CCl4 Removal Calculation For 10% Concentration Decrease

Hey guys! Today, we're diving into a fun chemistry problem involving solutions and concentrations. We've got a mixture of carbon tetrachloride (CCl₄) and benzene, and our goal is to figure out how much CCl₄ we need to remove to decrease the concentration of the solution by a specific amount. Sounds like a challenge? Let’s break it down step by step!

Understanding the Problem

So, here’s the scenario: We start with 50 grams of CCl₄ mixed into 150 mL of benzene. The crucial part? We want to reduce the volume/volume percent (v/v%) concentration of the solution by 10%. Now, before we start crunching numbers, let's make sure we're all on the same page about what v/v% concentration actually means. It’s the volume of the solute (in our case, CCl₄) divided by the total volume of the solution, all multiplied by 100 to get a percentage. Remember, density is our friend here because it helps us convert grams of CCl₄ into milliliters, which we need for the v/v% calculation. The density of CCl₄ is given as 1.6 g/mL, a key piece of information for solving this puzzle. To really get a handle on this problem, it's super important to visualize what's going on. We're not just dealing with abstract numbers; we're dealing with actual volumes and concentrations. Imagine pouring CCl₄ into benzene, creating a solution, and then trying to figure out how to 'unmix' it just enough to hit that 10% concentration reduction target. Thinking about it this way makes the problem feel much more real and helps us anticipate the steps we need to take. For example, we know we'll need to find the initial volume of CCl₄, then the initial v/v% concentration, and from there, we can figure out the target concentration after the 10% reduction. Finally, we can work backward to find out how much CCl₄ needs to be removed. Each step is a logical progression, and visualizing the process makes it easier to keep track of where we are and where we're going. With a clear picture in our minds, we're ready to jump into the calculations!

Step 1: Convert Mass of CCl₄ to Volume

The first thing we need to do is to convert the mass of CCl₄ into its volume. This is where the density comes in handy! We know the density of CCl₄ is 1.6 g/mL, which means every 1 mL of CCl₄ weighs 1.6 grams. We can use this as a conversion factor. So, if we have 50 grams of CCl₄, we can divide that by the density to find the volume. It’s like saying, “If each milliliter weighs 1.6 grams, how many milliliters are in 50 grams?” The calculation looks like this: Volume of CCl₄ = Mass of CCl₄ / Density of CCl₄. Plugging in our values, we get Volume of CCl₄ = 50 g / 1.6 g/mL, which gives us 31.25 mL. That’s our starting point! Now we know that we have 31.25 mL of CCl₄. This is a crucial step because we need the volume to calculate the v/v% concentration. You might be wondering, why not just stick with grams? Well, v/v% is all about volumes, so we need to get everything into the same units. Think of it like comparing apples and oranges – we need to convert them to a common unit (like “fruit”) before we can meaningfully compare them. In this case, grams are like apples, milliliters are like oranges, and volume is the common fruit we need. This conversion also highlights why understanding units is so important in chemistry. Units are like the language of science; they tell us what the numbers actually mean. If we didn't pay attention to the units, we could easily end up with a nonsensical answer. Imagine if we forgot to convert grams to milliliters – we'd be trying to calculate a volume percent using mass, which just wouldn't work! So, always keep an eye on those units and make sure they're playing nicely together. Now that we've got the volume of CCl₄, we're one step closer to cracking this problem!

Step 2: Calculate the Initial Volume/Volume Percent (v/v%)

Now that we know the volume of CCl₄ (31.25 mL), we can figure out the initial concentration of the solution. Remember, the v/v% concentration is the volume of the solute (CCl₄) divided by the total volume of the solution, multiplied by 100. So, we need to find the total volume of the solution first. We started with 150 mL of benzene and added 31.25 mL of CCl₄. Assuming the volumes are additive (which is a common assumption for dilute solutions), the total volume is simply the sum of these two: 150 mL + 31.25 mL = 181.25 mL. Now we've got all the pieces we need to calculate the initial v/v%: Initial v/v% = (Volume of CCl₄ / Total volume of solution) * 100. Plugging in the numbers, we get Initial v/v% = (31.25 mL / 181.25 mL) * 100, which works out to be approximately 17.24%. So, our solution initially has a CCl₄ concentration of about 17.24%. This tells us what our starting point is. We know that before we remove any CCl₄, the solution is about 17.24% CCl₄ by volume. This is like setting the baseline in a game – we need to know where we're starting from to figure out how to get to our goal. Understanding the initial concentration is also crucial for understanding the magnitude of the change we're trying to make. If our goal was to reduce the concentration by just 1%, removing a tiny amount of CCl₄ might do the trick. But since we're aiming for a 10% reduction, we know we'll need to remove a more significant amount. This sense of scale is important in problem-solving. It helps us check whether our final answer makes sense in the context of the problem. If we ended up with a result that seemed way too big or way too small, we'd know to go back and double-check our calculations. So, calculating the initial concentration is not just a step in the process; it's also a way of orienting ourselves and making sure we're on the right track.

Step 3: Determine the Target v/v% Concentration

Our next goal is to figure out what the target concentration should be after we reduce it by 10%. We know the initial concentration was approximately 17.24%. To reduce this by 10%, we need to calculate 10% of 17.24% and then subtract that from the initial concentration. This is a pretty straightforward percentage calculation, but it's essential to get it right. A small mistake here could throw off the rest of our calculations. So, 10% of 17.24% is (10/100) * 17.24%, which equals 1.724%. Now, we subtract this from the initial concentration: 17.24% - 1.724% = 15.516%. So, our target concentration is approximately 15.516%. This means we want the final solution to have a CCl₄ concentration of around 15.516% by volume. Knowing the target concentration is like having a destination in mind when you're driving. It tells us where we need to end up. Without it, we'd just be wandering aimlessly, hoping to stumble upon the right answer. In this case, the target concentration is our guide, helping us figure out how much CCl₄ needs to be removed. It also gives us a clear benchmark to compare our final result against. Once we've calculated how much CCl₄ needs to be removed, we can double-check that the resulting concentration is indeed close to 15.516%. If it's not, we know we've made a mistake somewhere along the way and need to go back and review our steps. So, determining the target concentration is not just about doing the math; it's about setting a goal and creating a way to verify our solution. With our destination firmly in mind, we're ready to move on to the next step and figure out how to get there.

Step 4: Calculate the Volume of CCl₄ Needed for the Target Concentration

Okay, now we're getting to the heart of the problem! We know our target concentration is 15.516%, and we know the final volume of benzene will still be 150 mL (since we're only removing CCl₄). What we need to figure out is the volume of CCl₄ that will give us this concentration when mixed with 150 mL of benzene. This is a bit like working backward from the concentration formula. We know the desired concentration and the volume of one component (benzene), and we need to find the volume of the other component (CCl₄). To do this, let's rearrange the v/v% formula to solve for the volume of CCl₄. We know: Target v/v% = (Volume of CCl₄ / Total volume of solution) * 100. The total volume of the solution will be the volume of benzene (150 mL) plus the unknown volume of CCl₄. Let's call the unknown volume of CCl₄