Limiting And Excess Reactants In Copper And Sulfur Reaction

In the realm of chemistry, understanding the concepts of limiting and excess reactants is crucial for predicting the yield of a reaction. When chemical reactions occur, reactants are not always present in the exact stoichiometric amounts required for complete conversion. The reactant that is completely consumed in a reaction is termed the limiting reactant, as it dictates the maximum amount of product that can be formed. Conversely, the reactant present in excess is known as the excess reactant. This excess reactant will have some amount remaining after the reaction is complete.

This article delves into the reaction between copper (Cu) and sulfur (S) to form copper(I) sulfide ($Cu_2S$), as represented by the balanced chemical equation:

$2 Cu + S ightarrow Cu_2S$

We will explore how to identify the limiting and excess reactants when given specific masses of copper and sulfur. Let's consider a scenario where we have 40.2 g of copper and 14.1 g of sulfur. Our goal is to determine which reactant will be completely consumed first (the limiting reactant) and which reactant will be left over (the excess reactant). This involves a step-by-step approach, converting masses to moles, comparing mole ratios, and ultimately, identifying the limiting and excess reactants.

Step-by-Step Determination of Limiting and Excess Reactants

To accurately determine the limiting reactant and excess reactant in the reaction between copper and sulfur, we need to follow a structured approach. This process involves converting the given masses of reactants into moles, using the molar masses of the respective elements. Then, we compare the mole ratios of the reactants to the stoichiometric ratios from the balanced chemical equation. This comparison allows us to identify which reactant will be completely consumed first (the limiting reactant) and which reactant will be in excess. Finally, we can calculate the amount of excess reactant remaining after the reaction is complete.

1. Convert Grams to Moles

The initial step in identifying the limiting reactant is to convert the given masses of the reactants into moles. This conversion is essential because chemical reactions occur based on the molar ratios of the reactants, not their masses. To perform this conversion, we use the molar mass of each element, which can be found on the periodic table.

• Copper (Cu): The molar mass of copper is approximately 63.55 g/mol. To convert 40.2 g of copper to moles, we use the following calculation:

  Moles of Cu = (Mass of Cu) / (Molar mass of Cu)

  Moles of Cu = (40.2 g) / (63.55 g/mol) ≈ 0.632 mol

  Therefore, we have approximately 0.632 moles of copper.

• Sulfur (S): The molar mass of sulfur is approximately 32.07 g/mol. To convert 14.1 g of sulfur to moles, we use the following calculation:

  Moles of S = (Mass of S) / (Molar mass of S)

  Moles of S = (14.1 g) / (32.07 g/mol) ≈ 0.440 mol

  Therefore, we have approximately 0.440 moles of sulfur.

By converting the masses of copper and sulfur into moles, we now have a basis for comparing the amounts of each reactant in terms of molar ratios, which is crucial for determining the limiting reactant.

2. Determine the Mole Ratio

The next crucial step in identifying the limiting reactant is to compare the mole ratio of the reactants with the stoichiometric ratio from the balanced chemical equation. The balanced equation, $2Cu + S ightarrow Cu_2S$, tells us that 2 moles of copper (Cu) react with 1 mole of sulfur (S) to produce 1 mole of copper(I) sulfide ($Cu_2S$). This stoichiometric ratio of 2:1 (Cu:S) is the key to determining which reactant is limiting.

To compare the mole ratio, we can calculate the amount of one reactant required to react completely with the given amount of the other reactant. Let's start by determining how many moles of sulfur are required to react completely with the 0.632 moles of copper we have.

Using the stoichiometric ratio:

Moles of S required = (Moles of Cu) / 2 Moles of S required = (0.632 mol) / 2 ≈ 0.316 mol

This calculation shows that 0.316 moles of sulfur are needed to react completely with 0.632 moles of copper. We have 0.440 moles of sulfur, which is more than the 0.316 moles required. This suggests that sulfur is in excess and copper might be the limiting reactant.

Alternatively, we can calculate how many moles of copper are required to react completely with the 0.440 moles of sulfur we have:

Moles of Cu required = (Moles of S) * 2 Moles of Cu required = (0.440 mol) * 2 = 0.880 mol

This calculation indicates that 0.880 moles of copper are needed to react completely with 0.440 moles of sulfur. However, we only have 0.632 moles of copper, which is less than the required 0.880 moles. This confirms that copper is the limiting reactant, as we have less copper than what is needed to react with all the sulfur.

