10.2 - Density of Solids & Liquids
The technique
Aim
To find the density of a liquid, of a regularly shaped solid, and of an irregularly shaped solid, by measuring the mass and the volume of each.
Background
- Density is the mass packed into a given volume, , where is the density, is the mass, and is the volume.
- Density depends on what something is made of, not on how big it is.
- You can't measure density directly, but you can measure a mass on a balance and find a volume.
- So in this practical you measure the mass and the volume of each sample and divide. Only the way you find the volume changes from one sample to the next.
Variables
Finding the density of a solid is a single measurement, so only the liquid part has variables.
- Independent variable - The volume of liquid in the measuring cylinder.
- Dependent variable - The mass of the liquid.
- Control variables - The liquid, the measuring cylinder, and the balance.
Method - The density of a liquid
- Weigh the empty cylinder - Put a dry, empty measuring cylinder on a balance and record its mass. Leave it on the balance from here on.
- Add the liquid in steps - Pour in about 10 cm3 at a time, and record the volume and the balance reading each time, until you have about six pairs. Read the volume at eye level, from the bottom of the meniscus.
- Plot the graph - Mass against volume.
Method - The density of a regularly shaped solid
- Measure the mass - Use a balance.
- Find the volume - Measure the sides with a ruler, or with callipers for something small. A cuboid's volume is length × breadth × height.
- Calculate the density - Divide the mass by the volume, and repeat for several blocks of the same material to find a mean.
Method - The density of an irregularly shaped solid
- Measure the mass - Use a balance.
- Fill the displacement can - Fill it until water runs out of the spout, then wait for it to stop dripping.
- Lower the object in - Stand an empty measuring cylinder under the spout, and lower the object into the can slowly on a thread.
- Measure the volume - Once the spout stops dripping, read the volume of water collected, which equals the object's volume. Without a can, use the rise in level in a part-filled measuring cylinder.
- Calculate the density - Divide the mass by the volume, and repeat three times to find a mean.
Safety
- Eye protection - Wear safety glasses.
- Spills - Mop up any spill straight away, before it reaches the balance.
- Heavy blocks - Keep metal blocks away from the edge of the bench.
Worked example - Density of a liquid
A student put an empty measuring cylinder on a balance, without zeroing the balance, and added a liquid 10 cm3 at a time. Each time, they recorded the balance reading and the total volume.
| Volume of liquid (cm3) | 0 | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|---|
| Mass of liquid and cylinder (g) | 40 | 48 | 56 | 64 | 72 | 80 |
Find the density of the liquid in g/cm3 and in kg/m3, and say what the point where the line crosses the y-axis shows.
Step 1 - Plot the graph
Plot mass on the y-axis and volume on the x-axis. The balance wasn't zeroed, so each mass includes the cylinder as well as the liquid. The points form a straight line.
Step 2 - Find the gradient
The gradient is the density of the liquid.
Step 3 - Say what the y-intercept shows
The line crosses the y-axis at 40 g, which is the mass of the empty cylinder. It moves the whole line up but doesn't change the gradient, so the density is still correct.
Step 4 - Convert to kg/m3
0.80 g/cm3 × 1,000 = 800 kg/m3
Common exam questions
Question 1
A metal block measures 2.0 cm by 3.0 cm by 5.0 cm and has a mass of 240 g. Calculate its density.
Volume = 2.0 × 3.0 × 5.0 = 30 cm3, so density = 240 ÷ 30 = 8.0 g/cm3.
Question 2
Why is the volume in a measuring cylinder read at eye level, from the bottom of the curved surface?
Looking from above or below lines the level up with the wrong mark, which is a parallax error. The surface is also curved, with the edges higher than the middle, so reading the bottom of the curve every time gives the true volume.
Question 3
Why is the object lowered into the displacement can slowly, on a thread?
Dropping it in splashes water over the side, so some of the displaced water never reaches the measuring cylinder and the volume comes out too small.
Question 4
Why is the displacement can filled until it overflows and then left to stop dripping?
So the water starts exactly at the level of the spout. If it were below the spout, some of the displaced water would fill the gap instead of running out, and the volume would be too small.
Question 5
Air bubbles cling to an object as it's lowered into the water. What effect does this have on the density found?
The bubbles push aside water of their own, so the volume collected is too large. Dividing the mass by a volume that's too large gives a density that's too small.