Solving A Mixture Of 21g Fe And 15g S Understanding The Reaction And Remaining Elements

Jun 17, 2025 by ADMIN 88 views

25 Solving a Mixture of 21g Fe and 15g S Understanding the Reaction and Remaining Elements

In the world of chemistry, understanding how elements react and combine is crucial for various applications, from industrial processes to everyday life. When dealing with mixtures of elements, predicting the outcome of a reaction and determining the quantities of remaining elements requires a solid grasp of stoichiometry and chemical principles. This article delves into a specific scenario: dissolving a mixture of 21 grams of iron (Fe) and 15 grams of sulfur (S). We will explore the chemical reaction that occurs, calculate the limiting reactant, and determine which element remains and its quantity. This detailed analysis will provide a comprehensive understanding of the reaction dynamics and the final composition of the mixture.

Chemical Reaction and Stoichiometry

To begin, let's identify the chemical reaction that takes place when iron (Fe) and sulfur (S) are mixed and heated. Iron and sulfur react to form iron(II) sulfide (FeS), a compound with distinct properties from its constituent elements. The balanced chemical equation for this reaction is:

Fe + S → FeS

This equation tells us that one mole of iron reacts with one mole of sulfur to produce one mole of iron(II) sulfide. The stoichiometry of this reaction is straightforward, with a 1:1:1 molar ratio between the reactants and the product. However, the masses of the reactants provided (21 grams of Fe and 15 grams of S) need to be converted to moles to determine the limiting reactant and the extent of the reaction.

To convert grams to moles, we use the molar masses of iron and sulfur. The molar mass of iron (Fe) is approximately 55.845 g/mol, and the molar mass of sulfur (S) is approximately 32.065 g/mol. Using these values, we can calculate the number of moles of each reactant:

Moles of Fe = 21 g / 55.845 g/mol ≈ 0.376 mol
Moles of S = 15 g / 32.065 g/mol ≈ 0.468 mol

Now that we have the number of moles of each reactant, we can determine the limiting reactant. The limiting reactant is the reactant that is completely consumed in the reaction, thereby limiting the amount of product formed. To identify the limiting reactant, we compare the mole ratio of the reactants to the stoichiometric ratio from the balanced equation.

Determining the Limiting Reactant

In this case, the stoichiometric ratio of Fe to S is 1:1. We have 0.376 moles of Fe and 0.468 moles of S. Since the ratio of moles of Fe to moles of S (0.376/0.468 ≈ 0.803) is less than 1, iron is the limiting reactant. This means that all the iron will be consumed in the reaction, and some sulfur will be left over. The amount of iron(II) sulfide formed will be determined by the amount of iron available.

To calculate the amount of sulfur that reacts with the iron, we use the stoichiometric ratio from the balanced equation. Since one mole of Fe reacts with one mole of S, 0.376 moles of Fe will react with 0.376 moles of S. Now we can calculate the mass of sulfur that reacts:

Mass of S reacted = 0.376 mol × 32.065 g/mol ≈ 12.056 g

This tells us that 12.056 grams of sulfur will react with all 21 grams of iron. To find out how much sulfur is left over, we subtract the mass of sulfur reacted from the initial mass of sulfur:

Mass of S remaining = 15 g - 12.056 g ≈ 2.944 g

Therefore, approximately 2.944 grams of sulfur will remain after the reaction is complete. This calculation is crucial for understanding the final composition of the mixture and for predicting the yield of the product, iron(II) sulfide.

Calculating the Mass of Iron(II) Sulfide Formed

Now that we know the limiting reactant (iron) and the amount of sulfur that reacts, we can calculate the mass of iron(II) sulfide (FeS) formed. According to the balanced chemical equation, one mole of Fe reacts to produce one mole of FeS. Therefore, 0.376 moles of Fe will produce 0.376 moles of FeS.

To find the mass of FeS produced, we need to calculate its molar mass. The molar mass of FeS is the sum of the molar masses of iron and sulfur:

Molar mass of FeS = 55.845 g/mol (Fe) + 32.065 g/mol (S) ≈ 87.91 g/mol

Now we can calculate the mass of FeS produced:

Mass of FeS produced = 0.376 mol × 87.91 g/mol ≈ 33.05 g

So, approximately 33.05 grams of iron(II) sulfide will be formed in this reaction. This value represents the theoretical yield of the reaction, assuming that the reaction proceeds to completion and there are no losses due to side reactions or experimental errors.

Detailed Analysis of the Remaining Elements

After the reaction between iron and sulfur, we determined that iron is the limiting reactant and sulfur is in excess. This means that all the iron (21 grams) will be converted into iron(II) sulfide, and a portion of the sulfur (approximately 2.944 grams) will remain unreacted. Understanding the implications of this outcome is crucial for various chemical processes and applications.

