Calculating Vapor Pressure Of N2SO4 Solution In Water Chemistry Problem Solved

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Hey everyone! Today, we're diving into a fascinating chemistry problem: calculating the vapor pressure of a solution. Specifically, we're going to figure out the vapor pressure when 0.02 moles of N2SO4 (that's sodium sulfate) are dissolved in 400 grams of water at 25 degrees Celsius. And just to spice things up, we know the vapor pressure of pure water at this temperature is 17.4 mmHg. Let's put on our thinking caps and get started!

Understanding Vapor Pressure and Raoult's Law

Before we jump into the calculations, let's quickly recap what vapor pressure actually means. Imagine you have a container of water. Some of those water molecules are constantly escaping into the air as vapor. The pressure exerted by these vapor molecules is what we call vapor pressure. Now, when we add a solute (like N2SO4) to the water, we're essentially making it harder for the water molecules to escape. This results in a lower vapor pressure compared to pure water. This phenomenon is beautifully described by Raoult's Law. Think of Raoult's Law as our trusty guide in this vapor pressure adventure.

Raoult's Law states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent in the solution. In simpler terms, the more solvent you have (compared to the solute), the closer the solution's vapor pressure will be to the pure solvent's vapor pressure. Mathematically, it's expressed as:

P_solution = X_solvent * P°_solvent

Where:

  • P_solution is the vapor pressure of the solution
  • X_solvent is the mole fraction of the solvent
  • P°_solvent is the vapor pressure of the pure solvent

So, our mission is clear: we need to find the mole fraction of water in the solution, and then we can use Raoult's Law to calculate the vapor pressure of the solution. Sounds like a plan, right? The key concept here is the mole fraction, which represents the ratio of the number of moles of a particular component (in our case, water) to the total number of moles in the solution. Think of it like a percentage, but instead of percentages, we're dealing with moles. To make this crystal clear, let's break it down further with an example. Imagine you have a solution containing 1 mole of sugar and 9 moles of water. The total number of moles in the solution is 10 (1 + 9). The mole fraction of water would then be 9/10, or 0.9. This tells us that 90% of the molecules in the solution are water molecules. This high proportion of water molecules is what dictates the solution's vapor pressure, as they are the ones escaping into the vapor phase. Remember, the solute (sugar in this case) plays a crucial role in reducing the vapor pressure because it occupies some of the space at the surface of the liquid, making it more difficult for water molecules to evaporate. The stronger the intermolecular forces between the solute and solvent, the lower the vapor pressure will be. This is because more energy is required for the solvent molecules to overcome these forces and escape into the vapor phase. In our problem, sodium sulfate (N2SO4) is an ionic compound that dissociates into ions when dissolved in water. These ions interact strongly with water molecules, further reducing the vapor pressure compared to a non-ionic solute. We need to take this dissociation into account when calculating the mole fraction of the solute, which we'll do in the next step.

Step-by-Step Calculation

Alright, let's roll up our sleeves and get into the nitty-gritty of the calculation. We'll break it down into manageable steps so it's super easy to follow. Our main goal here is to find the vapor pressure of the solution using Raoult's Law, and to do that, we need the mole fraction of water.

Step 1: Calculate Moles of Water

First, we need to figure out how many moles of water we have. We're given 400 grams of water, and we know the molar mass of water (H2O) is approximately 18 g/mol. So, we can use this simple formula:

Moles = Mass / Molar Mass

Moles of water = 400 g / 18 g/mol ≈ 22.22 moles

Easy peasy, right? We've got our first piece of the puzzle. Understanding this step is critical because it sets the foundation for calculating the mole fraction. We need to convert the mass of water into moles so that we can compare it to the number of moles of the solute (N2SO4) and determine the relative amounts of each in the solution. The molar mass of a substance is a fundamental concept in chemistry, representing the mass of one mole of that substance. It's like a conversion factor that allows us to switch between grams and moles. Without knowing the molar mass of water, we wouldn't be able to make this crucial conversion. Now that we have the moles of water, we can move on to the next step: figuring out the moles of the solute. This is where things get a bit more interesting because N2SO4 is an ionic compound, and it dissociates into ions when dissolved in water. This dissociation has a significant impact on the colligative properties of the solution, including vapor pressure. So, we need to account for this dissociation when calculating the total number of moles in the solution. The next step will guide us through this process, ensuring we have a complete picture of the composition of our solution.

Step 2: Calculate Total Moles in Solution

Now, this is where it gets a tad bit interesting. N2SO4 is an ionic compound, which means it dissociates into ions when dissolved in water. Specifically, one mole of N2SO4 breaks down into 2 sodium ions (Na+) and 1 sulfate ion (SO4^2-). So, in total, one mole of N2SO4 gives us 3 moles of ions in solution. This is a crucial point, guys! We need to account for this dissociation because it affects the total number of particles in the solution, which in turn affects the vapor pressure.

We have 0.02 moles of N2SO4, so it will produce:

  1. 02 moles N2SO4 * 3 moles ions/mole N2SO4 = 0.06 moles of ions

To find the total moles in the solution, we add the moles of water and the moles of ions:

Total moles = 22.22 moles (water) + 0.06 moles (ions) = 22.28 moles

See? Not too scary! The key takeaway here is the dissociation of ionic compounds. It's not just about the number of moles of the original compound you added; you need to consider how many particles it breaks down into. Failing to account for this dissociation would lead to an incorrect calculation of the mole fraction and, ultimately, the vapor pressure. The van't Hoff factor is a term often used to quantify this dissociation. It represents the ratio of the actual number of particles in solution after dissociation to the number of moles of solute initially dissolved. In the case of N2SO4, the van't Hoff factor is 3, reflecting the three ions produced per formula unit. Understanding the concept of dissociation and the van't Hoff factor is essential for accurately predicting the colligative properties of solutions, including vapor pressure, boiling point elevation, and freezing point depression. These properties depend on the concentration of solute particles, not the nature of the solute itself. Now that we've accounted for the dissociation of N2SO4 and calculated the total moles in the solution, we're ready to tackle the next step: determining the mole fraction of water. This is the key ingredient we need to finally apply Raoult's Law and solve for the vapor pressure of the solution.

