Problem 99 - Chemistry: An Atoms-Focused Approach

Question

Many of the explosive materials of concern to airport security contain nitrogen and oxygen. Calculate the masses of the molecular ions formed by (a) \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{N}_{6} \mathrm{O}_{6},\) (b) \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{N}_{8} \mathrm{O}_{8},\) (c) \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{N}_{4} \mathrm{O}_{12},\) and (d) \(\mathrm{C}_{14} \mathrm{H}_{6} \mathrm{N}_{6} \mathrm{O}_{12}\)

Step-by-Step Solution

Answer

Question: Calculate the masses of the molecular ions formed by the following four molecules: \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{N}_{6} \mathrm{O}_{6}\), \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{N}_{8} \mathrm{O}_{8}\), \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{N}_{4} \mathrm{O}_{12}\), and \(\mathrm{C}_{14} \mathrm{H}_{6} \mathrm{N}_{6} \mathrm{O}_{12}\). Answer: The masses of the molecular ions formed by the four molecules are 222.15 amu, 296.20 amu, 316.17 amu, and 450.26 amu, respectively.

Step 1: Molecular mass of \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{N}_{6} \mathrm{O}_{6}\)

To find the molecular mass of this compound, we can use the formula: Molecular mass = (number of C atoms × atomic mass of C) + (number of H atoms × atomic mass of H) + (number of N atoms × atomic mass of N) + (number of O atoms × atomic mass of O) Molecular mass = (3 × 12.01) + (6 × 1.01) + (6 × 14.01) + (6 × 16.00) = 36.03 + 6.06 + 84.06 + 96.00 = 222.15 amu

Step 2: Molecular mass of \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{N}_{8} \mathrm{O}_{8}\)

Using the same formula as before, we get: Molecular mass = (4 × 12.01) + (8 × 1.01) + (8 × 14.01) + (8 × 16.00) = 48.04 + 8.08 + 112.08 + 128.00 = 296.20 amu

Step 3: Molecular mass of \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{N}_{4} \mathrm{O}_{12}\)

Applying the formula to this molecule, we get: Molecular mass = (5 × 12.01) + (8 × 1.01) + (4 × 14.01) + (12 × 16.00) = 60.05 + 8.08 + 56.04 + 192.00 = 316.17 amu

Step 4: Molecular mass of \(\mathrm{C}_{14} \mathrm{H}_{6} \mathrm{N}_{6} \mathrm{O}_{12}\)

Finally, applying the formula to the last molecule, we get: Molecular mass = (14 × 12.01) + (6 × 1.01) + (6 × 14.01) + (12 × 16.00) = 168.14 + 6.06 + 84.06 + 192.00 = 450.26 amu So, the masses of the molecular ions formed by the four molecules are 222.15 amu, 296.20 amu, 316.17 amu, and 450.26 amu, respectively.

Key Concepts

Molecular Formula

A molecular formula is a succinct way of presenting the precise chemical constituents of a compound. It tells you exactly which atoms are present and in what quantity. For instance, the formula \( \mathrm{C}_{3}\mathrm{H}_{6}\mathrm{N}_{6}\mathrm{O}_{6} \) tells us that there are three carbon atoms, six hydrogen atoms, six nitrogen atoms, and six oxygen atoms in one molecule. This is essential for understanding the composition of chemical substances.
Understanding molecular formulas is crucial, especially when dealing with complex compounds. This helps identify how elements interact and form larger compounds. Knowing the makeup of a compound can help you predict its properties and its interactions with other substances.

• The number associated with each element in the formula represents how many atoms of that element are present.
• Molecular formulas are the starting point for calculating molecular mass, giving a clearer picture of the compound’s makeup.

This knowledge is not just for chemistry enthusiasts. It has practical applications in many fields such as pharmaceuticals, environmental science, and materials engineering.

Atomic Mass Unit (amu)

An Atomic Mass Unit, abbreviated as amu, is the standard unit of mass that quantifies the weight of atoms and molecules. It is incredibly tiny and is defined as one-twelfth the mass of a carbon-12 atom, which equals approximately to \(1.66 \times 10^{-27}\) kilograms. Amu provides a scaled-down, manageable way to express the mass of atoms and molecules in chemistry.
This unit is used widely in chemistry and physics because it helps scientists to calculate the weight of atoms and molecules, simplifying the expressions of these tiny masses in our calculations. A key fact to remember is that the atomic masses listed on the periodic table are usually expressed in amu.

• Molecular mass is the sum of all the atomic masses in a molecule, calculated using amu.
• This unified mass system makes it straightforward to compare different molecules and compounds.

For students and researchers, understanding and using the amu helps in evaluating the relative weights of molecules and atoms, making it pivotal in the broader chemical analysis and reactions.

Chemical Composition

Chemical composition refers to the identity and relative number of the elements that make up a chemical compound. Understanding a compound's chemical composition helps to predict its properties and how it reacts with other substances. For instance, a compound like \( \mathrm{C}_{4}\mathrm{H}_{8}\mathrm{N}_{8}\mathrm{O}_{8} \) has a unique combination of elements that influences its chemical behavior.
The concept of chemical composition pinpoints exactly what comprises a compound. It's crucial for determining everything from chemical reactions to the stability of the compound under different conditions.

• Chemical composition is often given in a molecular formula, highlighting the actual count of atoms of each element within a molecule.
• It is essential in fields ranging from material science to pharmacology.

A thorough understanding of chemical composition is vital as both a scientific tool for research and a practical requirement when engaging in activities such as synthesis of materials or the examination of unknown substances.

Explosive Materials Analysis

Explosive materials present unique challenges and safety concerns, making their analysis a significant area of study, particularly in fields related to safety and security. Understanding their molecular composition is crucial, as many explosive materials contain elements like nitrogen and oxygen, which are reactive under certain conditions.
Analyses often involve determining the molecular mass using the elements present, providing insights into the potential behavior of the explosive. For instance, knowing the molecular mass can help predict the energy release upon activation.

• Analyses of explosive materials often take into account the molecular formula to predict reaction byproducts and potential energy yield.
• Security agencies use such analyses to identify threats and ensure safety protocols are in place where these compounds might be encountered.

A foundational understanding of explosive materials analysis assists not only in scientific research but also plays a critical role in public safety, regulatory, and law enforcement efforts.