Problem 112 - Chemistry The Molecular Science

Question

(a) Calculate the mass of one molecule of nitrogen. (b) Calculate the mass of one molecule of oxygen. (c) Calculate the ratio of masses of these two molecules. How does it compare with the ratio of the atomic weights of \(\mathrm{N}\) and \(\mathrm{O}\) ?

Step-by-Step Solution

Answer

The mass of one \(\text{N}_2\) is \(4.65 \times 10^{-23} \, \text{g}\), one \(\text{O}_2\) is \(5.31 \times 10^{-23} \, \text{g}\), and their mass ratio is 0.875, matching their atomic weight ratio.

Step 1: Understanding Molecule Composition

Nitrogen exists as diatomic molecules, denoted as \(\text{N}_2\), meaning each nitrogen molecule consists of two nitrogen atoms. Similarly, oxygen exists as diatomic molecules, denoted as \(\text{O}_2\), comprising two oxygen atoms.

Step 2: Find Atomic Masses

The atomic mass of nitrogen (N) is approximately 14 u (unified atomic mass units), and the atomic mass of oxygen (O) is approximately 16 u.

Step 3: Calculate Molecular Mass of Nitrogen

To find the mass of one \(\text{N}_2\) molecule, add the atomic masses of the two nitrogen atoms: \(2 \times 14 \, \text{u} = 28 \, \text{u}\).

Step 4: Calculate Mass of One Nitrogen Molecule

Convert the mass in atomic mass units to grams for one molecule using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol). The mass of one \(\text{N}_2\) molecule is \(\frac{28 \, \text{g/mol}}{6.022 \times 10^{23} \, \text{molecules/mol}} = 4.65 \times 10^{-23} \, \text{g}\).

Step 5: Calculate Molecular Mass of Oxygen

For \(\text{O}_2\), add the atomic masses of the two oxygen atoms: \(2 \times 16 \, \text{u} = 32 \, \text{u}\).

Step 6: Calculate Mass of One Oxygen Molecule

Similarly, convert the mass in atomic mass units to grams for one molecule using Avogadro's number. The mass of one \(\text{O}_2\) molecule is \(\frac{32 \, \text{g/mol}}{6.022 \times 10^{23} \, \text{molecules/mol}} = 5.31 \times 10^{-23} \, \text{g}\).

Step 7: Calculate Ratio of Masses

To find the ratio of the mass of \(\text{N}_2\) to \(\text{O}_2\), divide the mass of one nitrogen molecule by the mass of one oxygen molecule: \(\frac{4.65 \times 10^{-23} \, \text{g}}{5.31 \times 10^{-23} \, \text{g}} = 0.875\).

Step 8: Compare with Atomic Weight Ratio

The atomic weight ratio of nitrogen to oxygen is \(\frac{14}{16} = 0.875\). Thus, the ratio of the molecular masses \(0.875\) matches the ratio of atomic weights.

Key Concepts

Avogadro's Number

Avogadro's Number is a fundamental constant that is essential for understanding molecular and atomic measurements. It represents the number of atoms, ions, or molecules contained in one mole of a substance. This number is an astonishingly large figure: \(6.022 \times 10^{23}\) particles per mole.

In chemistry, Avogadro's Number allows scientists to translate between atomic scales and more tangible, macroscopic measurements. When conducting molecular mass calculations, this number facilitates converting mass from atomic mass units (amu) to grams, thus bridging the gap between theoretical calculations and laboratory experiments.

• Allows conversion from moles to number of particles.
• Used to calculate the mass of individual molecules.
• Makes mass calculation relevant in real-world scenarios.

By understanding how Avogadro’s Number connects the vast world of atoms to our everyday world, students can better grasp the molecular mass calculations like those carried out in the problem for nitrogen and oxygen molecules.

Diatomic Molecules

Diatomic molecules are a class of molecules where two atoms of the same element are bonded together. This concept is crucial because many elements, like nitrogen and oxygen, naturally occur in this form. For instance, when you encounter nitrogen in a textbook, it typically refers to \(\text{N}_2\), and similarly, oxygen typically means \(\text{O}_2\).

Understanding the diatomic nature is vital because news media, academic papers, and other sources often default to mentioning elements in their diatomic states.

• Each nitrogen molecule (\(\text{N}_2\)) consists of two nitrogen atoms.
• Each oxygen molecule (\(\text{O}_2\)) consists of two oxygen atoms.
• It affects the calculation of molecular masses significantly.

By realizing that these molecules are composed of two atoms, students can correctly perform calculations involving atomic mass, further exploring molecular interactions and reactions in chemistry.

Atomic Mass Units (u)

Atomic Mass Units, abbreviated as u, are the standard unit for indicating mass on an atomic or molecular scale. The atomic mass unit provides a convenient way to express the mass of atoms and molecules close to their actual mass.

The basis for the atomic mass unit is one twelfth the mass of a carbon-12 atom, which is defined as exactly 12 u. This unit provides a relative scale and is handy for calculating molecular masses.

• Atomic mass of nitrogen (N) is approximately 14 u.
• Atomic mass of oxygen (O) is approximately 16 u.
• Used to calculate molecular mass of diatomic molecules like \(\text{N}_2\) and \(\text{O}_2\).

When chemistry students convert atomic mass units to grams using Avogadro’s number, they can physically relate atomic-scale calculations to macroscopic observations and experimental measurements, enhancing the overall understanding of chemical reactions and processes.