Calculating Liquid Density: A & B To C!

by SLV Team 40 views
Calculating Liquid Density: A & B to C!

Hey there, physics enthusiasts! Today, we're diving into a cool problem involving densities and mixtures. Specifically, we're going to figure out the density of a new liquid (Liquid C) formed by mixing two other liquids (Liquid A and Liquid B). This is a classic type of problem in physics, and it's super handy to understand for various real-world applications. Let's break it down step-by-step to see how it works!

Understanding the Basics: Density

Alright, before we get our hands dirty with the calculations, let's quickly recap what density is all about. Density is a fundamental property of matter that tells us how much mass is packed into a given volume. Think of it like this: imagine you have a box. If you fill that box with feathers, it will have a certain mass. Now, if you fill the same box with rocks, it will have a much greater mass. The rocks are more dense because they pack more mass into the same amount of space. Density is usually expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). The formula for density is pretty straightforward:

  • Density = Mass / Volume

So, to find the density of something, you need to know its mass and its volume. Easy peasy, right?

Now, let's apply this knowledge to our liquids. We're given the densities of Liquid A and Liquid B, and we're asked to find the density of Liquid C, which is a mixture of the two. This means we'll need to figure out the total mass and the total volume of the mixture. This is how we are going to solve the problem!

Gathering the Information: The Given Data

Okay, let's gather all the information we have, so we can get to the good stuff. Here's what we know:

  • Density of Liquid A: 0.7 g/cm³
  • Density of Liquid B: 1.6 g/cm³
  • Mass of Liquid A: 140 g
  • Mass of Liquid B: 128 g

That's everything we need to calculate the density of Liquid C. First, let's calculate the volume of Liquid A and Liquid B, and then move on to the total mass and volume.

Calculating the Volume of Liquid A and Liquid B

We know the density and mass of both liquids. What we need is the volume, since the total volume is required to find the density. Using the density formula (Density = Mass / Volume), we can rearrange it to solve for volume:

  • Volume = Mass / Density

Let's apply this to Liquid A:

  • Volume of Liquid A = Mass of Liquid A / Density of Liquid A
  • Volume of Liquid A = 140 g / 0.7 g/cm³ = 200 cm³

Great job, we found the volume of Liquid A! Now, let's do the same for Liquid B:

  • Volume of Liquid B = Mass of Liquid B / Density of Liquid B
  • Volume of Liquid B = 128 g / 1.6 g/cm³ = 80 cm³

Awesome, now we know the volumes of both Liquid A and Liquid B before they are mixed. This gives us the final step, which is calculating the total volume of Liquid C.

Finding the Total Volume of Liquid C

Here’s where it starts to become much simpler. We know the volume of Liquid A and Liquid B, and we also know that Liquid C is the mixture of the two. This makes the total volume of Liquid C is the sum of the volumes of Liquid A and B.

  • Volume of Liquid C = Volume of Liquid A + Volume of Liquid B
  • Volume of Liquid C = 200 cm³ + 80 cm³ = 280 cm³

There you have it! The total volume of Liquid C is 280 cm³. Now, for the final step.

Calculating the Density of Liquid C

We're in the home stretch, guys! We have all the information needed to calculate the density of Liquid C. First, let's find the total mass of the mixture. This is simply the sum of the masses of Liquid A and Liquid B:

  • Total Mass = Mass of Liquid A + Mass of Liquid B
  • Total Mass = 140 g + 128 g = 268 g

Alright! Now we know the total mass of Liquid C is 268 grams and the total volume is 280 cm³. We can now use the density formula to calculate the density of the mixture. Remember, Density = Mass / Volume.

  • Density of Liquid C = Total Mass / Total Volume
  • Density of Liquid C = 268 g / 280 cm³
  • Density of Liquid C ≈ 0.957 g/cm³

So, the density of Liquid C is approximately 0.957 g/cm³. We did it!

Summary of the Steps

Let's recap the steps we took to solve this problem:

  1. Understand Density: Know the definition and formula (Density = Mass / Volume).
  2. Gather Data: Identify the knowns (densities, masses).
  3. Calculate Volumes: Use the density formula to find the volume of each liquid (Volume = Mass / Density).
  4. Find Total Volume: Add the volumes of Liquid A and Liquid B to find the total volume of Liquid C.
  5. Find Total Mass: Add the masses of Liquid A and Liquid B to find the total mass of Liquid C.
  6. Calculate Density of C: Use the density formula again to find the density of Liquid C (Density = Total Mass / Total Volume).

Conclusion: You Got This!

And there you have it! We've successfully calculated the density of Liquid C. This problem highlights how important it is to understand the relationships between density, mass, and volume. Remember, it's all about breaking down the problem into smaller, manageable steps.

I hope you found this helpful and that you now have a better grasp of how to solve these kinds of density problems. Keep practicing, and you'll become a pro in no time! If you have any questions or want to try another problem, feel free to ask. Cheers!