Mole Fraction Calculation: Ethyl Alcohol And Water Solution

Hey guys! Today, we're diving into a cool chemistry problem: calculating the mole fraction of components in a solution. Specifically, we'll tackle a mixture of 40 grams of ethyl alcohol (CH3CH2OH) and 100 grams of water. Don't worry, it sounds more intimidating than it is! We'll break it down step by step, so you'll be a pro in no time. Let's get started!

What is Mole Fraction?

Before we jump into the calculations, let's quickly recap what mole fraction actually means. In simple terms, the mole fraction of a component in a mixture represents the number of moles of that component divided by the total number of moles of all components in the mixture. It's a way of expressing the concentration of a substance in a solution. Think of it like a percentage, but instead of percentages, we're dealing with moles, which are a chemist's way of counting atoms and molecules.

Why is mole fraction important? You might ask. Well, it's a super useful concept in chemistry, especially when dealing with properties of solutions that depend on concentration, like vapor pressure and boiling point elevation. These are called colligative properties, and they're directly related to the mole fraction of the solute (the substance being dissolved) in the solvent (the substance doing the dissolving).

In our case, we have two components: ethyl alcohol (CH3CH2OH) and water (H2O). Ethyl alcohol will be our solute, and water will be our solvent. Our goal is to find the mole fraction of each of these components in the solution. To do this, we'll need to follow a few key steps:

1. Calculate the number of moles of each component.
2. Calculate the total number of moles in the solution.
3. Calculate the mole fraction of each component.

Let's dive into step one!

Step 1: Calculate the Number of Moles of Each Component

To calculate the number of moles, we'll use the following formula:

Number of moles = Mass (in grams) / Molar mass (in grams per mole)

So, we need the molar masses of both ethyl alcohol and water. If you have a periodic table handy, you're in business! If not, no worries, I've got you covered.

Molar Mass of Ethyl Alcohol (CH3CH2OH)

The molar mass of a compound is the sum of the atomic masses of all the atoms in the molecule. For ethyl alcohol, we have:

• 2 carbon atoms (C): 2 * 12.01 g/mol = 24.02 g/mol
• 6 hydrogen atoms (H): 6 * 1.01 g/mol = 6.06 g/mol
• 1 oxygen atom (O): 1 * 16.00 g/mol = 16.00 g/mol

Adding these up, we get the molar mass of ethyl alcohol:

24. 02 + 6.06 + 16.00 = 46.08 g/mol

Now we can calculate the number of moles of ethyl alcohol:

Moles of ethyl alcohol = 40 g / 46.08 g/mol = 0.868 moles

Molar Mass of Water (H2O)

Similarly, for water, we have:

• 2 hydrogen atoms (H): 2 * 1.01 g/mol = 2.02 g/mol
• 1 oxygen atom (O): 1 * 16.00 g/mol = 16.00 g/mol

Adding these up, we get the molar mass of water:

25. 02 + 16.00 = 18.02 g/mol

Now we can calculate the number of moles of water:

Moles of water = 100 g / 18.02 g/mol = 5.55 moles

Awesome! We've successfully calculated the number of moles of both ethyl alcohol and water. Let's move on to the next step.

Step 2: Calculate the Total Number of Moles in the Solution

This step is super straightforward. We simply add the number of moles of each component together:

Total moles = Moles of ethyl alcohol + Moles of water

Total moles = 0.868 moles + 5.55 moles = 6.418 moles

Perfect! We now know the total number of moles in our solution. Only one step left to go!

Step 3: Calculate the Mole Fraction of Each Component

Remember the definition of mole fraction? It's the number of moles of a component divided by the total number of moles. So, let's calculate the mole fraction for both ethyl alcohol and water.

Mole Fraction of Ethyl Alcohol

Mole fraction of ethyl alcohol = Moles of ethyl alcohol / Total moles

Mole fraction of ethyl alcohol = 0.868 moles / 6.418 moles = 0.135

Mole Fraction of Water

Mole fraction of water = Moles of water / Total moles

Mole fraction of water = 5.55 moles / 6.418 moles = 0.865

And there you have it! We've calculated the mole fractions of both ethyl alcohol and water in the solution. The mole fraction of ethyl alcohol is approximately 0.135, and the mole fraction of water is approximately 0.865.

Quick Check: One thing you can always do to double-check your work is to make sure that the mole fractions of all components add up to 1 (or very close to 1, allowing for slight rounding errors). In our case, 0.135 + 0.865 = 1, so we're good to go!

Key Takeaways and Deeper Dive

Let's recap the important things we've learned in calculating the mole fraction:

• Mole fraction is a way to express the concentration of a component in a mixture.
• It's calculated by dividing the number of moles of a component by the total number of moles in the mixture.
• You need to know the molar mass of each component to convert grams to moles.
• The sum of the mole fractions of all components in a mixture should equal 1.

This calculation is super important in the chemistry world because mole fraction helps us understand the properties of solutions. Remember those colligative properties we mentioned earlier? The changes in boiling point and freezing point of a solution compared to the pure solvent are directly related to the mole fraction of the solute.

For example, if you add salt to water, the boiling point of the water will increase, and the freezing point will decrease. The amount of this change depends on how much salt you add, specifically, on the mole fraction of salt in the solution. This is why you add salt to pasta water – it slightly increases the boiling point, allowing the pasta to cook at a higher temperature, and, some say, makes it taste better!

Similarly, antifreeze in your car's radiator works by lowering the freezing point of the water, preventing it from freezing in cold temperatures. The effectiveness of the antifreeze depends on the mole fraction of the antifreeze in the water.

Practice Makes Perfect

To really solidify your understanding, try tackling similar problems on your own. Here are a few ideas:

1. Calculate the mole fraction of each component in a solution containing 25 grams of glucose (C6H12O6) and 75 grams of water.
2. A solution is made by dissolving 10 grams of sodium chloride (NaCl) in 50 grams of water. What is the mole fraction of NaCl in the solution?
3. If the mole fraction of a solute in a solution is 0.2, and the total number of moles in the solution is 5, how many moles of the solute are present?

By working through these practice problems, you'll become a mole fraction master in no time!

Conclusion

So, there you have it! Calculating the mole fraction might seem a bit daunting at first, but as you've seen, it's just a matter of breaking it down into manageable steps. By calculating the number of moles of each component, finding the total number of moles, and then dividing, you can easily determine the mole fraction of any component in a solution.

Remember, this concept is crucial for understanding the behavior of solutions, especially when it comes to colligative properties. So, keep practicing, and you'll be a chemistry whiz in no time! Now you guys know how to calculate mole fractions like pros. Keep up the awesome work, and I'll see you in the next chemistry adventure!