Before you start
You need these ideas and skills for this practical. If any of them are new, read this section first.
Key words
- Mass (m): the amount of matter in an object, measured in grams (g) or kilograms (kg) with a balance.
- Volume (V): the space something takes up, measured in cm³ (the same as millilitres, ml) or m³.
- Density (ρ): the mass of each cubic centimetre (or cubic metre) of a substance.
- Meniscus: the curved surface of a liquid in a narrow tube. For water and most liquids it curves down in the middle.
- Parallax error: a reading error caused by looking at a scale from an angle instead of straight on.
- Tare (zero): setting a balance to read 0 with a container on it, so it then shows only the mass of what you add.
Skills you need
- Reading a measuring cylinder: eye level with the liquid surface, reading the bottom of the meniscus. Work out what one small division is worth first (here 1 cm³).
- Using a top-pan balance: zero it with the empty container on the pan, and wait for the reading to settle.
- Recording results in a table with units in the headings, e.g. Volume / cm³ and Mass / g.
- Plotting a graph and finding its gradient from a large triangle drawn on the best-fit line.
- Converting units: 1 g/cm³ = 1000 kg/m³.
Reading the meniscus
Put your eye level with the liquid surface, so that the near and far edges of the meniscus line up. Read the scale at the lowest point of the curve.
- Eye above the meniscus: the reading looks too high.
- Eye below the meniscus: the reading looks too low.
Between two marks? Record the nearest mark, or estimate to half a division. If the bottom of the meniscus is just below the 50 line (between 49 and 50, nearer 50), record 50 cm³, or 49.5 cm³ if it is about halfway. Do not always take the lower mark: that makes every reading too small (a systematic error). The reading is uncertain by about ±0.5 cm³. Better still, use the dropper to bring the meniscus exactly onto a line.
Try all three eye positions with the magnifier in the lab, and watch the reading change.
Why zero the balance?
The measuring cylinder has its own mass (about 100 g). If you press Tare while the empty cylinder is on the balance, the balance reads 0.0 g. Every reading after that is the mass of the liquid only, so you do not have to subtract the cylinder's mass each time.
If you forget, you can still find the liquid's mass: subtract the mass of the empty cylinder from each reading.
Aim and apparatus
Aim
To find the densities of water, salt water and oil by measuring the mass and volume of different amounts of each liquid, and plotting a graph of mass against volume.
Syllabus link: Cambridge IGCSE Physics 0625 / 0972, topic 1.4 Density: define density, and describe how to find the density of a liquid. Supplement: predict whether one liquid will float on another, using density data.
Apparatus
- 100 cm³ measuring cylinder, with 1 cm³ divisions
- Top-pan balance, reading to 0.1 g, with a tare (zero) button
- Beakers of water, salt water solution and cooking oil
- Dropper (pipette), to add the last few drops accurately
- Paper towels, to dry the cylinder between liquids
- Safety goggles
Theory
Density
Density tells you how much mass is packed into each unit of volume.
With mass in g and volume in cm³, density is in g/cm³. The SI unit is kg/m³.
Why the gradient is the density
For one liquid, doubling the volume doubles the mass. So mass is proportional to volume, and a graph of mass against volume is a straight line through the origin:
A denser liquid has a steeper line. Using a graph is better than a single reading because it averages out small reading errors.
Densities of some liquids
| Liquid | Density / g/cm³ | Density / kg/m³ |
|---|---|---|
| Ethanol (alcohol) | 0.79 | 790 |
| Cooking oil | 0.92 | 920 |
| Water | 1.00 | 1000 |
| Salt water (a strong solution) | 1.10 | 1100 |
| Glycerol | 1.26 | 1260 |
| Mercury | 13.6 | 13 600 |
Use this table to identify the Mystery liquid in the lab.
Floating and layers (Supplement)
Liquids that do not mix (immiscible liquids) settle in layers: the least dense on top and the densest at the bottom. So oil (0.92 g/cm³) floats on water (1.00 g/cm³), and water floats on salt water (1.10 g/cm³).
The same rule tells you whether an object floats: an object less dense than a liquid floats in it. Try the density tower in the lab.
