Iron And Sulfur Reaction: Calculating The Remaining Substance

Hey everyone, let's dive into a chemistry problem involving the reaction between iron and sulfur! We're going to figure out which substance is left over after the reaction and how much of it remains. This is a classic example of stoichiometry, which is just a fancy word for calculating the amounts of reactants and products in a chemical reaction. So, grab your calculators, and let's get started!

Understanding the Problem: Iron, Sulfur, and a Chemical Reaction

Alright, guys, the problem gives us a scenario where 28 grams of iron powder (Fe) react with 20 grams of sulfur (S). The reaction that takes place is:

$Fe(s) + S(s) \rightarrow FeS(s)$

This equation tells us that one atom of iron reacts with one atom of sulfur to produce iron sulfide (FeS). The big question here is: after the reaction is complete, which substance (iron or sulfur) will be left over, and how much of it will we have? This is a limiting reactant problem, which means one of the reactants will be completely used up, thus limiting the amount of product that can be formed. The reactant that runs out first is called the limiting reactant.

To solve this, we need to do a bit of calculation involving the molar masses and the mole ratios from the balanced chemical equation. Don't worry; it's not as scary as it sounds! We'll break it down step by step. First, let's gather the information we need: the atomic masses of iron (Fe) and sulfur (S). We're given that the atomic mass of iron (Ar Fe) is 56 g/mol, and the atomic mass of sulfur (Ar S) is 32 g/mol. Armed with this information, we can determine the number of moles for each reactant.

This initial step is super crucial, so pay close attention! We'll convert the mass of each reactant to moles, then determine which one is the limiting reactant. Knowing this helps us figure out which one is left over and how much of it remains. Understanding stoichiometry like this is essential in chemistry because it helps us predict how much product we can make from a certain amount of reactants, as well as what's left over. It's the foundation for many chemical calculations and experiments, so mastering the basics will make the rest of the journey in chemistry much easier. We're going to turn those grams into moles, which is the chemists' unit of measurement for the number of atoms or molecules.

Calculating Moles: The First Step to Chemical Success

Now, let's calculate the number of moles for each reactant. Remember, the number of moles (n) is calculated by dividing the mass (m) by the molar mass (M). We'll use the formula:

$n = m / M$

For Iron (Fe):

• Mass of Fe = 28 g
• Molar mass of Fe = 56 g/mol

$n_{Fe} = 28 g / 56 g/mol = 0.5 mol$

So, we have 0.5 moles of iron.

For Sulfur (S):

• Mass of S = 20 g
• Molar mass of S = 32 g/mol

$n_{S} = 20 g / 32 g/mol = 0.625 mol$

We have 0.625 moles of sulfur. Now, with the number of moles of each reactant at hand, we can figure out which is the limiting reactant. Since the reaction is 1:1, we can compare the mole ratios directly. Iron has fewer moles than sulfur. In this case, since the reaction between iron and sulfur is a 1:1 ratio, the reactant with the least number of moles is the limiting reactant. Iron has only 0.5 moles, while sulfur has 0.625 moles. Therefore, iron is the limiting reactant, and sulfur is in excess.

This process of calculating moles is something you will use again and again in chemistry. Think of it as converting measurements to a standardized unit. Once you have the number of moles, you can compare the amounts of reactants and products easily. Make sure you remember that the molar mass is just the atomic mass expressed in grams per mole, so we can use it to convert grams to moles. These calculations will eventually become second nature as you continue practicing.

Determining the Limiting Reactant and Excess Reactant

As mentioned, the limiting reactant determines how much product can be formed. In this case, iron (Fe) is the limiting reactant because it has fewer moles (0.5 mol) compared to sulfur (S), which has 0.625 mol. That means all the iron will be used up, and some sulfur will be left over. The next step is to calculate how much sulfur is used to react with all the iron and then calculate how much sulfur remains after the reaction.

Since the reaction ratio is 1:1 (one mole of iron reacts with one mole of sulfur), 0.5 moles of iron will react with 0.5 moles of sulfur. To find out how much sulfur is left, we subtract the amount of sulfur that reacted from the initial amount of sulfur:

• Initial moles of sulfur = 0.625 mol
• Moles of sulfur that reacted = 0.5 mol

Remaining moles of sulfur = 0.625 mol - 0.5 mol = 0.125 mol

Now, we have 0.125 moles of sulfur remaining after the reaction. Now we need to convert those moles back into grams. This is very important because the answer choices are in grams, not moles.

The concept of limiting reactants is fundamental in understanding chemical reactions. It tells us how much product can be formed and which reactant runs out first. The excess reactant, in this case, is sulfur, and it is what's left over. Knowing the limiting reactant is important because it helps us to know exactly what reactants we need to fully complete the experiment. Without the proper amount of a specific reactant, you will not yield the expected products. This also helps determine which is cost effective, and we can also predict the outcome of the reactions. Mastering the calculation of limiting reactants is a cornerstone for success in any chemistry course, from introductory to advanced levels.

Calculating the Remaining Sulfur

We have the moles of sulfur left. Let's convert the remaining moles of sulfur back to grams using the molar mass of sulfur (32 g/mol):

Mass of remaining sulfur = Moles × Molar mass

Mass of remaining sulfur = 0.125 mol × 32 g/mol = 4 g

Therefore, 4 grams of sulfur remain after the reaction is complete.

Now, let's look at the answer choices:

a. 0.13 g sulfur b. 8 c. 7 d. 6 e. 5

None of the choices are correct. The closest answer is 4 grams, so there may be a slight error in the provided answer choices.

Conclusion: Putting It All Together

Alright, guys, we've walked through the entire process! We started with the mass of iron and sulfur, calculated the moles of each, identified the limiting reactant, figured out how much sulfur reacted, and finally calculated the mass of sulfur remaining. The key takeaway is that the limiting reactant controls the amount of product formed, and the excess reactant is what's left over. Stoichiometry problems like these are super important to learn in chemistry. Once you grasp the concepts, you can apply them to many reactions, predict outcomes, and understand chemical processes more deeply.

Keep practicing these types of problems, and you'll become a pro in no time! Remember to always balance your equations, calculate moles correctly, and pay attention to the mole ratios. With practice, you'll find these calculations become easier and more intuitive. Good luck with your chemistry studies, and keep exploring the amazing world of chemical reactions!