Density equation

0:00- [Instructor] You find a key that is claimed to be made of pure gold and you want to check for yourself, you want to gain some confidence in this claim that it is indeed made of gold. How do you do that? Well, a cool place to start is by figuring out its density.

0:13Remember, density is a measure of how much mass is packed in a given volume. But why measure its density? How does that help? Well, guess what? Density is an intrinsic property. It does not depend upon the amount of stuff. It only depends upon the substance. Okay, but how exactly can we do this?

0:30That's what we're gonna find out in this video. So let's begin. Remember that density is measured in grams per centimeter cubed. How many grams are packed per centimeter cubed? So from this we can write an equation for density. We can say density is mass divided by volume.

0:46Look, grams divided by centimeter cubed, which means if I know the mass and the volume of any object, then I can figure out its density using this equation. So let's get some practice first. Say you have a sample whose mass is given to be 89.3 grams and its volume is given to be 12.5 cm cubed.

1:07We wanna figure out what its density is. Well, we know density is mass divided by volume, so we can just do that. So density will be this number divided by this number. And now I can just plug this in my calculator. 89.3 divided by 12.5 gives me 7.144. And we can round this off.

1:28Let's not worry too much about how many digits we need to round it off. And how do we figure this out? For now, just let's round it off to two digits. So it'll be 7.14 grams per centimeter cubed. That's the density of this material. Now, to identify what this material is, we can take a look at some common metals or common materials that we have.

1:46And by comparing, you can see, hey, zinc happens to have exactly 7.14 grams per cm cubed. This means there's a good chance that this is indeed zinc. Now, of course, it's not 100% guaranteed. So we can do further tests. For example, zinc is grain color. A checks out, it's non lustrous, it's also not magnetic.

2:04So we can bring a magnet close by and see if it's magnetic or not. And we can do all of those tests to just increase our confidence. But this is a great way to get started, right? Okay, you try one. Here's another sample that's given to us. Again, we know it's mass and we know it's volume.

2:19Why don't you pause the video, calculate density, and then see which material this could be. Alright, so again, density is mass divide by volume. So we get this divided by this. And again, we can bring in our handy calculator, 64.4 divided by 23.9, and that gives you 2.694.

2:44And again, rounding it off to two decimals. Without worrying too much about why we're rounding it off to two decimals, we get 2.69 grams per cm cubed. That's the density of this material. And again, we can now compare it with various materials and you can see, hey, this is very close to the density of aluminum.

2:59So there's a very good chance that this is aluminum. And again, we might wanna do further tests to confirm that. Okay, time to go back to our alleged golden key. So to figure out its density, we need to know its mass and volume. Now this time we need to figure this out ourselves, right?

3:14Nobody's gonna give that to us. So how do we figure its mass and how do we figure out its volume? Well, for mass, we can just like, you know, put it on a digital weighing scale and just look at the number and you can see that, hey, this key is pretty heavy. It's 222 grams. So we found its mass.

3:29But now the big question is how do we figure out its volume? It has an irregular shape. So how do we do that? A cool way to do this is by using water displacement method. So what you do is you take some amount of water in a graduated cylinder and note its initial volume.

3:44If we zoom in, we have filled a cylinder to precisely 80, what is it, 80 ml. So this is 80 cm cubed, 80 ml. Remember, ml is the same as cm cubed. So this is the initial volume that we have filled it to. Let's go back. Okay? Now what we're gonna do is we're gonna carefully place the key inside of here, because when the key goes inside, well, you probably know the water gets displaced a little bit.

4:10So let's do that. So here we go. We place the key inside carefully to make sure the water doesn't spill out anywhere. And now look, the volume has increased. So again, let's note down what the new volume is. Again, if we carefully see, it's 90, 91 and it's about 91, somewhere in between 91 and 92.

4:30So it's, I could say 91.5, all right? So this is the new volume. Now, since it's the key that displaced the water, the amount of the volume of the water displaced must be exactly equal to the volume of the key. Does that make sense? This is how scientists usually figure out the volume of irregular objects.

4:52So to find the volume of the key, we just need to figure out how much this displaced volume is. And how do you figure out this displaced volume? Well, you just subtract them. Final minus initial. So 91.5 ml minus 80 ml. If you do that 80.0 ml, that will be the displaced volume and that will be the volume of the key.

5:09And that is 11.5. So the volume of our key is 11.5 ml, or we can also say it is 11.5 cm cubed. Remember, ml is the same thing as cm cubed. And so now we can figure out its density. So the density would be mass divided by its volume. Moment of truth! Let's bring back our calculator one more time.

5:32222 divided by 11.5 we get 19.304. And again, if we just round this off, we'll get 19.3 grams per cm cubed. And if we look over here, oh indeed, gold has a density of 19.3 grams per cm cubed. This is awesome, this means this could actually be pure gold. We have now really, really strong confidence in that.

5:57Of course, we probably need to do further tests to be absolutely sure that this is gold, but this is awesome. So we did indeed find a gold key. So to summarize, to find the density of any object, just divide the mass of that object by the volume of that object.

6:11And since density is an intrinsic property, meaning it does not depend upon the amount of stuff, it only depends upon the material, we can use the density values to try and identify what material we're dealing with. And whenever we have irregular objects, we can find the volume using the water displacement method.