The remaining sulfur exists in its elemental form, meaning it has not chemically bonded with any other element. This unreacted sulfur can be separated from the iron(II) sulfide using various techniques, depending on the specific requirements of the application. For instance, if the iron(II) sulfide needs to be purified, the remaining sulfur can be removed through methods such as dissolution in a suitable solvent or through physical separation techniques.

From a chemical perspective, the presence of unreacted sulfur can influence the properties of the final mixture. For example, if the iron(II) sulfide is intended for use as a catalyst, the presence of free sulfur might affect its catalytic activity. Therefore, it's essential to consider the potential impact of the remaining elements on the desired outcome of the reaction.

In industrial settings, understanding the excess of one reactant over another is critical for optimizing reaction conditions and minimizing waste. By carefully controlling the amounts of reactants, chemists and engineers can ensure that the desired product is formed in the highest possible yield, while also reducing the amount of unreacted material that needs to be disposed of or recycled.

Implications and Applications

The reaction between iron and sulfur and the subsequent analysis of remaining elements have significant implications across various scientific and industrial domains. Understanding the stoichiometry and limiting reactants in chemical reactions is fundamental to fields such as materials science, metallurgy, and chemical engineering.

In metallurgy, for instance, the reaction between iron and sulfur is relevant in the production of various iron-based alloys. The presence of sulfur as an impurity in iron ore can affect the properties of the final metal product, such as its strength and ductility. By understanding the chemical reactions and the role of sulfur, metallurgists can develop processes to remove or control sulfur levels in iron and steel, thereby improving their quality.

In the field of materials science, iron(II) sulfide itself has various applications. It can be used as a component in certain types of batteries, as a pigment in paints and coatings, and as a precursor for synthesizing other iron compounds. The ability to control the stoichiometry of the reaction between iron and sulfur is essential for producing FeS with specific properties tailored to these applications.

In chemical engineering, the principles of stoichiometry and limiting reactants are applied in the design and optimization of chemical reactors. Chemical engineers need to carefully calculate the amounts of reactants required to achieve the desired conversion and yield of a product. Understanding the behavior of limiting reactants and excess reactants is crucial for minimizing waste and maximizing the efficiency of chemical processes.

Practical Examples and Real-World Scenarios

To further illustrate the significance of this analysis, let's consider some practical examples and real-world scenarios. Imagine a scenario in a laboratory where a chemist is synthesizing iron(II) sulfide for a specific application. The chemist needs to ensure that the FeS produced has a high purity and a defined composition. By carefully controlling the amounts of iron and sulfur used in the reaction, and by understanding the concept of limiting reactants, the chemist can minimize the amount of unreacted sulfur in the final product.

Another scenario can be found in the environmental field. Sulfur compounds are often found in industrial waste streams and can pose environmental challenges if not properly managed. Understanding the reactions involving sulfur and the conditions under which they occur is essential for developing effective waste treatment processes. For example, in wastewater treatment, sulfur compounds might need to be oxidized or reduced to less harmful forms before the water can be safely discharged.

In the energy sector, the reaction between iron and sulfur is relevant in the context of certain types of batteries, such as iron-sulfur batteries. These batteries have the potential to store energy efficiently and are being explored as alternatives to traditional battery technologies. The performance of these batteries depends on the precise control of the chemical reactions taking place within them, including the reaction between iron and sulfur.

Summary and Key Takeaways

In summary, dissolving a mixture of 21 grams of iron (Fe) and 15 grams of sulfur (S) results in a chemical reaction that forms iron(II) sulfide (FeS). By applying stoichiometric principles and calculating the moles of each reactant, we identified iron as the limiting reactant and sulfur as the excess reactant. This analysis allowed us to determine that approximately 2.944 grams of sulfur would remain unreacted after the reaction is complete.

The key takeaways from this analysis include:

Understanding the balanced chemical equation is crucial for determining the stoichiometric ratios between reactants and products.
Calculating the moles of each reactant allows us to identify the limiting reactant, which dictates the amount of product formed.
The limiting reactant is the reactant that is completely consumed in the reaction, while the excess reactant is present in a larger amount than required.
By calculating the mass of the excess reactant that reacts, we can determine the amount of the excess reactant that remains after the reaction.
The analysis of remaining elements is essential for understanding the composition of the final mixture and for optimizing chemical processes in various applications.

This comprehensive exploration of the reaction between iron and sulfur provides valuable insights into the principles of stoichiometry, limiting reactants, and the practical implications of chemical reactions in various fields. By mastering these concepts, chemists, engineers, and scientists can effectively design and control chemical processes to achieve desired outcomes and minimize waste.