Problem 23 - Chemistry The Science in Context

Question

Which substance in each of the following pairs of quantities contains more moles of sulfur? a. 3 moles of \(\mathrm{Al}_{2} \mathrm{S}_{3}\) or 4 moles of \(\mathrm{Fe}_{2} \mathrm{S}_{3}\) b. 3 moles of \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) or 4 moles of \(\mathrm{CaS}\) c. 2 moles of \(\mathrm{SO}_{3}\) or 2 moles of \(\mathrm{SO}_{2}\)

Step-by-Step Solution

Answer

b) 3 moles of Li2SO4 or 4 moles of CaS? c) 2 moles of SO3 or 2 moles of SO2? Answer: a) 4 moles of Fe2S3 contain more moles of sulfur. b) 4 moles of CaS contain more moles of sulfur. c) Both 2 moles of SO3 and 2 moles of SO2 contain an equal number of moles of sulfur.

Step 1: a. Compare moles of sulfur in 3 moles of Al2S3 and 4 moles of Fe2S3

For Al2S3: The ratio of sulfur atoms to the compound is 3:1, so in 3 moles of Al2S3, there will be 3 moles x 3 sulfur atoms = 9 moles of sulfur. For Fe2S3: The ratio of sulfur atoms to the compound is also 3:1, so in 4 moles of Fe2S3, there will be 4 moles x 3 sulfur atoms = 12 moles of sulfur. Since 12 moles > 9 moles, 4 moles of Fe2S3 contains more moles of sulfur.

Step 2: b. Compare moles of sulfur in 3 moles of Li2SO4 and 4 moles of CaS

For Li2SO4: The ratio of sulfur atoms to the compound is 1:1, so in 3 moles of Li2SO4, there will be 3 moles x 1 sulfur atom = 3 moles of sulfur. For CaS: The ratio of sulfur atoms to the compound is 1:1, so in 4 moles of CaS, there will be 4 moles x 1 sulfur atom = 4 moles of sulfur. Since 4 moles > 3 moles, 4 moles of CaS contains more moles of sulfur.

Step 3: c. Compare moles of sulfur in 2 moles of SO3 and 2 moles of SO2

For SO3: The ratio of sulfur atoms to the compound is 1:1, so in 2 moles of SO3, there will be 2 moles x 1 sulfur atom = 2 moles of sulfur. For SO2: The ratio of sulfur atoms to the compound is also 1:1, so in 2 moles of SO2, there will be 2 moles x 1 sulfur atom = 2 moles of sulfur. Since 2 moles = 2 moles, both 2 moles of SO3 and 2 moles of SO2 contain an equal number of moles of sulfur.

Key Concepts

Moles of Sulfur

Understanding moles is crucial for any chemistry student, as it provides a way to relate the massive world of atoms and molecules to a scale we can practically work with.
Moles refer to a specific number of particles, usually atoms or molecules, quantified as Avogadro's number, which is approximately \(6.022 \times 10^{23}\).
In stoichiometry, we calculate the moles of sulfur in each chemical compound by determining how many sulfur atoms are in one molecule of each compound.

For a compound like \(\text{Al}_2\text{S}_3\), each molecule contains three sulfur atoms.
This means that for every mole of \(\text{Al}_2\text{S}_3\), there are three moles of sulfur atoms.
Similarly, in \(\text{Fe}_2\text{S}_3\), there are also three sulfur atoms per molecule, making it three moles of sulfur per mole of the compound.
Conceptualizing this allows us to multiply the number of moles of the entire compound by the number of sulfur atoms in each molecule to find the moles of sulfur present.

The real-life application of this concept is in determining how much of a product can be made in a chemical reaction, which is a central idea in stoichiometry.

Chemical Compounds

Chemical compounds are substances formed when two or more elements chemically bond together.
These bonds involve sharing or transferring electrons between atoms, leading to stable configurations.
In chemistry, we represent compounds through chemical formulas, which serve as a shorthand for their composition.

Compounds like \(\text{Li}_2\text{SO}_4\) and \(\text{CaS}\) have distinctly different structures and properties.
The formula \(\text{Li}_2\text{SO}_4\) indicates that each molecule contains one sulfur atom, in addition to other elements such as lithium and oxygen.
On the other hand, \(\text{CaS}\) is simpler, containing just one sulfur atom and one calcium atom.
This simpler structure often contributes to the compound’s specific properties like solubility and reactivity.

Recognizing the chemical formula helps in understanding the proportions of elements involved and predicting the outcome of chemical reactions.

• Each element in a compound contributes differently to the physical and chemical characteristics of the compound.
• The understanding of chemical formulas is essential in stoichiometry to perform various calculations.

Comparative Analysis

Comparative analysis in chemistry involves evaluating different substances or conditions to determine outcomes based on specific criteria.
When comparing substances to find which contains more moles of an element, such as sulfur, the process involves examining chemical formulas and the moles given.

For instance, in comparing \(\text{SO}_3\) and \(\text{SO}_2\), both compounds have a 1:1 ratio of sulfur to the compound since each contains one sulfur atom per molecule.
However, in other examples, where one compound may have a higher ratio of sulfur atoms, analysis allows us to discern differences more clearly.
This ability to compare becomes vital when calculating possible yields in a chemical reaction or evaluating environmental impacts of different compounds.

In practical applications, comparative analysis assists not just in theoretical calculations, but also in real-world scenarios like material selection in engineering, or even analyzing chemical reactions in pharmaceuticals.
This type of analysis embodies critical thinking and careful examination of all components involved in a chemical context.