Sulfur Needed To React With 246g Mercury: Calculation Guide

Hey guys! Ever wondered how much sulfur you need to react completely with a specific amount of mercury? It's a common question in chemistry, and today, we're diving deep into calculating just that. Specifically, we'll figure out how many grams of sulfur (S) are required to fully react with 246 grams of mercury (Hg) to form mercury sulfide (HgS). This might sound complex, but don't worry, we'll break it down step by step. Let's get started!

Understanding the Reaction: Mercury and Sulfur

First, let's understand the chemistry behind the reaction. Mercury (Hg) and sulfur (S) react to form mercury sulfide (HgS). This is a classic chemical reaction, and to understand how much sulfur we need, we need to look at the balanced chemical equation. The balanced equation tells us the stoichiometric ratio, which is the ratio in which the reactants combine. In this case, the reaction is quite straightforward:

Hg + S → HgS

This equation tells us that one atom of mercury reacts with one atom of sulfur to produce one molecule of mercury sulfide. The crucial takeaway here is the 1:1 molar ratio between mercury and sulfur. This means for every mole of mercury, we need one mole of sulfur for a complete reaction. Knowing this is the key to solving our problem.

Now, why is this important? Think of it like a recipe. If you're making cookies and the recipe calls for 2 cups of flour for every 1 cup of sugar, you need to maintain that ratio to get the cookies right. Similarly, in chemical reactions, the molar ratio ensures that neither reactant is left over; everything reacts completely. Understanding this concept of molar ratios is fundamental in stoichiometry, which is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. We'll be using this concept extensively in our calculations.

Moreover, the reaction between mercury and sulfur has practical applications. Mercury sulfide, the product of this reaction, exists in two crystal forms: red mercury sulfide (cinnabar) and black mercury sulfide (metacinnabar). Cinnabar is the most important ore of mercury and has been used as a pigment (vermilion) for centuries. Understanding the reaction allows for controlled synthesis of mercury sulfide, which is crucial in various industrial and scientific applications. So, let's proceed to the next step to calculate the exact amount of sulfur required, keeping this fundamental understanding in mind. It's not just about numbers; it's about understanding the underlying chemical principles that govern these reactions.

Step 1: Convert Grams of Mercury to Moles

The first thing we need to do is convert the given mass of mercury (246 g) into moles. Why moles? Because, as we discussed, chemical reactions happen based on molar ratios. To do this, we'll use the molar mass of mercury. The molar mass is the mass of one mole of a substance and is numerically equal to the atomic mass expressed in grams per mole (g/mol). You can find the molar mass of mercury on the periodic table. It's approximately 200.59 g/mol.

So, we'll use the following formula:

Moles = Mass (g) / Molar mass (g/mol)

Plugging in the values:

Moles of Hg = 246 g / 200.59 g/mol

Moles of Hg ≈ 1.226 moles

So, we have approximately 1.226 moles of mercury. This conversion is crucial because now we're talking in terms of the number of particles (in moles), which directly relates to the number of particles of sulfur needed. Think of it as translating from one language to another. Grams are like one language, and moles are like another. To understand the chemical reaction, we need to "speak" in moles.

This step is a fundamental concept in chemistry. Converting grams to moles allows us to relate macroscopic measurements (grams, which we can weigh in the lab) to the microscopic world of atoms and molecules. Without this conversion, we would be trying to compare apples and oranges. Now that we know how many moles of mercury we have, we can use the stoichiometric ratio from our balanced equation to determine how many moles of sulfur we need. Remember, chemistry is all about precision and understanding these relationships allows us to predict and control chemical reactions accurately.

Also, a quick tip here: always pay attention to significant figures. In this case, 246 g has three significant figures, and 200.59 g/mol has five. Our final answer for the moles of Hg should have three significant figures, which is why we rounded 1.2256... to 1.226. Attention to detail like this ensures the accuracy of your calculations.

Step 2: Use the Stoichiometric Ratio to Find Moles of Sulfur

Now that we know the moles of mercury, we can use the stoichiometric ratio from the balanced chemical equation to find the moles of sulfur required. As we established earlier, the balanced equation is:

Hg + S → HgS

This equation shows a 1:1 molar ratio between mercury (Hg) and sulfur (S). This means that for every 1 mole of Hg, we need 1 mole of S. It's a direct relationship, making this step relatively simple.

So, if we have 1.226 moles of Hg, we will need the same amount of moles of S:

Moles of S = Moles of Hg = 1.226 moles

That's it! We've determined that we need 1.226 moles of sulfur to react completely with the 1.226 moles of mercury. This step highlights the power of balanced chemical equations. They are not just symbolic representations of reactions; they provide a quantitative framework for understanding how substances react with each other. The stoichiometric coefficients (the numbers in front of the chemical formulas) tell us the exact proportions in which reactants and products are involved.

Think of the stoichiometric ratio as a conversion factor. Just like we used the molar mass to convert grams to moles, we use the stoichiometric ratio to convert moles of one substance to moles of another. In this case, it's a straightforward 1:1 conversion, but in other reactions, you might have ratios like 2:1 or 3:2, making this step even more critical.

Understanding stoichiometric ratios is crucial for anyone studying chemistry. It's the foundation for many calculations, including limiting reactants, percent yield, and reaction rates. Now that we know the moles of sulfur needed, the final step is to convert these moles back into grams, which is a unit we can actually measure in the lab. Let's move on to the final calculation and get our answer in grams of sulfur.

Step 3: Convert Moles of Sulfur to Grams

We're almost there! We now know that we need 1.226 moles of sulfur to react completely with 246 g of mercury. The last step is to convert these moles of sulfur back into grams. To do this, we'll use the molar mass of sulfur. Just like we did for mercury, we can find the molar mass of sulfur on the periodic table. It's approximately 32.06 g/mol.

We'll use the same formula we used earlier, but rearranged to solve for mass:

Mass (g) = Moles × Molar mass (g/mol)

Plugging in the values:

Mass of S = 1.226 moles × 32.06 g/mol

Mass of S ≈ 39.30 grams

Therefore, approximately 39.30 grams of sulfur are needed to react completely with 246 grams of mercury to form mercury sulfide. This is our final answer!

This final conversion brings our calculation full circle. We started with a mass in grams, converted it to moles to understand the reaction at a particle level, and then converted back to grams to get our answer in a practical unit. This three-step process – grams to moles, use the stoichiometric ratio, and moles to grams – is a fundamental strategy in stoichiometry.

So, to recap:

1. We converted the grams of mercury to moles using its molar mass.
2. We used the 1:1 stoichiometric ratio from the balanced equation to determine the moles of sulfur needed.
3. We converted the moles of sulfur back to grams using its molar mass.

This calculation not only answers the question but also illustrates key concepts in chemistry, such as molar mass, stoichiometric ratios, and the importance of balanced chemical equations. Remember, guys, chemistry is all about understanding these relationships and applying them to solve problems. Now you know how to calculate the amount of sulfur needed for this reaction, and you can apply these same principles to other chemical reactions as well!

Final Answer

So, how much sulfur do we need? To completely react with 246 grams of mercury, you need approximately 39.30 grams of sulfur. This calculation highlights the importance of understanding molar masses and stoichiometric ratios in chemistry. By breaking down the problem into manageable steps, we've shown how you can tackle complex-sounding questions with confidence. Keep practicing, and you'll become a stoichiometry pro in no time! Understanding these fundamentals opens the door to mastering more advanced chemical concepts and applications. Good luck, and happy calculating!