By comparing the mole ratios and considering the stoichiometric coefficients from the balanced equation, we can confidently identify the limiting reactant. This information is crucial for predicting the maximum amount of product that can be formed in the reaction.

3. Identify the Limiting Reactant

Based on the mole ratio comparison in the previous step, we can now definitively identify the limiting reactant. The limiting reactant is the one that is completely consumed in the reaction, thereby determining the maximum amount of product that can be formed.

In our analysis, we found that 0.316 moles of sulfur are required to react completely with the 0.632 moles of copper present. Since we have 0.440 moles of sulfur, which is more than the required amount, sulfur is in excess. Conversely, we calculated that 0.880 moles of copper are required to react completely with the 0.440 moles of sulfur. However, we only have 0.632 moles of copper, which is less than the required amount.

Therefore, copper (Cu) is the limiting reactant in this reaction. This means that the reaction will stop once all the copper is consumed, even though there will be some sulfur remaining. The amount of copper present will dictate the maximum amount of copper(I) sulfide ($Cu_2S$) that can be produced.

Identifying the limiting reactant is a critical step in stoichiometry, as it allows us to predict the theoretical yield of the product. The theoretical yield is the maximum amount of product that can be formed from a given amount of reactants, assuming the reaction goes to completion with 100% efficiency. In real-world scenarios, the actual yield may be less than the theoretical yield due to factors such as incomplete reactions or loss of product during purification.

4. Identify the Excess Reactant

Having identified copper as the limiting reactant, the next logical step is to determine the excess reactant. The excess reactant is the reactant that is present in a greater amount than what is required to react completely with the limiting reactant. In other words, some of the excess reactant will be left over after the reaction has reached completion.

In our scenario, we have two reactants: copper and sulfur. We have already established that copper is the limiting reactant because it will be completely consumed during the reaction. Therefore, by process of elimination, sulfur (S) is the excess reactant.

This means that after all the copper has reacted with sulfur to form copper(I) sulfide ($Cu_2S$), there will still be some sulfur remaining. To quantify how much sulfur will be left over, we need to calculate the amount of sulfur that actually reacted with the copper and subtract that from the initial amount of sulfur we had.

This calculation is essential for understanding the stoichiometry of the reaction and for predicting the composition of the final reaction mixture. Knowing the amount of excess reactant can also be important in industrial processes, where minimizing waste and maximizing the utilization of reactants are crucial for economic efficiency.

5. Determine the Amount of Excess Reactant Remaining

To determine the amount of excess reactant remaining after the reaction is complete, we need to calculate how much of the excess reactant actually reacted with the limiting reactant. Then, we subtract this amount from the initial amount of the excess reactant.

In our case, sulfur is the excess reactant, and copper is the limiting reactant. We know that 0.632 moles of copper reacted completely. From the balanced chemical equation ($2Cu + S ightarrow Cu_2S$), we know that 2 moles of copper react with 1 mole of sulfur. Therefore, we can calculate the moles of sulfur that reacted with the 0.632 moles of copper:

Moles of S reacted = (Moles of Cu) / 2 Moles of S reacted = (0.632 mol) / 2 = 0.316 mol

So, 0.316 moles of sulfur reacted with the copper. Now, we subtract this amount from the initial amount of sulfur (0.440 mol) to find the moles of sulfur remaining:

Moles of S remaining = Initial moles of S - Moles of S reacted Moles of S remaining = 0.440 mol - 0.316 mol = 0.124 mol

Therefore, 0.124 moles of sulfur are left over after the reaction is complete. To convert this back to grams, we multiply by the molar mass of sulfur (32.07 g/mol):

Mass of S remaining = (Moles of S remaining) * (Molar mass of S) Mass of S remaining = (0.124 mol) * (32.07 g/mol) ≈ 3.98 g

Thus, approximately 3.98 grams of sulfur will remain unreacted after all the copper has been converted to copper(I) sulfide. This calculation provides a quantitative understanding of the excess reactant and its impact on the reaction outcome.

Conclusion

In summary, determining the limiting reactant and excess reactant is a fundamental aspect of stoichiometry. By following a systematic approach, we can accurately predict which reactant will be completely consumed and how much of the excess reactant will remain. In the reaction between 40.2 g of copper and 14.1 g of sulfur, we have shown that copper is the limiting reactant and sulfur is the excess reactant, with approximately 3.98 g of sulfur remaining after the reaction is complete. This understanding is crucial for optimizing chemical reactions and predicting product yields in various applications, from laboratory experiments to industrial processes.