Grams Of Water: Calculating Mass From Molecules

Hey guys! Today, we're diving into a chemistry problem that involves calculating the mass of water in a sample, given the number of water molecules. It might sound a bit intimidating at first, but don't worry, we'll break it down step by step so it's super easy to understand. We're given that our water sample has a whopping 3.6132 x 10^24 molecules, and we'll be using Avogadro's number (NA = 6.022 x 10^23) to help us out. Let's get started!

Understanding the Problem

Before we jump into the calculations, let's make sure we understand what the problem is asking. We have a sample of water, and we know exactly how many water molecules are floating around in it: 3.6132 x 10^24 molecules to be precise. What we want to figure out is the total mass of all those water molecules, expressed in grams. This is where Avogadro's number comes into play, acting as our trusty conversion factor between the microscopic world of molecules and the macroscopic world of grams that we can actually measure on a scale. Think of it like this: Avogadro's number is the magical bridge that lets us go from counting individual molecules to weighing them collectively.

The key concept here is the mole, which is a unit of measurement that chemists use to deal with large numbers of atoms and molecules. One mole is defined as exactly 6.02214076 × 10^23 entities (like molecules), which is Avogadro's number. So, if we can figure out how many moles of water we have, we can then use the molar mass of water (the mass of one mole of water) to find the total mass in grams. The molar mass of water is approximately 18.015 grams per mole (g/mol). This value comes from adding up the atomic masses of two hydrogen atoms (about 1.008 g/mol each) and one oxygen atom (about 16.00 g/mol). Now that we have a good grasp of the problem and the concepts involved, we are in a great position to move on and start crunching the numbers. Remember, chemistry can seem daunting at first, but by breaking it down into smaller, manageable steps, we can tackle even the most complex problems with confidence. So let's roll up our sleeves and convert those molecules into grams!

Step 1: Convert Molecules to Moles

The first step in solving this problem is to convert the number of water molecules into moles. Remember, a mole is just a specific number of things (in this case, molecules), much like a dozen is always 12 things. To do this conversion, we'll use Avogadro's number (NA), which tells us how many molecules are in one mole. Avogadro's number is approximately 6.022 x 10^23 molecules per mole. This number is a cornerstone in chemistry, acting as a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and liters that we can measure in a lab.

So, we start with the number of water molecules we have: 3.6132 x 10^24 molecules. To convert this to moles, we'll divide by Avogadro's number. This is because we're essentially asking, "How many 'Avogadro's number' of molecules do we have?" The setup looks like this:

(3. 6132 x 10^24 molecules) / (6.022 x 10^23 molecules/mol)

Notice how the units "molecules" cancel out, leaving us with the unit "mol," which is what we want. When we perform this calculation, we get approximately 6 moles of water. This means our sample contains six "Avogadro's numbers" worth of water molecules. Isn't that mind-blowing? We've just taken a huge number of individual molecules and condensed it into a much more manageable unit: the mole. This is a crucial step because moles are the currency of chemistry. They allow us to relate the number of particles to the mass of a substance, which is what we're trying to find in this problem. Now that we know how many moles of water we have, we're just one step away from finding the mass in grams. We've already conquered the trickiest part, so let's keep the momentum going and finish this calculation strong!

Step 2: Convert Moles to Grams

Now that we know we have approximately 6 moles of water, the next step is to convert this amount into grams. To do this, we'll use the molar mass of water. The molar mass is the mass of one mole of a substance, and it's usually expressed in grams per mole (g/mol). For water (H2O), the molar mass is approximately 18.015 g/mol. This value is derived from the atomic masses of hydrogen and oxygen. Each hydrogen atom has an atomic mass of about 1.008 g/mol, and since there are two hydrogen atoms in a water molecule, that's 2 * 1.008 = 2.016 g/mol. Oxygen has an atomic mass of about 16.00 g/mol. Adding these together, we get 2.016 + 16.00 = 18.016 g/mol, which we round to 18.015 g/mol.

