Solving Chemistry Problems: Mr Of X, Mole Fraction, & Vapor Pressure

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Hey guys! Let's dive into some cool chemistry problems. We'll be calculating the molecular weight (Mr) of a substance, the mole fraction of a solution, and the vapor pressure of water. Get ready to flex those chemistry muscles! Let's break down these problems step by step, making sure we understand every bit of it. No need to be intimidated; we'll approach this like we're chatting over coffee. I am certain that this will clear all your doubts.

1. a. Calculating the Molecular Weight (Mr) of Substance X

Alright, let's tackle the first problem. We've got 100 grams of substance X mixed with 400 grams of water, resulting in a 2.5 m (molal) solution. Our mission? To figure out the Mr of substance X. First, let's refresh our memory on what molality means. Molality (m) is defined as the number of moles of solute per kilogram of solvent. This is super important; it's the core concept we'll use. Knowing this, we can begin solving the problem, and let me tell you, this is not a big deal.

So, we know that the solution is 2.5 m, which tells us there are 2.5 moles of substance X for every 1 kilogram (1000 grams) of water. But we only have 400 grams of water in our problem. Time for a little proportion magic! Let's figure out how many moles of X are actually in our solution. If 2.5 moles are in 1000 grams of water, then in 400 grams of water, there will be: (2.5 moles / 1000 grams) * 400 grams = 1 mole of X. See, guys? Not too hard, right?

Now we know that we have 1 mole of substance X. We also know that we started with 100 grams of substance X. The molecular weight (Mr) is defined as the mass of one mole of a substance. Therefore, the Mr of X is the mass of X divided by the number of moles. Using that, we can easily find the Mr. It's simply the grams of X divided by the number of moles of X, which is 100 grams / 1 mole = 100 g/mol. Voila! The Mr of substance X is 100 g/mol. Pretty neat, eh? We successfully calculated the Mr of the substance. Now, let us proceed to the next part of this problem. Remember, always pay close attention to the units and what each of them means!

This method is super useful for many types of chemistry problems, so keep it in mind. This is one of the many types of problems that you may encounter, so you better get used to the method we used. We started with the molality, then calculated the number of moles, and finally, determined the Mr. It's like a recipe; follow the steps, and you'll get the right answer. Always start with the information you have and break the problem down into smaller, more manageable steps. This will make any complex problem super easy.

1. b. Determining the Mole Fraction of a Glucose Solution

Moving on, let's calculate the mole fraction of a 20% glucose (C6H12O6) solution. We're given the atomic masses: H = 1, C = 12, and O = 16. The mole fraction is a way to express the concentration of a solution, and it's all about the ratio of moles of a component to the total moles in the solution. We will use the percentage, which is super important.

Okay, so what does a 20% glucose solution mean? It means that in 100 grams of the solution, there are 20 grams of glucose. Therefore, the rest must be water, which means there are 80 grams of water (since 100 - 20 = 80). First, let's calculate the molar mass of glucose (C6H12O6). It's (6 * 12) + (12 * 1) + (6 * 16) = 72 + 12 + 96 = 180 g/mol. This is crucial for our calculations. Now, we'll calculate the number of moles of glucose in the solution. Using the given mass of glucose (20 grams) and its molar mass, we can find that number. It's 20 grams / 180 g/mol = 0.111 moles of glucose. Easy peasy!

Next, let's find the number of moles of water. We know we have 80 grams of water, and the molar mass of water (H2O) is (2 * 1) + 16 = 18 g/mol. So, the number of moles of water is 80 grams / 18 g/mol = 4.44 moles of water. We are almost there! Finally, to calculate the mole fraction of glucose, we divide the moles of glucose by the total moles in the solution (glucose + water). The mole fraction of glucose is 0.111 moles / (0.111 moles + 4.44 moles) = 0.024. This value means that for every mole in the solution, 0.024 moles are glucose. The mole fraction is a dimensionless quantity and ranges between 0 and 1. Remember this; it will help you remember the concept.

This shows us how to work with percentages and molar masses to find the mole fraction, and it all works by knowing the relation between the percentages and the molar mass, which are the basis to the whole solution. Remember to always work step by step, and the problem will start to solve itself. So, in summary, we found the mole fraction by breaking down the percentage into masses, calculating the moles of each component, and then calculating the mole fraction using the mole ratio. Fantastic! Let's jump on the next problem!

2. Vapor Pressure of Water

Okay, guys, let's talk about the vapor pressure of water. The vapor pressure of a liquid is the pressure exerted by its vapor when the liquid and vapor are in dynamic equilibrium in a closed system. It is a critical property that helps us understand the behavior of liquids. Let's dig deeper into the concept to better understand it. Do you know why? Because understanding the concept behind it is as important as the concept itself.

First, let's understand a little bit about what's going on at the molecular level. Water molecules are constantly moving, right? Some of them have enough energy to escape the liquid phase and become a gas (vapor). This happens at the surface of the water, and this is what we call evaporation. So, when the water evaporates, it creates water vapor in the air above the water. In a closed container, these water vapor molecules can collide with the surface of the water and condense back into the liquid phase. This is called condensation. When the rate of evaporation equals the rate of condensation, we reach a state of dynamic equilibrium. At this point, the pressure exerted by the water vapor is called the vapor pressure.

The vapor pressure of water depends on temperature. As the temperature increases, more water molecules have enough energy to escape the liquid phase. This means the rate of evaporation increases, and the vapor pressure goes up. If the temperature goes down, the rate of evaporation slows down, and the vapor pressure decreases. Different liquids have different vapor pressures at the same temperature. For example, a liquid with weak intermolecular forces (like some organic solvents) will have a higher vapor pressure than a liquid with strong intermolecular forces (like water). The stronger the intermolecular forces, the harder it is for the molecules to escape the liquid phase.

In addition, we need to know that the vapor pressure also helps us with other concepts, such as boiling point. The boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure (usually atmospheric pressure). If you increase the external pressure, you'll need a higher temperature to reach the boiling point. This is why water boils at a lower temperature at higher altitudes (where the atmospheric pressure is lower). Moreover, the vapor pressure is influenced by the presence of solutes. When a solute is added to water, it can reduce the vapor pressure because the solute molecules take up some of the surface area, and they also create intermolecular forces with the water molecules, making it harder for the water molecules to escape.

This is why vapor pressure is a fundamental concept in chemistry. It helps us understand the behavior of liquids and solutions, and it's essential for a wide range of applications, from understanding the behavior of the atmosphere to designing industrial processes. Remember that vapor pressure is a function of temperature and is also impacted by the presence of solutes. Make sure you fully understand the concepts, as they are crucial in chemistry. Keep practicing, and you will become a pro in no time.