Planning the investigation
Variables
| Type | Variable | How |
|---|---|---|
| Independent | Volume of liquid | 50, 60, 70, 80, 90 and 100 cm³ |
| Dependent | Mass of liquid | Read from the zeroed balance |
| Control | The liquid | Test one liquid at a time; empty and dry the cylinder between liquids |
| Control | Apparatus | Same measuring cylinder and balance throughout |
| Control | Temperature | Do the experiment at room temperature |
Prediction
Write a prediction before you start, for example: “Salt water will have the steepest line because it is the densest, and oil will have the least steep line because it floats on water.”
Range and number of readings
Six readings per liquid, from 50 cm³ to 100 cm³, give enough points to draw a reliable best-fit line. Large volumes are used because the reading errors (about ±0.5 cm³ and ±0.1 g) are then small compared with the readings.
Method in a real lab
- Zero the balance. Put the clean, dry, empty measuring cylinder on the balance and press the tare (zero) button. The balance should read 0.0 g.
- Add about 50 cm³ of water. Pour most of it from the beaker, then use the dropper to bring the bottom of the meniscus exactly to the 50 cm³ line.
- Read and record. With your eye level with the meniscus, record the volume. Wait for the balance to settle and record the mass.
- Add 10 cm³ at a time up to 100 cm³, recording the volume and mass each time.
- Empty and dry the cylinder, zero the balance again, and repeat for the salt water and then the oil.
- Plot a graph of mass (y-axis) against volume (x-axis) for all three liquids on the same grid, draw a best-fit line for each, and find each gradient.
How to use this virtual lab
- Choose a liquid at the top of the panel: Water, Salt water, Oil or Mystery.
- Step 1, Zero: press Tare. The balance reads 0.0 g, so it now measures only the liquid.
- Step 2, Pour: press and hold “Hold to pour”, and let go at about 50 cm³. Use + a few drops to reach a line exactly. Then press Next.
- Step 3, Read: a magnifier shows the scale and the meniscus. Keep your eye Level, type the volume you read, and press Record reading. Stuck? Help me read it draws a red line at the bottom of the meniscus.
- Repeat: the lab takes you back to step 2. Add about 10 cm³ each time, up to 100 cm³ (6 readings).
- See your results: press Table & graph, then Plot graph. Each liquid gets its own line; its gradient is the density.
- Try parallax: in step 3, choose Above or Below and see how the reading changes. A wrong reading is saved with ⚠ so you can see its effect on the graph.
- More to explore (bottom of the panel): the density tower and a close-up of the cylinder.
Results
Results tables
Draw one table for each liquid. Sample results:
| Water | Salt water | Oil | |||
|---|---|---|---|---|---|
| V / cm³ | m / g | V / cm³ | m / g | V / cm³ | m / g |
| 50.0 | 49.9 | 50.5 | 55.6 | 49.5 | 45.5 |
| 60.0 | 59.8 | 60.5 | 66.5 | 59.5 | 54.8 |
| 70.5 | 70.4 | 70.0 | 76.9 | 70.0 | 64.4 |
| 79.5 | 79.4 | 80.0 | 88.1 | 80.5 | 74.1 |
| 90.5 | 90.2 | 90.5 | 99.6 | 90.5 | 83.2 |
| 100.0 | 99.7 | 99.5 | 109.3 | 100.0 | 92.0 |
Calculating density from one reading
Example for salt water at 80.0 cm³: ρ = 88.1 g ÷ 80.0 cm³ = 1.10 g/cm³ = 1100 kg/m³.
Work out m ÷ V for every row. If one value is very different from the rest, that reading is anomalous: check it, and leave it out of your best-fit line.
Analysis and conclusion
Drawing the graph
- Put volume on the x-axis and mass on the y-axis, with units: Volume / cm³, Mass / g.
- Start both axes at 0, so you can check the lines pass through the origin.
- Plot all three liquids on the same grid, using a different symbol or colour for each, and label each line.
- Draw a straight best-fit line through each set of points and the origin.
Finding the gradient
Draw a large triangle on the line: the bigger the triangle, the more accurate the gradient. For the sample water line, from (0, 0) to (100, 99.7):
The sample results give: water 1.00 g/cm³, salt water 1.10 g/cm³, oil 0.92 g/cm³.
