Iron And Acid Reaction: Calculating Water For A Solution

Hey guys! Let's dive into a fascinating chemistry problem that involves iron, hydrochloric acid, and a bit of a solution-making adventure. The core of our puzzle revolves around a reaction where 22.4 grams of iron filings get cozy with an excess of hydroiodic acid (HI). This leads to the release of hydrogen gas, which then decides to play with chlorine. Our mission? To figure out just how much water we need to add to the resulting hydrochloric acid solution to get a 22.6% concentration. It's like a culinary recipe, but instead of baking a cake, we are cooking up a precise chemical concoction. This journey will guide you through the meticulous steps to calculate water volume, a common yet crucial task in chemistry. Ready to put on your lab coats and get started?

First things first, it's super important to grasp the underlying chemical reactions at play. When iron (Fe) reacts with hydroiodic acid (HI), it produces iron(II) iodide (FeI₂) and hydrogen gas (H₂). The equation that represents this is: Fe + 2HI -> FeI₂ + H₂. The amount of iron we begin with is key, and we need to use this to find out how much hydrogen gas is created. Once we know the amount of hydrogen, we can figure out the quantity of chlorine that reacts with it. This ultimately gives us the amount of hydrochloric acid (HCl) produced. Once we know the mass of HCl, our task of calculating the water amount for a specific concentration becomes straightforward. The entire process hinges on understanding stoichiometry, which is basically the chemistry of proportions in reactions, ensuring that we get every step right. It is like a dance of atoms and molecules where everything reacts in fixed ratios. Each step plays a crucial role to achieve the final outcome. In short, understanding the chemistry behind this is going to be super fun.

Now, let's break down the whole shebang into manageable steps. Knowing the initial mass of iron, our first step involves finding the moles of iron. The atomic mass of iron is about 55.845 grams per mole (g/mol). We'll use this to convert the mass of iron to moles, using the simple formula: Moles = Mass / Molar Mass. Next, we determine the moles of hydrogen gas produced. According to the balanced chemical equation, 1 mole of iron produces 1 mole of hydrogen gas. Thus, the moles of hydrogen gas are equal to the moles of iron. After we found the amount of hydrogen gas, this gas reacts with chlorine (Cl₂), and this produces hydrochloric acid (HCl). The equation for this reaction is H₂ + Cl₂ -> 2HCl. The equation tells us that 1 mole of hydrogen reacts with 1 mole of chlorine to produce 2 moles of HCl. Knowing that H₂ reacted fully with Cl₂, the moles of HCl generated are twice the moles of H₂. With the number of moles of HCl, the mass of HCl is easy to calculate using the formula: mass = moles × molar mass. The molar mass of HCl is around 36.46 g/mol. Finally, using the percentage concentration, we can calculate the mass of the solution needed and subsequently determine the water mass needed. Each phase holds importance in the calculation. By breaking it into pieces, we will have an easier time understanding the whole process.

The Iron and Hydroiodic Acid Reaction: Step-by-Step

Alright, let's get those chemistry gears turning with a detailed walkthrough of the iron and hydroiodic acid reaction. This part is where we crunch the numbers and bring our problem to life. It's a journey from grams to moles, and from one substance to another, with our goal always in sight: the amount of water needed to create that perfect 22.6% hydrochloric acid solution. We will use the chemical equations to make our calculations accurate and reliable. So, are you ready to get started? Let us begin!

Firstly, we calculate the moles of iron (Fe). The molar mass of iron is 55.845 g/mol, and we're starting with 22.4 g of iron filings. Applying the formula: Moles of Fe = Mass of Fe / Molar mass of Fe = 22.4 g / 55.845 g/mol ≈ 0.401 mol. This is the amount of iron that is reacting. Since the reaction between iron and hydroiodic acid goes like this: Fe + 2HI -> FeI₂ + H₂, for every one mole of iron that reacts, one mole of hydrogen (H₂) is produced. Therefore, the moles of hydrogen produced also equal 0.401 mol.

Next up, we need to find out how much hydrochloric acid (HCl) is created. Remember how the hydrogen gas produced in the initial reaction then reacts with chlorine gas (Cl₂)? The equation is H₂ + Cl₂ -> 2HCl. This tells us that one mole of hydrogen gas yields two moles of hydrochloric acid. Therefore: Moles of HCl = 2 × Moles of H₂ = 2 × 0.401 mol = 0.802 mol.

Now that we know the moles of HCl, let’s find its mass. Using the molar mass of HCl (36.46 g/mol), the calculation becomes: Mass of HCl = Moles of HCl × Molar mass of HCl = 0.802 mol × 36.46 g/mol ≈ 29.23 g. This is the mass of hydrochloric acid that we have. Knowing this value is critical in the next stage.

Solving for the Perfect Solution: Water Calculation

With the mass of hydrochloric acid calculated, we're now at the final stretch. Here, we're pinpointing the amount of water needed to achieve our target concentration of 22.6%. This is where the magic of dilutions really comes into play. It's about finding the perfect ratio of solute (HCl in our case) to solvent (water). The goal here is simple: to make sure that our solution has exactly the right concentration. It's like making sure your coffee tastes just right – the right amount of coffee and water! Let's get down to the calculation.

We know that the concentration of the solution is 22.6%, meaning that 22.6 g of HCl is present in every 100 g of the solution. So, knowing this, we can calculate the total mass of the solution needed to have 29.23 g of HCl by rearranging the following formula: Concentration = (Mass of solute / Mass of solution) * 100%. Therefore: Mass of solution = (Mass of HCl / Concentration) * 100% = (29.23 g / 22.6%) * 100% ≈ 129.34 g. This calculation lets us know how much the entire solution should weigh to have the concentration that we want.

Now, here is the final step! We need to find the mass of water to add. The mass of water is the difference between the mass of the solution and the mass of HCl. The calculation is: Mass of water = Mass of solution - Mass of HCl = 129.34 g - 29.23 g = 100.11 g. This is what we were looking for. So, to make a 22.6% concentration of hydrochloric acid, you need to add approximately 100.11 grams of water. Fantastic! We've made it to the finish line, successfully navigating the chemical reaction and dilution processes. The hard work and the precise calculations have all paid off.

Conclusion: The Final Dilution

To wrap it up, we started with iron filings and through a series of chemical reactions, we arrived at a hydrochloric acid solution with a specific concentration. This journey involved stoichiometric calculations, the ability to convert between grams and moles, and the use of the solution concentration formula. Through these steps, we could determine the mass of water required to achieve our desired concentration. Now, with the answer in hand, we can appreciate the importance of these calculations in practical chemistry. We can also appreciate how these calculations are so crucial in the laboratory and in various industrial processes. From start to finish, the exercise shows us the beauty of chemistry in real life. Keep up the enthusiasm and keep asking questions, because there’s always more to discover in the world of chemistry!

This entire process is just one of the many examples of the use of chemistry in everyday life. From the moment we wake up in the morning to the moment we go to sleep, we interact with chemistry and science in one way or another. So, the more we learn, the more we grow. With each problem, we strengthen our understanding and enhance our problem-solving skills.