Concentration Calculation Of $Al_2(SO_4)_3$ Solution In Water

Hey there, chemistry enthusiasts! Today, we're diving deep into the fascinating world of concentration calculations. We'll be tackling a specific problem: 500 g of $Al_2(SO_4)_3$ dissolved in 2 dm³ of water. But before we jump into the nitty-gritty calculations, let's make sure we're all on the same page with the fundamental concepts.

5.5.1 Defining Concentration: What Does It Really Mean?

So, what exactly is concentration? In simple terms, concentration tells us how much of a particular substance, known as the solute, is mixed into another substance, called the solvent. Think of it like this: if you add a spoonful of sugar to a glass of water, the sugar is the solute, and the water is the solvent. The resulting sweet liquid is a solution, and its concentration describes how sugary it is. A highly concentrated solution has a large amount of solute dissolved in the solvent, while a dilute solution has a small amount. There are many ways to express concentration, such as molarity (moles per liter), molality (moles per kilogram), percentage by mass, and parts per million (ppm). Each method provides a different perspective on the composition of the solution, and the best one to use depends on the specific application.

Understanding Concentration in Detail

To truly grasp the concept, let's break down the key elements. Concentration is a quantitative measure, meaning it involves numerical values. It's not just about saying something is "strong" or "weak"; it's about specifying the exact amount of solute present in a given amount of solution or solvent. This precision is crucial in many scientific and industrial applications, from preparing medications to controlling chemical reactions. The solute, as we mentioned, is the substance being dissolved. It can be a solid, liquid, or gas. For example, salt dissolving in water, alcohol mixing with water, and carbon dioxide dissolving in soda are all examples of solutions where the solute is a solid, liquid, and gas, respectively. The solvent is the substance that does the dissolving. It's usually a liquid, but it can also be a solid or gas. Water is often called the "universal solvent" because it dissolves so many different substances. However, other solvents like ethanol, acetone, and hexane are also commonly used in various applications.

Expressing Concentration in Different Ways

As mentioned earlier, there are several ways to express concentration, each with its own advantages and disadvantages. Molarity, which is the most common unit used in chemistry, is defined as the number of moles of solute per liter of solution. It's convenient for stoichiometric calculations because it directly relates the amount of solute to the volume of the solution. Molality, on the other hand, is defined as the number of moles of solute per kilogram of solvent. Molality is temperature-independent, which makes it useful for experiments where temperature changes significantly. Percentage by mass expresses the mass of the solute as a percentage of the total mass of the solution. It's a simple and intuitive way to express concentration, especially in everyday applications. Parts per million (ppm) is used for very dilute solutions and expresses the mass of solute per million parts of the solution. It's often used to measure trace amounts of pollutants in water or air.

The Importance of Concentration in Chemistry and Beyond

Concentration is a fundamental concept in chemistry and plays a vital role in many different fields. In the lab, it's essential for preparing solutions with the correct amounts of reactants for experiments. In medicine, it's crucial for ensuring that medications are administered in the correct dosages. In environmental science, it's used to monitor pollutants and assess water and air quality. In industry, it's used to control the composition of products and optimize manufacturing processes. Understanding concentration is therefore essential for anyone working in science, technology, engineering, or mathematics (STEM) fields, as well as for anyone interested in the world around them. So, whether you're a student learning about solutions for the first time or a seasoned scientist conducting cutting-edge research, a solid grasp of concentration is key to success. Now that we have a firm understanding of what concentration is, let's move on to the exciting part: calculating the concentration of our specific solution!

5.5.2 Calculating the Concentration of the $Al_2(SO_4)_3$ Solution

Alright, guys, now comes the fun part! We need to figure out the concentration of the solution made by dissolving 500 g of $Al_2(SO_4)_3$ in 2 dm³ of water. To do this, we'll use the concept of molarity, which, as we discussed, is the number of moles of solute per liter of solution. So, our plan is simple: first, we'll convert the mass of $Al_2(SO_4)_3$ to moles, then we'll convert the volume of water from dm³ to liters, and finally, we'll divide the number of moles by the volume in liters to get the molarity.