Conclusion
“All three graphs are straight lines through the origin, so for each liquid the mass is proportional to the volume. Salt water has the steepest line and the highest density (1.10 g/cm³); oil has the least steep line and the lowest density (0.92 g/cm³). Oil is less dense than water, so it floats on water.”
Predicting layers
If the three liquids are poured into one container, they settle with salt water at the bottom, water in the middle and oil on top. This is why an oil spill at sea floats on the surface and can be skimmed off or contained with floating booms.
Evaluation
| Source of error | Effect | How to reduce it |
|---|---|---|
| Parallax: eye not level with the meniscus | Every volume reading too high (eye above) or too low (eye below) | Crouch so your eye is level with the liquid surface; read the bottom of the meniscus. |
| Reading the scale to the nearest division only | Volume uncertain by about ±0.5 cm³ | Use large volumes so the uncertainty is a small fraction of the reading; use the dropper to reach a line exactly. |
| Balance not zeroed, or zeroed with liquid in the cylinder | Every mass wrong by the same amount (a systematic error): the line does not pass through the origin | Zero the balance with the clean, dry, empty cylinder. |
| Liquid left in the cylinder from the last liquid (especially oil) | The next liquid is contaminated; its density changes | Rinse and dry the cylinder thoroughly between liquids, and test oil last. |
| Drops on the outside of the cylinder or spilled on the pan | Mass readings too high | Pour carefully; wipe the outside of the cylinder and the pan. |
| Salt water concentration not known exactly | Your value may differ from the textbook value | Make the solution with a measured mass of salt in a measured volume of water. |
| Temperature | Liquids expand slightly when warm, so density falls a little | Keep all liquids at room temperature. |
Comparing with other groups: if your gradients differ slightly from other groups', the best estimate of the true density is the mean of all the groups' values, leaving out any anomalous ones.
Safety
- Wear safety goggles: salt water and some liquids can irritate the eyes.
- Wipe up spills straight away: oil on the floor is very slippery.
- Keep liquids away from the electrical socket of the balance.
- Glass measuring cylinders break easily: keep them away from the edge of the bench and report any breakage.
- Ethanol (a possible mystery liquid) is flammable: keep it away from flames.
Exam practice
Practical-style questions like those in Paper 5 (Practical Test) and Paper 6 (Alternative to Practical). Try each one before opening the answer.
1. 40.0 cm³ of a liquid has a mass of 31.6 g. Calculate its density in g/cm³ and in kg/m³.
ρ = m ÷ V = 31.6 ÷ 40.0 = 0.79 g/cm³ = 790 kg/m³. (This is ethanol.)
2. Describe how you would read the volume of water in a measuring cylinder accurately.
Place the cylinder on a flat, level surface. Put your eye level with the water surface, to avoid parallax error, and read the scale at the bottom of the meniscus.
3. A student reads the volume with her eye above the level of the liquid. What effect does this have?
She makes a parallax error: the volume she reads is larger than the true volume, so the density she calculates (m ÷ V) is too small.
4. Explain why the student zeroed the balance with the empty measuring cylinder on it.
So that the balance reads only the mass of the liquid. Otherwise every reading would include the mass of the cylinder, and the mass of the liquid would have to be found by subtraction.
5. On a graph of mass against volume, line A is steeper than line B. Which liquid is denser, and which would float on the other?
Liquid A is denser, because the gradient of the line is the density. Liquid B is less dense, so B floats on A (if they do not mix).
6. A student's mass–volume line does not pass through the origin; it crosses the mass axis at about 2 g. Suggest a reason.
A systematic error in the mass: for example, the balance was not zeroed properly, or there was liquid left in the cylinder or on the pan when it was zeroed. The gradient (density) can still be correct, because the same error is in every reading.
7. An oil spill happens at sea. A student says it cannot be cleaned up because the oil and water will mix. Is the student right?
No. Oil and water are immiscible (they do not mix), and oil is less dense than sea water, so the oil floats on the surface as a layer. It can be contained with floating booms and skimmed off.