Moles Of $SO_3$ From S And $O_2$: A Chemistry Calculation

Nov 12, 2025 by ADMIN 58 views

$How Many Moles of $SO_3$ Can Be Produced from the Reaction of 1.56 Moles of S and 1.36 Moles of $O_2$ According to the Equation Below? $2 S+3 O_2 \rightarrow 2 SO_3$$

Alright, chemistry enthusiasts! Let's dive into a classic stoichiometry problem. We're going to figure out how much sulfur trioxide ( $SO_3$ ) we can make from a given amount of sulfur (S) and oxygen ( $O_2$ ). This is a typical limiting reactant problem, where we need to determine which reactant will run out first and, therefore, dictate the amount of product formed. So, grab your calculators, and let's get started!

Understanding the Stoichiometry

Before we jump into the calculations, let's make sure we understand the balanced chemical equation:

$2 S + 3 O_2 \rightarrow 2 SO_3$

This equation tells us that 2 moles of sulfur (S) react with 3 moles of oxygen ( $O_2$ ) to produce 2 moles of sulfur trioxide ( $SO_3$ ). These coefficients are super important because they give us the mole ratios we need to solve the problem. Think of it like a recipe: if you don't have the right proportions of ingredients, you can't make the dish correctly.

The mole ratio between S and $SO_3$ is 2:2, which simplifies to 1:1. This means that for every mole of S that reacts, we get one mole of $SO_3$ . The mole ratio between $O_2$ and $SO_3$ is 3:2. This means that for every 3 moles of $O_2$ that react, we produce 2 moles of $SO_3$ .

Knowing these ratios is crucial. They act as conversion factors that allow us to move from moles of reactants to moles of products. Now, let's see how to apply this knowledge to find the limiting reactant.

Identifying the Limiting Reactant

We are given 1.56 moles of S and 1.36 moles of $O_2$ . To find the limiting reactant, we need to determine which of these will be completely consumed first. There are a couple of ways to do this, but here’s a straightforward method:

Calculate the Moles of $SO_3$ Produced from Each Reactant:
- From Sulfur (S): Since the mole ratio between S and $SO_3$ is 1:1, if all 1.56 moles of S react, we would produce 1.56 moles of $SO_3$ .
- From Oxygen ( $O_2$ ): Using the mole ratio between $O_2$ and $SO_3$ (3:2), we can calculate the moles of $SO_3$ produced from 1.36 moles of $O_2$ . Moles of $SO_3$ = (1.36 moles $O_2$ ) * (2 moles $SO_3$ / 3 moles $O_2$ ) = 0.907 moles $SO_3$ (approximately).
Determine the Limiting Reactant:
- The limiting reactant is the one that produces the least amount of product. In this case, $O_2$ produces only 0.907 moles of $SO_3$ , while S could produce 1.56 moles of $SO_3$ . Therefore, $O_2$ is the limiting reactant.

So, what does this mean? It means that even though we have 1.56 moles of sulfur, we can't use all of it because we'll run out of oxygen first. The amount of oxygen we have will dictate how much $SO_3$ we can actually make. This is a crucial concept in stoichiometry, and it's essential for any chemist to master. Understanding the limiting reactant allows us to accurately predict the yield of a reaction and optimize our use of resources. Now that we've identified the limiting reactant, let's calculate the theoretical yield of $SO_3$ .

Calculating the Moles of $SO_3$ Produced

Since $O_2$ is the limiting reactant, the amount of $SO_3$ produced will be determined by the amount of $O_2$ available. We already calculated this in the previous step:

Moles of $SO_3$ = (1.36 moles $O_2$ ) * (2 moles $SO_3$ / 3 moles $O_2$ ) = 0.907 moles $SO_3$ (approximately).

Therefore, the reaction of 1.56 moles of S and 1.36 moles of $O_2$ will produce approximately 0.907 moles of $SO_3$ .

So, the final answer is that approximately 0.907 moles of $SO_3$ can be produced. Remember, this is a theoretical yield, assuming the reaction goes to completion with 100% efficiency. In reality, reactions rarely achieve 100% yield due to various factors like side reactions, incomplete reactions, and loss of product during purification.

Additional Considerations and Tips

Here are some extra tips and considerations to keep in mind when tackling stoichiometry problems like this:

Always Balance the Chemical Equation: This is the foundation of any stoichiometry problem. Make sure the equation is correctly balanced before proceeding with any calculations. If the equation isn't balanced, your mole ratios will be incorrect, leading to wrong answers.
Pay Attention to Units: Keep track of your units throughout the calculation. This will help you avoid mistakes and ensure that your final answer has the correct units. In this case, we're working with moles, but in other problems, you might encounter grams, liters, or other units.
Understand Limiting Reactant Concept: Make sure you grasp the concept of limiting reactants. The limiting reactant is not necessarily the reactant with the smallest number of moles; it's the reactant that runs out first based on the stoichiometry of the reaction.
Practice, Practice, Practice: The best way to master stoichiometry is to practice solving problems. Work through a variety of examples to build your skills and confidence.

Real-World Applications: Stoichiometry isn't just a theoretical exercise; it has numerous practical applications in chemistry and related fields. For example, it's used in industrial chemistry to optimize chemical processes, in analytical chemistry to determine the composition of substances, and in environmental science to assess pollution levels. By mastering stoichiometry, you're gaining valuable skills that can be applied to solve real-world problems.

So, there you have it! We've successfully determined how many moles of $SO_3$ can be produced from the reaction of 1.56 moles of S and 1.36 moles of $O_2$ . Remember to always balance your equations, identify the limiting reactant, and pay attention to your units. Keep practicing, and you'll become a stoichiometry pro in no time!

Common Mistakes to Avoid

When working with stoichiometry, it's easy to make mistakes if you're not careful. Here are some common pitfalls to avoid:

Forgetting to Balance the Equation: As mentioned earlier, this is a critical first step. An unbalanced equation will lead to incorrect mole ratios and, consequently, wrong answers.
Using Incorrect Mole Ratios: Double-check your mole ratios to make sure they correspond to the balanced chemical equation. A simple mistake here can throw off your entire calculation.
Assuming the Given Amounts are Directly Proportional: Don't assume that if you have more of one reactant, you'll automatically get more product. The limiting reactant dictates the maximum amount of product that can be formed.
Ignoring Units: Always include units in your calculations and make sure they cancel out correctly. This will help you avoid dimensional analysis errors.
Rounding Too Early: Avoid rounding intermediate results, as this can introduce errors in your final answer. Wait until the very end to round your answer to the appropriate number of significant figures.

By being aware of these common mistakes and taking steps to avoid them, you'll increase your chances of success in solving stoichiometry problems.

Conclusion

In summary, determining the amount of $SO_3$ produced from the reaction of S and $O_2$ involves understanding stoichiometry, balancing chemical equations, identifying the limiting reactant, and applying mole ratios correctly. By mastering these concepts and practicing regularly, you'll be well-equipped to tackle a wide range of stoichiometry problems. Remember, chemistry is a fascinating field with many real-world applications, so keep exploring and learning!