Water Molecule Problems: Volume, Ocean & More

Hey guys! Ready to dive into some cool chemistry problems? We're gonna explore the fascinating world of water molecules, volumes, and even the vastness of the ocean. This is going to be fun, I promise! So, let's get started with some real-world calculations and comparisons. Think of it as a fun brain teaser with a bit of science thrown in. We will use the original Russian text in our calculations to make them more accurate. So grab your calculators, and let's get started! These problems are designed to get you thinking and applying basic scientific principles. Don't worry if it seems a little tricky at first. It's all about breaking down the problems step by step. We'll start with the basics, like calculating the number of molecules in a single drop of water, and then we'll scale things up to liters and oceans. It's all connected, and it's all super interesting. Let's make chemistry fun, right?

Problem 1: How many water molecules in 1 liter?

Okay, so the first problem we're tackling is all about figuring out how many water molecules are packed into a liter of water. It's like asking how many tiny LEGO bricks you can fit inside a big box. Except, instead of LEGOs, we have water molecules! The problem gives us some key info to begin with: a single drop of water has a volume of 0.05 ml and contains approximately $1.7 imes 10^{21}$ water molecules. This is important data to start with. First, we need to convert everything into the same units. We know that 1 liter (L) equals 1000 milliliters (mL). Then, we will also use the given information from the problem statement: In one drop there are about $1.7 imes 10^{21}$ molecules. This will allow us to make calculations based on this.

So, here's how we'll break it down. We're going to start by calculating the number of drops in one liter. Remember, 1 L = 1000 mL. Each drop is 0.05 mL. So, to find the number of drops, we divide the total volume (1000 mL) by the volume of a single drop (0.05 mL). That will give us the number of drops in a liter. Then, we know that each drop contains $1.7 imes 10^{21}$ molecules. So, to find the total number of molecules in one liter, we multiply the number of drops by the number of molecules per drop. It's all about using what we know to find what we don't know, a bit like a detective solving a case. Let's write down the steps to find the solution. And we'll get there together! This problem helps us understand just how incredibly small water molecules are, and how many of them there are in even a small amount of water. It's mind-boggling when you think about it. And it is very essential to calculate it by doing this simple math.

Let's do the calculations!

1. Calculate the number of drops in 1 liter:
   • 1 L = 1000 mL
   • Number of drops = 1000 mL / 0.05 mL/drop = 20,000 drops
2. Calculate the total number of molecules in 1 liter:
   • Molecules in 1 drop = $1.7 imes 10^{21}$
   • Total molecules = 20,000 drops * $1.7 imes 10^{21}$ molecules/drop = $3.4 imes 10^{25}$ molecules

So, there are approximately $3.4 imes 10^{25}$ water molecules in 1 liter of water. That's a huge number! This is the answer to the first part of the problem. Pretty impressive, huh?

Problem 2: Comparison: Molecules in 1 Liter vs. Ocean Drops

Now for the second part, which is a bit more comparative, guys. We're going to compare the number of water molecules in a single liter to the number of drops in the world's oceans. Talk about a massive scale difference! This kind of comparison helps you grasp the sheer scale of the ocean and the incredible number of molecules involved. We already know how many molecules are in a liter. Now, let's look at the size of the ocean. The ocean is vast and it is a good idea to realize it for the purpose of a better understanding. This step requires a bit of estimation. You don't need to know the exact number of drops in the ocean. This is the whole point of our next calculation. If we can't find the exact number, we can start by getting an estimate.

To compare, we need to estimate the number of drops in the ocean. We can do this by estimating the volume of the ocean and then calculating how many drops fit in that volume. I will not go deep into the mathematical calculation as that is not our main goal here. It's difficult to calculate the exact number of water drops in the ocean. The volume of the oceans is about $1.3 imes 10^{18}$ cubic meters. I'm going to take this number and make it a little easier to digest. We know from the previous calculation that 1 liter of water has $3.4 imes 10^{25}$ molecules. It is a good starting point to compare and estimate. To start estimating, we need to convert the ocean's volume to liters because we already know the number of molecules per liter. This conversion helps us to get a good number to compare. Then, we can find out the total number of molecules in the ocean. This will enable us to make a comparison between the number of molecules in 1 liter vs. the ocean. Remember, the ocean is huge, and the difference will be very noticeable. The goal here is to get a sense of the scale.

Let's estimate!

1. Ocean Volume: Approximately $1.3 imes 10^{18} m^3$
2. Convert to Liters: $1 m^3 = 1000 L$, so $1.3 imes 10^{18} m^3 = 1.3 imes 10^{21} L$
3. Molecules in the Ocean:
   • Molecules per liter: $3.4 imes 10^{25}$
   • Total molecules in ocean: $(1.3 imes 10^{21} L) imes (3.4 imes 10^{25} molecules/L) = 4.42 imes 10^{46} molecules$

Now, let's compare! We have approximately $3.4 imes 10^{25}$ molecules in 1 liter and a whopping $4.42 imes 10^{46}$ molecules in the ocean. This comparison illustrates the incredible size difference, highlighting just how massive the ocean is when you consider the number of water molecules it contains. That's an astronomical number! These calculations are really cool and help bring the scale of the world into perspective.

Conclusion: The Grand Scale of Water

So, what have we learned, guys? We've explored the number of water molecules in a liter and compared that to the grand scale of the ocean. Hopefully, this gave you a better understanding of the magnitude of molecules and volumes. It also helps to illustrate the relative sizes of things. Science is all about discovery, and it is fun! Water is such a fundamental substance, and understanding it at this level is incredibly important. You can apply these kinds of calculations to many other areas of science. Hopefully, this exercise made you see the world a bit differently. These problems teach us that the world is more complex and bigger than we can imagine. Keep exploring, keep questioning, and keep having fun with science! Understanding the properties of water at the molecular level is key to many scientific disciplines. Hope you enjoyed the journey!