You have a graduated cylinder, which is filled with water up to the 150mL mark.
So there it is right there.
Then you add a hunk of Iron, and the water level rises to 425mL.
And the question asks, what is the mass of the Iron?
Okay, so we know we’re dealing with density here so these are the three variables that
were playing with.
The question asks us what the mass of the Iron is.
So we know it's going to be mass that we're solving for, let's talk about how to get these
other two variables.
Okay, we’re not given a volume for this piece of Iron, alright?
Instead, we talk about what happens with water when we add the Iron to a graduated cylinder.
You might remember this is one of the ways that we can determine the volume of something
by putting it into water and seeing how much the water rises, okay?
We have to do a little bit of math but that's how we're going to figure out the volume of
the other piece of Iron by looking at how much the water in the graduated cylinder moved.
So that's how we're going to figure out the volume.
Now in order to get mass we are also going to need to get density.
This tells us that we're dealing with Iron in the problem but it doesn't tell us the
density of Iron so what do you do?
Well it turns out that it's really easy to find the densities for common materials.
You can get it off the internet, you can get them in books and stuff.
Even though the question doesn't give us a density, we can easily figure it out.
So that's how we can get these two variables and then we're going to be able to figure
out what the mass is.
So the first thing I want to do is I want to figure out the volume of the piece of Iron
and we can do that by looking at the water levels.
So we're going to take the final water level and subtract the initial water level from
it and that's going to tell us how much went up and that is going to be equal to the volume
of the Iron that we put in there, okay?
So, volume of the Iron is going to be the final reading which is 425mL minus the initial
which is 150mL and how much it changed is going to be 275mL.
Now, when we're talking about volume and density, we often use cubic centimeters or centimeters
cubed instead of milliliters.
These units though are exactly the same quantity so all I got to do is just rewrite milliliters
as centimeters cubed and there is volume for the Iron, okay?
So now I have a volume for the Iron, 275 cubic centimeters and now only the density.
I can just look this up online really easily and I find out that it’s 7.87 grams per
cubic centimeter so now I'm ready to go.
I’ve got the two things that I need.
So I’ll start with the volume which is 275 cubic centimeters.
Now I like to use the density as like a conversion factor to go between volume and mass so let's
look at the two ways that we can write the density as a conversion factor to go from
volume to mass here, okay?
Density of Iron is 7.87 grams over cubic centimeters which means we can rewrite this as over 1
centimeter cubed, okay?
We can also flip this fraction so we do 1 centimeter cubed divided by 7.87 grams.
Which of these do you want to use?
This one or this one?
Well, we're hoping to cancel out cubic centimeters and be left with grams so that means since
cubic centimeters is on the top here we're going to want to choose the version of the
density conversion factor that gives us centimeter cubed on the bottom.
Here it is right here.
We going to use this one.
So now when I multiply through, centimeters cubed down the top, centimeters cubed on the
bottom, so they cancel out and I'm left with grams.
I'm going to do 275 times 7.87 divided by 1 and answer’s going to be 2164.25.
What do I round this to?
I’ve got three sig figs here, three sig figs here, 1 is a counting number is part
of the definition here so we don't worry about it.
So I'm going to do two-thousand, rounding it to three sig figs, two-thousand-one-hundred-sixty---the
sixty stays the same because there is a four here and I replace the four with zero.
2,160, what are the units here?
I canceled out centimeters cubed so I’m left with grams.
2,160 grams is the mass of the Iron.
Just to review this really quickly, we needed the density of Iron.
We got that from the internet that was easy.
And to figure out the volume of this piece of Iron, we had to look at how much the water
level rose when we added the Iron to the graduated cylinder and from that we could figure out
the volume of the Iron, then we use density as a conversion factor to go from volume to
mass.