Problem 70 - Chemistry: An Atoms-Focused Approach

Question

The following quantities of trace gases were found in a 1.0 mL sample of air. Calculate the number of moles of each compound in the sample. a. \(1.4 \times 10^{13}\) molecules of \(\mathrm{H}_{2}\) b. \(1.5 \times 10^{14}\) atoms of \(\mathrm{He}\) c. \(7.7 \times 10^{12}\) molecules of \(\mathrm{N}_{2} \mathrm{O}\) d. \(3.0 \times 10^{12}\) molecules of \(\mathrm{CO}\)

Step-by-Step Solution

Answer

Question: Calculate the number of moles for the following given their number of molecules or atoms: a. H2: \(1.4 \times 10^{13}\) b. He: \(1.5 \times 10^{14}\) c. N2O: \(7.7 \times 10^{12}\) d. CO: \(3.0 \times 10^{12}\) Answer: a. H2: \(2.325 \times 10^{-11}\) moles b. He: \(2.492 \times 10^{-10}\) moles c. N2O: \(1.279 \times 10^{-11}\) moles d. CO: \(4.983 \times 10^{-12}\) moles

Step 1: Write down the given number of molecules

The given number of H2 molecules is \(1.4 \times 10^{13}\).

Step 2: Calculate the number of moles

Number of moles = \(\frac{1.4 \times 10^{13}}{6.022 \times 10^{23}}\) Number of moles = \(2.325 \times 10^{-11}\) moles #b. He#

Step 1: Write down the given number of atoms

The given number of He atoms is \(1.5 \times 10^{14}\).

Step 2: Calculate the number of moles

Number of moles = \(\frac{1.5 \times 10^{14}}{6.022 \times 10^{23}}\) Number of moles = \(2.492 \times 10^{-10}\) moles #c. N2O#

Step 1: Write down the given number of molecules

The given number of N2O molecules is \(7.7 \times 10^{12}\).

Step 2: Calculate the number of moles

Number of moles = \(\frac{7.7 \times 10^{12}}{6.022 \times 10^{23}}\) Number of moles = \(1.279 \times 10^{-11}\) moles #d. CO#

Step 1: Write down the given number of molecules

The given number of CO molecules is \(3.0 \times 10^{12}\).

Step 2: Calculate the number of moles

Number of moles = \(\frac{3.0 \times 10^{12}}{6.022 \times 10^{23}}\) Number of moles = \(4.983 \times 10^{-12}\) moles

Key Concepts

Avogadro's number

Avogadro's number is a cornerstone concept in chemistry, which is exactly equal to \(6.022 \times 10^{23}\). This number represents the quantity of particles, such as atoms or molecules, in one mole of a substance. Imagine it as a bridge between the atomic world and the macroscopic world we live in. Knowing Avogadro's number allows you to convert between atoms or molecules and moles. This is essential for understanding chemical reactions and compositions.

Molecular count

The molecular count is simply the number of individual molecules in a sample. In the exercise, we are given specific counts of different molecules, such as \(1.4 \times 10^{13}\) molecules of \(\mathrm{H}_{2}\). To determine the amount of substance in moles, you divide this molecular count by Avogadro's number. This process helps convert an unimaginable quantity of tiny entities into a more manageable unit.

Chemical compounds

Chemical compounds like \(\mathrm{H}_{2}\), \(\mathrm{He}\), \(\mathrm{N}_{2} \mathrm{O}\), and \(\mathrm{CO}\) are formed when elements are bonded together. These compounds can exist as molecules or atoms. For instance, \(\mathrm{H}_{2}\) is a molecule containing two hydrogen atoms bonded together, while \(\mathrm{He}\) is a single atom. Understanding the nature of these compounds makes it easier to calculate their moles from molecular counts.

Trace gases

Trace gases are minor components of the atmosphere that are present in small quantities. They include compounds like \(\mathrm{H}_{2}\), \(\mathrm{He}\), \(\mathrm{N}_{2} \mathrm{O}\), and \(\mathrm{CO}\). Even though they are present in tiny amounts, trace gases play significant roles in environmental processes and chemical reactions. Calculating the moles of trace gases helps in evaluating their concentration, which is important for studying atmospheric chemistry and environmental science.