So, how do we use this molar mass to convert moles to grams? It's quite simple! We multiply the number of moles by the molar mass. This is because the molar mass tells us how many grams are in each mole, so multiplying by the number of moles gives us the total mass. The setup looks like this:

(6 moles) * (18.015 g/mol)

Notice how the units "mol" cancel out, leaving us with the unit "g," which is what we want: grams. When we perform this calculation, we get approximately 108.09 grams. This is the mass of our water sample! We've successfully converted from the number of molecules all the way to grams, which is a common and important type of calculation in chemistry. Think about it: we started with a mind-bogglingly large number of molecules, used Avogadro's number to bridge the gap to moles, and then used the molar mass to find the mass in grams. This process highlights the power of the mole concept and how it allows us to work with the tiniest particles on a scale that we can actually measure and understand. So, give yourself a pat on the back – you've just tackled a classic chemistry problem like a pro!

Answer

Therefore, in a water sample containing 3.6132 x 10^24 molecules, there are approximately 108.09 grams of water. Isn't it amazing how we can calculate the mass of something by knowing the number of molecules? This is the beauty of chemistry, guys! We can relate the microscopic world of atoms and molecules to the macroscopic world we experience every day.

Key Takeaways

Let's recap the key steps we took to solve this problem. First, we converted the number of water molecules to moles using Avogadro's number. This is a crucial step in many chemistry calculations because it allows us to work with manageable numbers and relate the number of particles to the mass of a substance. Avogadro's number (approximately 6.022 x 10^23 entities per mole) is like a magical bridge that connects the microscopic world of atoms and molecules to the macroscopic world we can see and measure.

Next, we converted moles to grams using the molar mass of water. The molar mass (approximately 18.015 g/mol for water) tells us the mass of one mole of a substance. By multiplying the number of moles by the molar mass, we can easily find the mass in grams. This step highlights the importance of the mole concept as a central unit in chemistry. It allows us to convert between the number of particles, the mass, and even the volume of a substance, making it an incredibly versatile tool for solving a wide range of problems.

Understanding these conversions is fundamental to mastering stoichiometry, which is the study of the quantitative relationships between reactants and products in chemical reactions. Stoichiometry is the heart of chemistry, allowing us to predict how much of a substance we need for a reaction, how much product we'll get, and so much more. So, by mastering these basic conversions, you're building a solid foundation for understanding more complex chemical concepts. Remember, chemistry is all about building blocks, and these skills are essential blocks in your chemical knowledge tower. Keep practicing, and you'll be a chemistry whiz in no time!

Practice Problems

To really solidify your understanding, let's try a couple of practice problems. These will give you a chance to apply what you've learned and boost your confidence in tackling similar questions. Remember, practice makes perfect, and the more you work through these types of problems, the more comfortable you'll become with the concepts.

1. How many grams are there in a sample of NaCl (sodium chloride) that contains 1.2044 x 10^24 molecules? (Hint: First find the molar mass of NaCl.)
2. If you have 54 grams of glucose (C6H12O6), how many molecules of glucose do you have? (Hint: Remember to convert grams to moles first.)

Work through these problems step-by-step, just like we did in the example. Break them down into smaller, manageable steps, and don't be afraid to refer back to the explanation if you get stuck. The key is to practice the process and understand why you're doing each step, not just memorizing the formulas. And if you're feeling extra ambitious, try creating your own practice problems! This is a great way to test your understanding and challenge yourself. Chemistry might seem like a tough subject at first, but with consistent practice and a solid grasp of the fundamentals, you can conquer any problem that comes your way. So, grab a pen and paper, dive into these practice problems, and keep building your chemistry skills!

Conclusion

So there you have it, guys! We've successfully calculated the mass of water in a sample given the number of molecules. Remember, the key is to convert molecules to moles using Avogadro's number and then moles to grams using the molar mass. This is a fundamental skill in chemistry, and mastering it will open doors to understanding more complex concepts. Keep practicing, and you'll be a pro in no time! And remember, if you ever get stuck, don't hesitate to ask for help. Chemistry is a team sport, and we're all in this together!