Step 3: Calculate Mole Fraction of Water

Now we're getting to the good stuff! Remember, the mole fraction is the ratio of the moles of a component to the total moles in the solution. In this case, we want the mole fraction of water:

X_water = Moles of water / Total moles

X_water = 22.22 moles / 22.28 moles ≈ 0.9973

So, the mole fraction of water in the solution is approximately 0.9973. This value tells us that water makes up a very large proportion of the solution, which makes sense given that we only added a small amount of N2SO4. A mole fraction close to 1 indicates that the solution is mostly solvent (water in our case). This high mole fraction of water also suggests that the vapor pressure of the solution will be close to the vapor pressure of pure water, but slightly lower due to the presence of the solute. The mole fraction is a dimensionless quantity, meaning it has no units. It's simply a ratio that expresses the relative amount of a particular component in a mixture. In the context of Raoult's Law, the mole fraction of the solvent is the crucial factor that determines the extent to which the vapor pressure is lowered. The lower the mole fraction of the solvent, the greater the reduction in vapor pressure. This is because the solute molecules interfere with the evaporation of the solvent molecules, reducing the number of solvent molecules that can escape into the vapor phase. Understanding the concept of mole fraction is not only essential for calculating vapor pressure but also for understanding other colligative properties of solutions. These properties depend on the number of solute particles present in the solution, and mole fraction is a convenient way to express the concentration of these particles. Now that we've calculated the mole fraction of water, we have all the pieces we need to finally apply Raoult's Law and determine the vapor pressure of the solution. This is the exciting part where all our hard work pays off!

Step 4: Apply Raoult's Law

Time to bring it all together! We have everything we need to use Raoult's Law:

P_solution = X_solvent * P°_solvent

We know:

  • X_solvent (mole fraction of water) = 0.9973
  • P°_solvent (vapor pressure of pure water) = 17.4 mmHg

Plug in the values:

P_solution = 0.9973 * 17.4 mmHg ≈ 17.35 mmHg

And there you have it! The vapor pressure of the solution is approximately 17.35 mmHg. Calculating the final answer is incredibly satisfying, but it's equally important to understand what this result means. The vapor pressure of the solution (17.35 mmHg) is slightly lower than the vapor pressure of pure water (17.4 mmHg). This reduction in vapor pressure is a direct consequence of the presence of the solute (N2SO4) in the solution. The solute particles interfere with the evaporation of water molecules, making it more difficult for them to escape into the vapor phase. This phenomenon is the essence of Raoult's Law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent. The smaller the mole fraction of the solvent, the lower the vapor pressure of the solution. In our case, the mole fraction of water is very close to 1 (0.9973), indicating that water makes up the vast majority of the solution. This is why the vapor pressure of the solution is only slightly lower than that of pure water. If we had added a larger amount of N2SO4, the mole fraction of water would have been lower, and the reduction in vapor pressure would have been more significant. This understanding of the relationship between solute concentration and vapor pressure is crucial for many applications, such as distillation, where the difference in vapor pressures of different components in a mixture is exploited to separate them. Now that we've successfully calculated the vapor pressure of the solution, let's recap the key steps and concepts involved in the problem.

Conclusion: Vapor Pressure Calculation Success!

Awesome job, guys! We've successfully calculated the vapor pressure of a solution containing N2SO4 in water. We started by understanding the concept of vapor pressure and Raoult's Law, then we broke down the problem into manageable steps:

  1. Calculating moles of water
  2. Accounting for the dissociation of N2SO4 and calculating total moles in solution
  3. Calculating the mole fraction of water
  4. Applying Raoult's Law to find the vapor pressure of the solution

We found that the vapor pressure of the solution is approximately 17.35 mmHg, slightly lower than the vapor pressure of pure water. This problem highlights the importance of understanding colligative properties and how solutes affect the physical properties of solutions. Remember, chemistry is all about understanding the world around us, one molecule at a time! And there you have it! We've successfully navigated this chemistry problem and gained a deeper understanding of vapor pressure and Raoult's Law. Remember, the key to solving complex problems is to break them down into smaller, more manageable steps. By carefully considering each step and understanding the underlying concepts, we can tackle even the most challenging chemistry questions. Now, go forth and conquer more chemistry challenges! This journey through vapor pressure calculation has not only equipped us with a valuable problem-solving skill but also reinforced the importance of fundamental chemical concepts such as molar mass, mole fraction, and dissociation of ionic compounds. These concepts are the building blocks of a solid understanding of chemistry, and mastering them will pave the way for tackling more advanced topics in the future. So, keep practicing, keep exploring, and most importantly, keep asking questions! The world of chemistry is vast and fascinating, and there's always something new to learn. And remember, even the most experienced chemists started somewhere, so don't be afraid to make mistakes and learn from them. Every problem solved is a step forward on your journey to becoming a chemistry whiz! Now, let's celebrate our success and look forward to the next exciting chemistry adventure!