Sugar Solution Density: Calculate Absolute, Relative & Brix

Hey guys! Let's dive into a sweet chemistry problem today. We're going to figure out the absolute density, relative density, and degrees Brix of a sugar solution. This involves some fundamental concepts in chemistry, so let's break it down step by step to make sure we understand everything clearly. We'll start with the basics of density and then apply them to our specific problem: a solution of 2.5 grams of sugar in 50 mL of water. Understanding these calculations is super useful not just in chemistry class, but also in real-world applications like food science and quality control. So, grab your calculators and let's get started!

Understanding the Problem: Sugar Solution Basics

In this section, we will deeply understand our problem, we have a sugar solution, which is a mixture of sugar (the solute) and water (the solvent). The amount of sugar is 2.5 grams, and the amount of water is 50 mL. Our mission is to find three key properties of this solution: absolute density, relative density, and degrees Brix. Before we jump into the calculations, it's crucial to understand what each of these terms means. Density, in general, is a measure of how much mass is contained in a given volume. It's a fundamental property that helps us characterize substances. For example, a dense material like lead feels heavy even in a small volume, while a less dense material like foam feels light even in a larger volume. When we talk about the absolute density of our sugar solution, we're referring to the mass of the solution divided by its volume. This will give us a direct measure of how compact the solution is. Think of it as a direct comparison of mass to volume – the higher the density, the more mass packed into the same space. The formula for density is simple but powerful: Density = Mass / Volume. This formula is the key to our first calculation, and we'll use it to determine the absolute density of our sugar solution. So, let's keep this formula in mind as we move forward. Understanding this is the first step in solving our problem.

Calculating Absolute Density

The absolute density is the mass per unit volume of a substance. To calculate the absolute density of the sugar solution, we first need to determine the total mass of the solution. We know that we have 2.5 grams of sugar. We also need to consider the mass of the water. We know we have 50 mL of water, and the density of water is approximately 1 gram per mL. This is a crucial piece of information because it allows us to convert the volume of water into mass. Since density = mass / volume, we can rearrange this to find mass = density × volume. For water, this means the mass of water = 1 g/mL × 50 mL = 50 grams. So, we have 50 grams of water and 2.5 grams of sugar. The total mass of the solution is the sum of these two masses: 50 grams (water) + 2.5 grams (sugar) = 52.5 grams. Now that we have the total mass, we can calculate the density. We know the total volume of the solution is 50 mL (the volume of the water, assuming the addition of sugar doesn't significantly change the volume, which is a reasonable approximation for this concentration). The formula for density is density = mass / volume. So, the absolute density of the sugar solution is: Density = 52.5 grams / 50 mL = 1.05 grams/mL. This value tells us how much mass is packed into each milliliter of the solution. A density of 1.05 grams/mL means that for every milliliter of the solution, there are 1.05 grams of mass. This is slightly denser than pure water (which is 1 g/mL), which makes sense because we've added sugar, which increases the mass without significantly increasing the volume. So, we've successfully calculated the absolute density of our sugar solution. Next, we'll move on to figuring out the relative density.

Determining Relative Density

Now, let's tackle relative density. Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of a reference substance, which is usually water at 4°C. The key thing about relative density is that it's a dimensionless quantity, meaning it doesn't have any units. It simply tells us how much denser or less dense a substance is compared to water. So, in our case, we're comparing the density of our sugar solution to the density of water. The density of water is approximately 1 gram per mL (1 g/mL). This is the standard value we use for comparison when calculating relative density. We've already calculated the absolute density of our sugar solution, which we found to be 1.05 grams/mL. Now, to find the relative density, we simply divide the density of the sugar solution by the density of water. The formula for relative density is: Relative Density = (Density of substance) / (Density of reference substance). In our case, this translates to: Relative Density = (Density of sugar solution) / (Density of water). Plugging in the values we have: Relative Density = (1.05 g/mL) / (1 g/mL) = 1.05. Notice that the units (g/mL) cancel out, leaving us with a dimensionless number. A relative density of 1.05 means that our sugar solution is 1.05 times as dense as water. This makes sense because we've dissolved sugar in water, which adds mass without significantly changing the volume, thus increasing the density compared to pure water. Relative density is a useful measure because it gives us a quick comparison of the densities of different substances. It's widely used in various fields, including chemistry, physics, and engineering. Now that we've calculated both absolute density and relative density, let's move on to the final part of our problem: determining the degrees Brix.

Calculating Degrees Brix

Alright, let's get to the last part of our problem: calculating degrees Brix. Degrees Brix (°Bx) is a measure of the sugar content of an aqueous solution. Specifically, it represents the percentage of sucrose by mass in the solution. So, if a solution has 25 °Bx, it means there are 25 grams of sucrose in 100 grams of solution. Degrees Brix is widely used in the food and beverage industry, particularly in the production of fruit juices, soft drinks, and wine, to ensure consistent sugar content and quality. The relationship between the concentration of sugar in a solution and its degrees Brix is not perfectly linear, especially at higher concentrations. However, for dilute solutions like the one we're working with (2.5 grams of sugar in 50 mL of water), we can use a simplified approximation. For dilute solutions, we can approximate degrees Brix by calculating the mass percentage of sugar in the solution. To do this, we'll use the formula: Degrees Brix ≈ (Mass of sugar / Mass of solution) × 100. We already know the mass of sugar is 2.5 grams, and we calculated the mass of the solution to be 52.5 grams (50 grams of water + 2.5 grams of sugar). Plugging these values into the formula, we get: Degrees Brix ≈ (2.5 grams / 52.5 grams) × 100. Degrees Brix ≈ 0.0476 × 100. Degrees Brix ≈ 4.76 °Bx. So, our sugar solution has approximately 4.76 degrees Brix. This means that for every 100 grams of solution, there are about 4.76 grams of sugar. While this is an approximation, it gives us a good estimate of the sugar content in our solution. For more precise measurements, especially in industrial settings, a refractometer is used. A refractometer measures the refractive index of the solution, which is directly related to the sugar concentration, and provides a more accurate degrees Brix reading. But for our purposes, the approximation gives us a solid understanding of the sugar content. With this, we've successfully calculated degrees Brix for our sugar solution!

Conclusion: Putting It All Together

Okay, guys, we've done it! We've successfully calculated the absolute density, relative density, and degrees Brix for our sugar solution. Let's quickly recap what we found: The absolute density of the solution is 1.05 grams/mL, which tells us the mass per unit volume. The relative density is 1.05, indicating how much denser the solution is compared to water. And the degrees Brix is approximately 4.76 °Bx, representing the sugar content in the solution. Understanding these concepts is crucial in chemistry and has practical applications in various industries. By breaking down the problem step by step, we've made the calculations manageable and easy to follow. Remember, absolute density is a direct measure of mass per volume, relative density compares a substance's density to that of water, and degrees Brix gives us the sugar content in a solution. These are fundamental concepts that will come in handy in many scientific and real-world scenarios. So, whether you're in the lab, the kitchen, or just curious about the world around you, these calculations can help you understand the properties of solutions better. Keep practicing, and you'll become a pro at these calculations in no time! Well done, everyone!