Steam Reaction: Calculating Product Mass

Hey there, chemistry enthusiasts! Let's dive into a fun problem involving a chemical reaction. We're going to calculate the total mass of the products formed when steam reacts completely with carbon. The reaction in question is: $H_2O(g) + C(s) \longrightarrow CO(g) + H_2(g)$. Don't worry, it's not as scary as it looks. We'll break it down step-by-step, making sure everyone understands what's going on. It's all about understanding the relationships between reactants, products, and their masses.

Understanding the Chemical Equation and the Goal

First things first, let's decode the chemical equation. It tells us that gaseous water (steam), $H_2O(g)$, reacts with solid carbon, $C(s)$, to produce carbon monoxide, $CO(g)$, and hydrogen gas, $H_2(g)$. Our mission? To figure out the total mass of $CO$ and $H_2$ that are produced when 1000 kg of steam completely reacts. This problem is a classic example of stoichiometry, which is basically the study of the quantitative relationships between reactants and products in chemical reactions. Understanding this is key to performing all kinds of calculations in chemistry. We'll need to use the concept of molar mass, which is the mass of one mole of a substance. And as you'll see, we're going to use this information to convert between the mass of the reactants and the mass of the products. Let's make sure we have a clear plan.

Now, before we start crunching numbers, it's super important to understand what the question is asking. It's not just about knowing the chemical equation; it's about seeing how the amounts of reactants and products are connected. In this case, we're given the mass of steam (1000 kg) and we need to find the total mass of the products formed. This means we'll need to figure out how many moles of steam we have, use the balanced chemical equation to figure out how many moles of carbon monoxide and hydrogen are produced, and then convert those moles back into mass. Sounds like a plan, right? We're going to use the mole concept and molar masses to do this conversion. Remember that the mole is a unit of measurement that allows us to count the number of atoms or molecules in a substance. One mole of any substance contains Avogadro's number of particles (6.022 x 10^23). Understanding this is going to be important for our success in the problem.

So, why is stoichiometry so important? Well, in the real world, chemists and chemical engineers use these types of calculations all the time. They are crucial for designing and optimizing chemical reactions. Think about industrial processes: you need to know how much of each reactant to use to get the desired amount of product, and you want to do it in the most efficient and cost-effective way possible. Whether you're working in a lab or a large-scale manufacturing plant, knowing how to do these calculations is a fundamental skill. And this problem is a perfect starting point. The goal is to accurately predict the amount of product formed from a given amount of reactant. Let's go through the steps.

Step-by-Step Calculation of Product Mass

Alright, let's get down to the nitty-gritty and calculate the total mass of the products. We will break it into some steps.

Step 1: Convert the mass of steam to grams.

We're given 1000 kg of steam. Let's convert this to grams because molar masses are typically expressed in grams per mole. Remember that 1 kg = 1000 g. So, 1000 kg * 1000 g/kg = 1,000,000 g of $H_2O$. This will be the starting point for our calculations. Always make sure your units are consistent throughout the problem to avoid any mistakes. It's all about keeping track of the units, making sure they cancel out correctly so that you end up with the right units for your answer. Units are going to tell you whether you've set up your calculations correctly or whether you need to revisit them.

Step 2: Calculate the number of moles of steam.

Next up, we need to calculate the number of moles of steam. We can do this using the molar mass of water ($H_2O$), which is approximately 18 g/mol (16 g/mol for oxygen + 2 * 1 g/mol for hydrogen). So, the number of moles of $H_2O$ = (mass of $H_2O$) / (molar mass of $H_2O$) = 1,000,000 g / 18 g/mol ≈ 55,555.56 mol. Now we know how many moles of steam we are working with. The mole is a central concept in chemistry that links the mass of a substance to the number of particles (atoms, molecules, etc.) it contains.

Step 3: Determine the moles of $CO$ and $H_2$ produced.

Looking at the balanced chemical equation, $H_2O(g) + C(s) \longrightarrow CO(g) + H_2(g)$, we see that 1 mole of steam ($H_2O$) produces 1 mole of carbon monoxide ($CO$) and 1 mole of hydrogen gas ($H_2$). Therefore, if we have approximately 55,555.56 mol of steam, we will produce approximately 55,555.56 mol of $CO$ and 55,555.56 mol of $H_2$.

Step 4: Calculate the mass of $CO$ produced.

The molar mass of $CO$ is approximately 28 g/mol (12 g/mol for carbon + 16 g/mol for oxygen). The mass of $CO$ produced = (moles of $CO$) * (molar mass of $CO$) = 55,555.56 mol * 28 g/mol ≈ 1,555,555.68 g. We have to make sure we're keeping track of the units, so that we can have an accurate answer at the end of the calculation.

Step 5: Calculate the mass of $H_2$ produced.

The molar mass of $H_2$ is approximately 2 g/mol (2 * 1 g/mol for hydrogen). The mass of $H_2$ produced = (moles of $H_2$) * (molar mass of $H_2$) = 55,555.56 mol * 2 g/mol ≈ 111,111.12 g. The calculation for hydrogen gas is going to be similar to that of the carbon monoxide calculation.

Step 6: Calculate the total mass of products.

Finally, to get the total mass of the products, we add the mass of $CO$ and the mass of $H_2$. Total mass = mass of $CO$ + mass of $H_2$ = 1,555,555.68 g + 111,111.12 g ≈ 1,666,666.8 g. Let's convert this back to kilograms, as the original mass was given in kg. Since 1 kg = 1000 g, 1,666,666.8 g / 1000 g/kg ≈ 1666.67 kg. This is the answer we were looking for, the total mass of the products.

Conclusion: The Final Answer and Key Takeaways

So, guys, the total mass of the products ($CO$ and $H_2$) formed when 1000 kg of steam reacts completely with carbon is approximately 1666.67 kg. That's a lot of gas! This problem highlights the importance of stoichiometry in chemistry. Stoichiometry is more than just balancing equations; it's about predicting how much product will be formed or how much reactant is needed. It's an indispensable skill for anyone working in chemistry or a related field. Remember to always balance your chemical equations first. Then, convert the mass of the given substance to moles. Use the mole ratio from the balanced equation to find the moles of the desired product. Finally, convert the moles of the product back to mass. Always pay close attention to your units throughout the calculation and make sure they cancel out to give you the desired units in your final answer. Mastering these steps will give you a solid foundation for solving a wide variety of stoichiometry problems. Practice is key, so keep working at it, and you'll become a pro in no time! Keep practicing these types of problems, and you'll find that they become easier and more intuitive.