Step 1: Converting Mass to Moles

To convert the mass of $Al_2(SO_4)_3$ to moles, we need to use its molar mass. The molar mass is the mass of one mole of a substance and is numerically equal to its formula weight in grams per mole (g/mol). To find the molar mass of $Al_2(SO_4)_3$, we need to add up the atomic masses of all the atoms in the compound. The atomic masses can be found on the periodic table:

• Aluminum (Al): 26.98 g/mol
• Sulfur (S): 32.07 g/mol
• Oxygen (O): 16.00 g/mol

The formula for aluminum sulfate is $Al_2(SO_4)_3$, which means it contains 2 aluminum atoms, 3 sulfur atoms, and 12 oxygen atoms (3 x 4 = 12). Therefore, the molar mass of $Al_2(SO_4)_3$ is:

(2 x 26.98 g/mol) + (3 x 32.07 g/mol) + (12 x 16.00 g/mol) = 342.17 g/mol

Now that we have the molar mass, we can convert the mass of $Al_2(SO_4)_3$ (500 g) to moles using the following formula:

• Moles = Mass / Molar mass
• Moles of $Al_2(SO_4)_3$ = 500 g / 342.17 g/mol = 1.46 mol

So, we have 1.46 moles of $Al_2(SO_4)_3$.

Step 2: Converting Volume to Liters

The volume of water is given as 2 dm³. We need to convert this to liters (L). Luckily, 1 dm³ is equal to 1 liter, so the conversion is straightforward:

• Volume in liters = 2 dm³ x (1 L / 1 dm³) = 2 L

We have 2 liters of solution.

Step 3: Calculating Molarity

Now that we have the number of moles of $Al_2(SO_4)_3$ (1.46 mol) and the volume of the solution in liters (2 L), we can calculate the molarity using the formula:

• Molarity (M) = Moles of solute / Volume of solution (in liters)
• Molarity = 1.46 mol / 2 L = 0.73 M

Therefore, the concentration of the solution is 0.73 M. This means that there are 0.73 moles of $Al_2(SO_4)_3$ in every liter of solution.

Putting It All Together

We've successfully calculated the concentration of the solution! We started by understanding the definition of concentration and then applied this knowledge to a specific problem. We converted the mass of the solute to moles, converted the volume of the solvent to liters, and finally, calculated the molarity. This step-by-step approach can be used to solve many other concentration problems. Remember, the key is to break down the problem into smaller, manageable steps and use the correct formulas and units. Now you've got the tools to tackle your own concentration calculations! Keep practicing, and you'll become a pro in no time.

Why is this calculation important? Understanding the concentration of a solution is essential in various scientific and industrial applications. For instance, in chemical reactions, the concentration of reactants can significantly affect the reaction rate and yield. In medicine, the concentration of a drug in the bloodstream determines its effectiveness and potential side effects. In environmental monitoring, the concentration of pollutants in water or air is a crucial indicator of environmental quality. Therefore, mastering concentration calculations is not just an academic exercise; it's a practical skill that has real-world implications.

Tips for Mastering Concentration Calculations

To become proficient in concentration calculations, here are a few tips to keep in mind:

1. Understand the definitions: Make sure you have a clear understanding of the different ways to express concentration, such as molarity, molality, percentage by mass, and parts per million. Know the formulas and the units associated with each.
2. Pay attention to units: Units are crucial in chemistry calculations. Always include the units in your calculations and make sure they are consistent. If necessary, convert units before proceeding with the calculation.
3. Break down the problem: Complex problems can be intimidating, but they become easier to manage if you break them down into smaller steps. Identify what you are given, what you need to find, and the steps required to get there.
4. Practice, practice, practice: The more you practice, the more comfortable you will become with concentration calculations. Work through examples in your textbook, try practice problems online, and ask your instructor for help if you get stuck.
5. Use dimensional analysis: Dimensional analysis is a powerful technique for checking the correctness of your calculations. It involves tracking the units throughout the calculation to ensure that they cancel out correctly and you end up with the desired unit.

By following these tips and dedicating time to practice, you can master concentration calculations and confidently apply them in various contexts. So, keep exploring, keep learning, and remember that chemistry is all about understanding the world around us at the molecular level. Good luck, and happy calculating!