air pollution. - Atmospheric chemists use tools like spectroscopy and mass spectrometry to measure the composition of air samples. - Knowing the concentration of trace gases allows scientists to model atmospheric behavior and develop strategies to mitigate human impacts. Regions with high concentrations of certain trace gases may need more protective environmental policies to ensure air quality and public health.

Molecular Conversion

Molecular conversion in chemistry refers to transforming molecules from one form to another, often involving calculations like those seen in this exercise. This process is essential when estimating the amounts of reactants or products in a chemical reaction.
By understanding how to convert number counts of molecules (like those of \(\mathrm{CH}_4\), \(\mathrm{O}_3\), etc.) into moles, chemists can predict how substances will behave in larger quantities.
- This conversion helps in creating balanced chemical equations, ensuring that the mass and number of atoms are conserved during reactions.- It allows for the calculation of theoretical yields and determining limiting reagents in reactions.- Practically, it is crucial in industries to maximize efficiency and minimize waste when producing chemical products.By mastering molecular conversion, one can link the microscale world of molecules to macroscopic quantities used in everyday applications.