Mixing Acids: A Chemistry Problem Solved!

Hey guys! Ever wondered how chemists whip up specific solutions? It's all about precision and knowing your stuff. Today, we're diving into a classic chemistry problem: mixing acids. Imagine you're a chemist, and you need to prepare 20 liters of a solution that's precisely 30% acid. The catch? You've only got two solutions at hand: one that's 20% acid and another that's a whopping 50% acid. So, how much of each solution do you need to blend together to get the desired 30% solution? Let's break it down! This problem isn't just about mixing chemicals; it's a fantastic example of using algebra to solve real-world challenges. It's like a recipe where you're figuring out the perfect amounts of ingredients to get the flavor just right. Understanding this process can be super helpful, not only for chemistry class but also for various practical situations where you need to calculate concentrations or mixtures. We'll walk through the steps, making sure it's clear and easy to follow. So, grab your lab coats (or just your thinking caps), and let's get started on this acid-mixing adventure! We will use the concepts of percentages, equations, and a bit of problem-solving to crack this. The goal is simple: find the volumes of the two solutions needed to create our 20-liter, 30% acid mixture. Let's make chemistry fun and understandable for everyone. This is a common type of question. So, let us get to it.

Setting Up the Problem: The Chemistry Recipe

Alright, let's get our chemistry hats on and set up our problem. To make this easier, let's represent the unknowns with variables. Let: x be the volume (in liters) of the 20% acid solution, and y be the volume (in liters) of the 50% acid solution. We know a few key facts, which we can translate into equations. First, the total volume of the final solution must be 20 liters. This gives us our first equation: x + y = 20. This is a crucial starting point because it links the volumes of the two solutions to the total volume needed. Second, we know that the final solution should be 30% acid. This means the amount of acid in the final solution is 30% of 20 liters, which equals 6 liters (0.30 * 20 = 6). We can express the amount of acid in each solution as a percentage of its volume. The 20% acid solution contributes 0.20x liters of acid, and the 50% acid solution contributes 0.50y liters of acid. The second equation, therefore, is: 0.20x + 0.50y = 6. This equation is key because it balances the acid from the two solutions to the acid in the final solution. The first equation represents the total volume, and the second represents the acid concentration. Combining these two equations forms a system of equations. Our mission is to solve this system to find the values of x and y, which tell us exactly how much of each solution we need to mix. It might seem daunting at first, but don't worry, we'll break it down step by step to find the exact amounts required to achieve our desired solution.

Solving the System of Equations: Finding the Mix

Now, let's dive into solving this system of equations. We have two equations: x + y = 20 and 0.20x + 0.50y = 6. There are several ways to solve this, but we'll use the substitution method because it's generally straightforward. First, let's isolate one variable in the first equation. We can easily solve for x: x = 20 - y. Now, substitute this expression for x into the second equation: 0.20(20 - y) + 0.50y = 6. Simplify the equation: 4 - 0.20y + 0.50y = 6. Combine like terms: 0.30y = 2. Now, solve for y: y = 2 / 0.30, which gives us y = 6.67 liters (rounded to two decimal places). With the value of y in hand, we can now plug it back into the equation x = 20 - y to solve for x: x = 20 - 6.67, which gives us x = 13.33 liters. So, here is the answer. To prepare the 20-liter solution that is 30% acid, you need to mix 13.33 liters of the 20% acid solution with 6.67 liters of the 50% acid solution. See, it's not that hard. This process demonstrates how algebraic principles can provide precise solutions for real-world chemistry problems. This method is applicable in any situation where you need to create a specific mixture or concentration from available components. This is also applicable in other domains, such as calculating the right mix for making a certain item. Congratulations, we solved the problem! That is pretty straightforward, right?

Verification and Conclusion: The Perfect Blend

Let's do a quick check to ensure our answer is correct. We calculated that we need 13.33 liters of the 20% solution and 6.67 liters of the 50% solution. Let's calculate the total amount of acid in the final mixture. The 20% solution contributes 0.20 * 13.33 = 2.67 liters of acid, and the 50% solution contributes 0.50 * 6.67 = 3.33 liters of acid. Adding these together, 2.67 + 3.33 = 6 liters of acid. The final solution is indeed 6 liters of acid, which is 30% of the total volume (6 / 20 = 0.30 or 30%). This verification confirms our calculations are spot on! In conclusion, to prepare a 20-liter solution with a 30% acid concentration, you should mix 13.33 liters of the 20% acid solution with 6.67 liters of the 50% acid solution. This problem-solving approach is applicable not only in chemistry but also in various fields involving mixtures, concentrations, or ratios. By using mathematical models and precise calculations, we can confidently create desired solutions or mixtures, ensuring accuracy and efficiency. Isn't that great? It's all about understanding the principles and applying the right tools. Feel free to ask more questions if you have them. Always remember to wear the proper safety equipment. Keep experimenting, and keep learning, guys! The world of chemistry is fascinating, and with a little bit of knowledge and the right approach, you can solve some pretty interesting problems. This method is the fundamental basis for more advanced chemistry tasks. Keep practicing and applying these principles, and you'll become a pro at mixing solutions in no time! Keep mixing and have fun.